diff --git a/.buildinfo b/.buildinfo new file mode 100644 index 0000000000..d95675c49a --- /dev/null +++ b/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 2cca740605cef710b38d3bc90671a0b9 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 0000000000..e69de29bb2 diff --git a/_images/pipeline.svg b/_images/pipeline.svg new file mode 100644 index 0000000000..b9be3c3556 --- /dev/null +++ b/_images/pipeline.svg @@ -0,0 +1 @@ +Stainless PipelineUserFrontendCompilerCallBackRegistryComponentUse ICG: Incremental Computational GraphVerification and/orTermination;Run in threadsVerification and/orTerminationdotc, scalac, ...Update Code;Run FrontendRun CompilerTypecheckCompilation Unit(xlang.Trees)Register newFunDef & ClassDefUse ICG to identifywhat is ready orneed to be recomputed.Option[self-containedprogram]transform trees, generate VCs, send to the solvers, ...The "loop" is executed once more to trigger the verification ofnon-sealed classes now that all the overridden functions are known.wait for Component's ReportsReports...Reports...Reports...All ReportsDisplay reportsunder --watch modethe process restart.The Registry's ICG is the center piece thatenables stainless to verify modified functionswhen the code is updated.loop[for each compilation unit]opt[solve] \ No newline at end of file diff --git a/_sources/casestudies.rst.txt b/_sources/casestudies.rst.txt new file mode 100644 index 0000000000..abfa74e9f4 --- /dev/null +++ b/_sources/casestudies.rst.txt @@ -0,0 +1,308 @@ +.. _casestudies: + +Case Studies +============ + +Case Study #1: Proving invariants of actor systems +-------------------------------------------------- + +Actor system model +~~~~~~~~~~~~~~~~~~ + +Our model is loosely based on the modern definition of object-based actor systems, +and attempts to provide an idiomatic Scala API in the style of the Akka actor library. + +In this framework, each actor is addressed by a reference, through which other actors +can asynchronously send messages. Each actor has an associated behavior, which holds +the state of the actor, if any, and determines + +a) the operations which will be performed upon receiving a message +b) what is the next behavior to associate with its reference + +A behavior can thus be seen as a data type holding some immutable values representing +the state, and a method which takes in a message, performs some computation which might +involve sending messages to other actors, and finally returns a new behavior. + +State at the actor level is thus effectively handled in a functional way, by returning +a new behavior which holds the updated state. An actor system maintains a collection +of one-way channels (inboxes) between any two actors in the system. + +An inbox is an ordered list of messages awaiting delivery, the head of the list being +the next message to deliver. + +The system drives the execution by non-deterministically +picking a non-empty inbox, taking the first message of the list, and invoking the message +handler of the behavior associated with the destination reference. + +It then collects the messages to send, and appends them to the appropriate inboxes, +and update the destination actor’s behavior with the behavior returned by the message handler. + +Actor system implementation +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Imports +^^^^^^^ + +.. code-block:: scala + + import stainless.lang._ + import stainless.collection._ + import stainless.annotation._ + +Message +^^^^^^^ + +In our framework, messages are modeled as constructors of the abstract class ``Msg``. + +.. code-block:: scala + + abstract class Msg + +Actor reference +^^^^^^^^^^^^^^^ + +Each actor is associated with a persistent reference, modeled as instances of the case class ``ActorRef``. +Each reference has a name, and an underlying Akka ``akka.actor.ActorRef``, marked as extern and pure (see Section :doc:`wrap` for more information about extern fields). + +.. code-block:: scala + + case class ActorRef( + name: String, + @extern @pure + underlying: akka.actor.ActorRef + ) { + + @inline + def !(msg: Msg)(implicit ctx: ActorContext): Unit = { + ctx.send(this, msg) + } + } + +Actor Context +^^^^^^^^^^^^^ + +When a message is delivered to an actor, the latter is provided with a context, which holds a reference to itself, and a mutable list of messages to send. We mark this list as ghost to avoid having to persist in memory the list of all messages sent through the context. + +.. code-block:: scala + + case class ActorContext( + self: ActorRef, + @ghost + var toSend: List[(ActorRef, Msg)] = Nil() + ) { + + def send(to: ActorRef, msg: Msg): Unit = { + toSend = (to, msg) :: toSend + + sendUnderlying(to, msg) + } + + @extern @pure + private def sendUnderlying(to: ActorRef, msg: Msg): Unit = { + to.underlying ! msg + } + } + +Behavior +^^^^^^^^ + +A behavior specifies both the current state of an actor, and how this one should process the next incoming message. In our framework, these are modeled as a subclass of the abstract class ``Behavior``, which defines a single abstract method ``processMsg``, to be overridden for each defined behavior. + +Using the provided ``ActorContext``, the implementation of the ``processMsg`` method can both access its own reference, and send messages. It is also required to return a new ``Behavior`` for handling subsequent messages. + +.. code-block:: scala + + sealed abstract class Behavior { + def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior + } + +Actor System +^^^^^^^^^^^^ + +The state of the actor system at a given point in time is modeled as a case class, holding the behavior associated with each actor reference, and the list of in-flight messages between any two actors. + +It provides a ``step`` method which, whengiven two ``ActorRef``, will deliver the next message (if any) in the corresponding channel. + +Because the ``ActorSystem`` class is only used to model and prove properties about the underlying actor system, we mark the whole class as ghost in order to drop it from the resulting program. + +.. code-block:: scala + + @ghost + case class ActorSystem( + behaviors: CMap[ActorRef, Behavior], + inboxes: CMap[(ActorRef, ActorRef), List[Msg]] + ) { + + def step(from: ActorRef, to: ActorRef): ActorSystem = { + inboxes(from -> to) match { + case Nil() => + this + + case Cons(msg, msgs) => + val (newBehavior, toSend) = deliverMessage(to, msg) + + val newBehaviors = behaviors.updated(to, newBehavior) + val newInboxes = toSend.foldLeft(inboxes.updated(from -> to, msgs)) { + case (acc, (dest, m)) => acc.updated(to -> dest, m :: acc(to -> dest)) + } + + ActorSystem(newBehaviors, newInboxes) + } + } + + private def deliverMessage(actor: ActorRef, msg: Msg): (Behavior, List[(ActorRef, Msg)]) = { + val behavior = behaviors(actor) + + val ctx = ActorContext(actor, Nil()) + val nextBehavior = behavior.processMsg(msg)(ctx) + + (nextBehavior, ctx.toSend) + } + } + +Building a replicated counter +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: scala + + @extern + def noSender = akka.actor.ActorRef.noSender + + val Primary = ActorRef("primary", noSender) + val Backup = ActorRef("backup", noSender) + + case object Inc extends Msg + + case class Counter(value: BigInt) { + require(value >= 0) + + def increment: Counter = Counter(value + 1) + + def <=(that: Counter): Boolean = this.value <= that.value + } + + case class PrimBehav(backup: ActorRef, counter: Counter) extends Behavior { + require(backup.name == "backup") + + override + def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior = msg match { + case Inc => + backup ! Inc + PrimBehav(backup, counter.increment) + + case _ => this + } + } + + case class BackBehav(counter: Counter) extends Behavior { + + override + def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior = msg match { + case Inc => + BackBehav(counter.increment) + + case _ => this + } + } + +Proving preservation of an invariant +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +After having defined an actor system with our framework, one might want to verify that this system preserves some invariant between each step of its execution. That is to say, given an invariant ``inv: ActorSystem → Boolean``, for any ``ActorSystem`` `s` and any two ``ActorRef`` `n` and `m`, if ``inv(s)`` holds, then ``inv(s.step(n, m))`` should hold as well. In other words: + +:math:`\forall s: \texttt{ActorSystem}, n, m: \texttt{ActorRef}. \texttt{inv}(s) \implies \texttt{inv}(s.\texttt{step}(n, m))` + +We note that, because we are essentially doing a proof by induction over execution steps here, one needs also to ensure the invariant holds for some initial system. We show these two properties below: + +.. code-block:: scala + + @ghost + def invariant(s: ActorSystem): Boolean = { + s.inboxes(Primary -> Primary).isEmpty && + s.inboxes(Backup -> Primary).isEmpty && + s.inboxes(Backup -> Backup).isEmpty && + s.inboxes(Primary -> Backup).forall(_ == Inc) && { + (s.behaviors(Primary), s.behaviors(Backup)) match { + case (PrimBehav(_, p), BackBehav(b)) => + p.value == b.value + s.inboxes(Primary -> Backup).length + + case _ => false + } + } + } + + @ghost + def initialSystem = ActorSystem( + behaviors = CMap({ + case `Primary` => PrimBehav(Counter(0)) + case `Backup` => BackBehav(Counter(0)) + }), + inboxes = CMap(_ => List()) + ) + + @ghost + def initialInv = invariant(initialSystem).holds + + @ghost + def validRef(ref: ActorRef): Boolean = ref == Primary || ref == Backup + + @ghost + def theorem(s: ActorSystem, from: ActorRef, to: ActorRef): Boolean = { + require(invariant(s) && validRef(from) && validRef(to)) + val newSystem = s.step(from, to) + invariant(newSystem) + }.holds + +Running the system with Akka +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: scala + + @ignore + class ActorWrapper(initialBehavior: Behavior) extends akka.actor.Actor with akka.actor.ActorLogging { + + private def handler(behavior: Behavior): PartialFunction[Any, Unit] = { + case msg: Msg => + val me = ActorRef(context.self.path.name, context.self) + val ctx = ActorContext(me, Nil()) + val newBehavior = behavior.processMsg(msg)(ctx) + + log.info(s"Received: $msg, becoming $newBehavior") + context.become(handler(newBehavior), discardOld = true) + } + + def receive = handler(initialBehavior) + } + +.. code-block:: scala + + @ignore + def main(args: Array[String]): Unit = { + val initCounter = Counter(0) + + val system = akka.actor.ActorSystem("Counter") + + val backupRef = ActorRef( + "backup", + system.actorOf( + akka.actor.Props(new ActorWrapper(BackBehav(initCounter))), + name = "backup" + ) + ) + + val primaryRef = ActorRef( + "primary", + system.actorOf( + akka.actor.Props(new ActorWrapper(PrimBehav(backupRef, initCounter))), + name = "primary" + ) + ) + + implicit val ctx = ActorContext(primaryRef, Nil()) + + import system.dispatcher + import scala.concurrent.duration._ + system.scheduler.schedule(500.millis, 1000.millis) { + primaryRef ! Inc + } + } diff --git a/_sources/coq.rst.txt b/_sources/coq.rst.txt new file mode 100644 index 0000000000..b899cfdd98 --- /dev/null +++ b/_sources/coq.rst.txt @@ -0,0 +1,69 @@ +.. _coq: + +Translation from Stainless to Coq +================================= + +Initially based on a project done by `Bence Czipó +`_, this translation is an early experimental +stage. + +The `--coq` option of Stainless replaces the standard verification checker +(which uses Inox) by a translation to Coq. Each function from the `*.scala` file +is translated to a Coq file, and obligations corresponding to assertions, +preconditions, and postconditions are solved using predefined tactics in Coq. + +.. _coq-requirements: + +Requirements +------------ + +- Coq 8.11.2 +- Coq Equations 1.2.2+8.11 + +These can be installed using `opam +`_ as explained in the `Equations +README.md `_. + +.. _coq-option: + +Usage of the Coq option +----------------------- + +First, clone the `Stainless repository +`_. In the `slc-lib` directory, run +`./configure` and `make`. + +Then, assuming the Stainless binary ``stainless-scalac`` is in your path, run: +``stainless-scalac --coq File.scala`` on the file of your choice. As an example, +consider the ``test`` function from the `Arith.scala +`_ +file: + +.. code-block:: scala + + def test(a: BigInt, b: BigInt, c: BigInt): BigInt = { + require(a > b && c > BigInt(0)) + c + a + } ensuring( _ > c + b ) + +Running ``stainless-scalac --coq frontends/benchmarks/coq/Arith.scala`` +generates the file ``tmp/test.v`` which contains the following Coq definition. + +.. code-block:: coq + + Definition test (a: Z) (b: Z) (c: Z) (contractHyp4: (ifthenelse (Z.gtb a b) bool + (fun _ => Z.gtb c (0)%Z ) + (fun _ => false ) = true)) : {x___1: Z | (Z.gtb x___1 (Z.add c b) = true)} := + Z.add c a. + + Fail Next Obligation. + +The ``coqc`` executable in run on the file, and the status is reported by +Stainless. In the translation to Coq, the ``BigInt`` type is encoded as ``Z``. +The precondition (``require``) is encoded as an extra argument ``contractHyp4``, +and the postcondition is encoded as a refinement on the return type of `test`. +Here, the obligation related to the postcondition is solved automatically thanks +to the obligation tactic defined above in the ``tmp/test.v`` file. The statement +``Fail Next Obligation.`` then succeeds because all obligations have been solved +(any command in Coq can be prefixed with ``Fail``, and the resulting command +succeeds when the original command fails). diff --git a/_sources/equivalence.rst.txt b/_sources/equivalence.rst.txt new file mode 100644 index 0000000000..37e2c1f5ab --- /dev/null +++ b/_sources/equivalence.rst.txt @@ -0,0 +1,93 @@ +.. equivalence: + +Equivalence Checking +==================== + +Stainless can prove equivalence of recursive programs using automated functional induction. Additionaly, it can treat many programs at once, reusing the information obtained throughout the process, to reason about subsequent programs. `This paper +`_ explains the underlying algorithms. + +To run the equivalence checker, use the ``--equivchk`` option of Stainless. The option ``--comparefuns`` specifies the names of candidate functions. The option ``--models`` specifies the names of reference functions. + + +Example run +----------- + +Consider the following three functions ``isSortedA`` (incorrect), ``isSortedB`` and ``isSortedC`` (both correct), that implement a check whether a given input list is sorted in a non-decreasing order: + +.. code-block:: scala + + def isSortedA(l: List[Int]): Boolean = { + def leq(cur: Int, next: Int): Boolean = cur < next + def iter(l: List[Int]): Boolean = + if (l.isEmpty) true + else if (l.tail.isEmpty) true + else leq(l.head, l.tail.head) && iter(l.tail) + if (l.size < 2) true + else l.head <= l.tail.head && iter(l.tail) + } + +.. code-block:: scala + + def isSortedB(l: List[Int]): Boolean = { + if (l.isEmpty) + true + else if (!l.tail.isEmpty && l.head > l.tail.head) + false + else + isSortedB(l.tail) + } + +.. code-block:: scala + + def isSortedC(l: List[Int]): Boolean = { + def chk(l: List[Int], p: Int, a: Boolean): Boolean = { + if (l.isEmpty) a + else if (l.head < p) false + else chk(l.tail, l.head, a) + } + if (l.isEmpty) true + else chk(l, l.head, true) + } + +And the following reference function ``isSortedR``: + +.. code-block:: scala + + def isSortedR(l: List[Int]): Boolean = { + def loop(p: Int, l: List[Int]): Boolean = l match { + case Nil() => true + case Cons(x, xs) if (p <= x) => loop(x, xs) + case _ => false + } + if (l.isEmpty) true + else loop(l.head, l.tail) + } + +The following command invokes the equivalence checking (``isSortedA``, ``isSortedB``, ``isSortedC`` and ``isSortedR`` are defined in ``frontends/benchmarks/equivalence/isSorted/isSorted.scala``): + +``stainless frontends/benchmarks/equivalence/isSorted/isSorted.scala --equivchk=true --comparefuns=isSortedA,isSortedB,isSortedC --models=isSortedR --timeout=3`` + +Stainless automatically generates all the equivalence lemmas and reports resulting equivalence clusters. This is done by checking for equivalence of each function from the ``--comparefuns`` list against the model functions from the ``--models`` list, until the proof of equivalence or a counterexample is found for one of the models. + +The output of equivalence checking is a classification of candidate functions into the following categories: + + - ``Wrong``, if the signature is wrong; + - ``Correct``, if there is a reference program provably equivalent to this program; + - ``Incorrect``, if there is a counterexample that disproves the equivalence; + - ``Unknown``, when there is neither a proof nor a counterexample of equivalence. + +For our example run, we get the following output: + +.. code-block:: text + + [ Info ] Printing equivalence checking results: + [ Info ] List of functions that are equivalent to model IsSorted.isSortedB: IsSorted.isSortedC + [ Info ] List of functions that are equivalent to model IsSorted.isSortedR: IsSorted.isSortedB + [ Info ] List of erroneous functions: IsSorted.isSortedA + [ Info ] List of timed-out functions: + [ Info ] List of wrong functions: + [ Info ] Printing the final state: + [ Info ] Path for the function IsSorted.isSortedB: IsSorted.isSortedR + [ Info ] Path for the function IsSorted.isSortedC: IsSorted.isSortedB, IsSorted.isSortedR + [ Info ] Counterexample for the function IsSorted.isSortedA: + [ Info ] l -> Cons[Int](-1357890535, Cons[Int](-1089455080, Cons[Int](-1089455080, Nil[Int]()))) \ No newline at end of file diff --git a/_sources/faq.rst.txt b/_sources/faq.rst.txt new file mode 100644 index 0000000000..c80f0acb18 --- /dev/null +++ b/_sources/faq.rst.txt @@ -0,0 +1,98 @@ +.. _faq: + +FAQ: (Frequently) Asked Questions +================================= + +If you have a question, you may also post it at http://stackoverflow.com +(try `searching for the leon tag `_ +or `the stainless tag `_) +or contact one of the authors of this documentation. + +Below we collect answers to some questions that came up. + +How does Stainless compare to other verification tools? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +One can compare Stainless to proof assistants such as +`Isabelle/HOL `_, +`Coq `_, +`Lean `_, +`HOL4 `_, or +`ACL2 `_ in terms of the complexity of some of the program properties it can prove, though it was originally conceived more as a program verifier, such as +`Dafny `_ or +`Viper `_. +Stainless can be more automated when finding proofs of programs compared to proof assistants, and can also report counter-examples for invalid properties in many non-trivial cases, see counter-examples for bugs in benchmarks such as +`ConcRope.scala `_, +`ListOperations.scala `_, +`Mean.scala `_, +`PropositionalLogic.scala `_, +`AssociativityProperties.scala `_, +`InsertionSort.scala `_, +`more example reports `_, or check some of our +`regression tests `_. +On the other hand, proof assistants are much better at formalizing mathematics than Stainless, especially when it comes to libraries of formalized mathematics knowledge. + +How does Stainless compare to fuzzing tools? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Formal software verification finds proofs that programs work under all scenarios of interest. Formal verification tools help developers construct such proofs, automatically searching for proofs using theorem proving and constraint solving (using, e.g. SMT solvers), and static analysis to discover program invariants. When it succeeds, formal verification is guaranteed to identify all software errors, including, for example, security vulnerabilities or cases when the computation produces a wrong numerical or symbolic result. Because it involves building proofs, this approach may require knowledge of proofs by induction and substitution of equals for equals, typically covered in computer science undergraduate university education. The best approach to obtain formally verified software is to perform formal verification while software is developed. If we try to apply formal verification after software is already written, we should be prepared to invest at least the amount of effort needed to rewrite it. + +Testing can establish the presence of errors, but not their absence. Basic forms of testing can be easy to deploy, because running a program on a given input is a minimum requirement for software, but such testing is extremely limited. Suppose that we wish to test whether a program running on a smartphone performs multiplication of two machine numbers correctly. If we could check one test per *nanosecond*, we would still need many billions of years to enumerate all cases! This also illustrates how minuscule of a region of space around a given test a fuzzer can ever explore, despite an amazing speed at which some these fuzzing tools work. Formal software verification can cover all these cases with a single proof because it uses algebraic properties that are independent of the size of the data that software manipulates. + +To avoid enumeration, advanced testing methods such as symbolic execution embrace constraint solvers originally developed for formal verification. These techniques reduce to formal verification when programs have no loops or recursion; otherwise they end up sampling a small fraction of program executions, so they do not result in a proof. To cover more than just absence of crashes and vulnerabilities, testing also requires insights into the purpose of software, the environment in which the software needs to execute and the expected outputs for given inputs. + +Does Stainless use SMT solvers? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Stainless uses SMT solvers such as z3, CVC and Princess. The component that encodes formulas with executable higher-order functions into these solvers is Inox. Inox is designed to emit quantifier-free queries for these solvers, which increases its ability to generate counter-examples. The use of SMT solvers allows Stainless to achieve notable automation in reasoning about, for example, equality, case analysis, bitvectors, and algebraic data types. + + +What are the conditions required for Stainless to be applied to industry software? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +It is best to deploy formal verification when starting to develop software. In this way, software and its specifications are developed hand in hand, much like one can define a class hierarchy and other types during the process of writing an object-oriented program. It is also possible to focus on one part of an existing software system and rewrite it in Stainless; such efforts have been shown to work in industry for software components in Scala, Java, and C. Software that has well-defined modular structure with clear responsibility of different modules is a good candidate for verification because one can expect that specifications at module boundaries will be non-controversial. In terms of developer skills, good knowledge of discrete mathematics, such as proofs by induction and algebra will make developers more effective at verification. + +Can I use Stainless with Java? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Scala has excellent interoperability with Java, so external libraries can be used to build application where some parts are verified using Stainless. Stainless uses Scala syntax trees and does not support verification of Java itself. Whereas functional Scala works as a both specification and implementation language, Java does not appear to be a good language for specifications, so much that Java verification tools in the past introduced their own logical notation that developers then must learn in addition to Java. + +Can I use Stainless with Rust? +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Even though we had somewhat successful experiments translating Rust code into Stainless, we believe that, in the long term, it is more productive to use Scala as the starting point and generate low-level code. We are working on making this more practical in the future. + +Proving properties of size +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +I have defined a size function on my algebraic data type. + +.. code-block:: scala + + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case object Nil extends List + def size(l: List) : Int = (l match { + case Nil => 0 + case Cons(_, t) => 1 + size(t) + }) ensuring(_ >= 0) + +Stainless neither proves nor gives a counterexample. Why? + +**Answer:** You should consider using `BigInt`, which +denotes unbounded mathematical integers, instead of `Int`, +which denotes 32-bit integers. If you replace `Int` with +`BigInt` in the result type of `size`, the function should +verify. Note that algebraic data types can be arbitrarily +large, so, if the input list had the size `Int.MaxValue + 1` +(which is 2^32) then the addition `1 + size(t)` would wrap +around and produce `Int.MinValue` (that is, -2^31), so the +`ensuring` clause would not hold. + +Compiling Stainless programs to bytecode +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +If you don't use special constructs such as ``choose`` or unbounded ``forall``, you +should be able to compile Stainless programs to `.class` using `scalac` and +execute them directly on the JVM, or integrate them as part as other +Scala-based projects. See Section ":ref:`running-code`". diff --git a/_sources/genc.rst.txt b/_sources/genc.rst.txt new file mode 100644 index 0000000000..584a4928a5 --- /dev/null +++ b/_sources/genc.rst.txt @@ -0,0 +1,465 @@ +.. _genc: + +Generating C Code +================= + +Stainless can generate from Scala code an equivalent and safe C99 code. Using the verification, repair and +synthesis features of Stainless this conversion can be made safely. Additionally, the produced code can be +compiled with any standard-compliant C99 compiler to target the desired hardware architecture +without extra dependencies. The initial description of GenC, which has evolved since then, can be found in `Extending Safe C Support In Leon +`_. +Furthermore, this Master Thesis Report explains how to achieve compliance under the `MISRA C +`_ guidelines. + +To convert a Scala program, please use the ``--genc`` option of Stainless. + +The option ``--genc-output=file`` specifies the file name for GenC output (default: ``stainless.c``). + + +.. NOTE:: + Currently the memory model is limited to stack allocation and global state. Hence, no dynamic allocation + is done using ``malloc`` function family. + + +Requirements +------------ + +The following is required from the Scala program fed to GenC: + + - Functions compiled to C, and the types they use, + should be exclusively in the set of features described below, with the + exceptions of the (ghost) code used for verification conditions; + + - The program should be successfully verified with the ``--strict-arithmetic`` (enabled by default) + flag to ensure that arithmetic operations, array accesses, function + preconditions and so on, are safely converted into C code. + + +The generated C code should be compiled with a C99-compliant compiler that +satisfies these extra conditions: + + - ``CHAR_BITS`` is defined to be 8; + + - The ``int8_t``, ``int16_t``, ``int32_t``, ``int64_t`` and ``uint8_t``, ``uint16_t``, ``uint32_t``, ``uint64_t`` types are available (see :doc:`Pure Scala ` for description); + + - Casting from unsigned to signed integer, and vice-versa, is not well supported at the moment. + + +Export +------ + +Functions and classes can be marked with ``@cCode.export`` (``import stainless.annotation._``), +which affects GenC compilation in several ways. +First, the names of these functions and classes will not get mangled when generating the C code. +Second, the signatures of the functions, and the type definitions corresponding to exported classes, +will go into the header file (by default ``stainless.h``). +Finally, preconditions of exported functions (which are meant to be called from external C code), +are transformed into runtime assertions. + +Supported Features +------------------ + +The supported subset of Scala includes part of the core languages features, as well as some +imperative features, while ensuring the same expression execution order in both +languages. + + +Types +***** + +The following raw types and their corresponding literals are supported: + +.. list-table:: + :header-rows: 1 + + * - Scala + - C99 + * - ``Unit`` + - ``void`` + * - ``Boolean`` + - ``bool`` + * - ``Byte`` and ``Int8`` (8-bit integer) + - ``int8_t`` + * - ``Short`` and ``Int16`` (16-bit integer) + - ``int16_t`` + * - ``Int`` and ``Int32`` (32-bit integer) + - ``int32_t`` + * - ``Long`` and ``Int64`` (64-bit integer) + - ``int64_t`` + * - ``UInt8`` (8-bit unsigned integer) + - ``uint8_t`` + * - ``UInt16`` (16-bit integer) + - ``uint16_t`` + * - ``UInt32`` (32-bit integer) + - ``uint32_t`` + * - ``UInt64`` (64-bit integer) + - ``uint64_t`` + +Additionally, GenC has partial support for character and string literals made +of ASCII characters only but it has no API to manipulate strings at the moment: +``Char`` is mapped to ``char`` and ``String`` is mapped to ``char*``. + +Tuples +^^^^^^ + +Using ``TupleN[T1, ..., TN]`` results in the creation of a C structure with the +same fields and matching types for every combination of any supported type +``T1, ..., TN``. The name of the generated structure will be unique and reflect +the sequence of types. + + +Arrays +^^^^^^ + +Arrays are compiled by GenC into C structs that also store the length of the array. +For ``Array[Int]`` we get: + +.. code-block:: C + + typedef struct { + int32_t* data; + int32_t length; + } array_int32; + +.. NOTE:: + + Arrays live on the stack and therefore cannot be returned by functions. This limitation is + extended to other types having an array as field. In some cases, it is acceptable to use the + ``@cCode.inline`` annotation from Stainless's library to workaround this limitation. + +For case classes containing arrays whose length is known at compile time, we avoid +using a ``struct`` wrapper for the array, and instead directly inline the array +in the ``struct`` of the case class. We trigger this optimized transformation +when the array length is specified in the case class invariant (with ``require``) +as a conjunct. The left-hand-side needs to be ``a.length`` where ``a`` is the +array, and the right-hand-side needs to be a constant (or evaluate to a constant +at compile time). + +See below for a case class with a fixed length array and its transformation in C: + +.. code-block:: scala + + val CONSTANT1: UInt16 = 5 + val CONSTANT2: UInt16 = 12 + val CONSTANT3: UInt16 = CONSTANT1 + CONSTANT2 + + @cCode.export + case class W(x: Int, a: Array[Int], y: Int) { + require( + a.length == CONSTANT3.toInt && + 0 <= x && x <= 1000 && + 0 <= y && y <= 1000 + ) + } + +.. code-block:: C + + typedef struct { + int32_t x; + int32_t a[17]; + int32_t y; + } W; + +Classes +^^^^^^^ + +The support for classes is restricted to non-recursive ones so that instances +of such data-types live on the stack. The following language features are available: + + - ``case class`` with mutable ``var`` fields; + + - generics: + + + similarly to ``Array[T]`` or tuples, each combination of type parameters + is mapped to a specific C structure; + + - inheritance: + + + when all leaf classes have no fields, the class hierarchy is mapped to a + C enumeration, + + + otherwise, a tagged-union is used to represent the class hierarchy in C; + + - external types: + + + see ``@cCode.typedef`` below. + + +Functions +********* + +Functions with access to the variables in their respective scopes. The +following language features are available: + + - top level, nested or member functions: + + + both ``val`` and ``var`` are supported for local variable with the limitations imposed by + the imperative phases of Stainless + + - generics: + + + each combination of type parameters generates a different, specialised C function; + + - overloading: + + + the Scala compiler is responsible for identifying the correct function at each call site; + + - higher-order functions: + + + named functions that do not capture their environment can be used as value; + + - external functions: + + + see ``@cCode.function`` below; + +Since strings of characters are currently not (fully) available, in order to generate an executable +program, one has to define a main function without any argument, whose return type can be ``Int`` +or ``Unit``: + +.. code-block:: scala + + @cCode.export + def main(): Unit = { + // main code goes here + } + + +Constructs +********** + +The idiomatic ``if`` statements such as ``val b = if (x >= 0) true else false`` are converted into +a sequence of equivalent statements. + +Imperative ``while`` loops are also supported. + +*Pattern matching* is supported, with the exception of the *Unapply +Patterns*, as long as it is exempt of side effect. + +Assertions, invariant, pre- and post-conditions are not translated into C99 and are simply ignored. + + +Operators +********* + +The following operators are supported: + +.. list-table:: + :header-rows: 1 + + * - Category + - Operators + * - Boolean operators + - ``&&``, ``||``, ``!``, ``!=``, ``==`` + * - Comparision operators over integers + - ``<``, ``<=``, ``==``, ``!=``, ``>=``, ``>`` + * - Comparision operators over instances of classes + - ``==``, ``!=`` + * - Arithmetic operators over integers + - ``+``, ``-`` (unary & binary), ``*``, ``/``, ``%`` + * - Bitwise operators over integers + - ``&``, ``|``, ``^``, ``~``, ``<<``, ``>>>`` + + +Global State +------------ + +At the moment, Stainless does not support global mutable variables declared in objects. +It is however possible to simulate global state by using classes marked with ``@cCode.global``, +as shown in the `Global.scala +`_ +example: + +.. code-block:: scala + + @cCode.global + case class GlobalState( + val data: Array[Int] = Array.fill(100)(0), + var stable: Boolean = true, + var x: Int = 5, + var y: Int = 7, + ) { + require( + data.length == 100 && ( + !stable || ( + 0 <= x && x <= 100 && + 0 <= y && y <= 100 && + x + y == 12 + ) + ) + ) + } + +.. note:: + + In classes annotated with ``@cCode.global``, only arrays with a fixed length are + allowed. Please check the paragraph about arrays to learn how to specify the array length. + +This annotation triggers some checks to make sure that indeed the ``GlobalState`` class +(the name of the class can be changed, and there can be multiple such classes) is used as a global +state: + +* Functions can take as argument at most one instance per each global class such as ``GlobalState``. +* There can be at most one instance created for each global class such as ``GlobalState`` + (in a function that doesn't already take an instance of that class as argument). +* A ``GlobalState`` instance can only be used for reads and assignments (e.g. it cannot be let bound, except for the declaration mentioned above). +* The only global state that can be passed to other functions is the one we create or the one we received as a function argument. + +These checks ensure that the fields of ``GlobalState`` can be compiled as global variables in ``C``. +Consider the ``move`` function from the `Global.scala +`_ +example: + +.. code-block:: scala + + def move()(implicit state: GlobalState): Unit = { + require(state.stable && state.y > 0) + state.stable = false + state.x += 1 + state.y -= 1 + state.data(state.y) = 1 + state.stable = true + if (state.y > 0) move() + }.ensuring(_ => state.stable) + +After compilation to C, we get the following function, with global declarations +``stable``, ``x``, ``y``, and ``data``. + +.. code-block:: C + + int32_t data[100] = { 0 }; + bool stable = true; + int32_t x = 5; + int32_t y = 7; + + void move() { + stable = false; + x = x + 1; + y = y - 1; + data[y] = 1; + stable = true; + if (y > 0) { + move(); + } + } + +Note that the initial values for the global variables correspond to the default values given +in the Stainless class declaration (default values are mandatory when using the ``@cCode.global`` +annotation). When creating a global state instance (the only one), we do not pass arguments, to +make sure that the instance is created using the default values: + +.. code-block:: scala + + @cCode.export + def main() { + implicit val gs = GlobalState() + StdOut.print(gs.x) + StdOut.print(gs.y) + move() + StdOut.print(gs.data(6)) + StdOut.print(gs.data(7)) + StdOut.print(gs.x) + StdOut.println(gs.y) + } + +Stainless supports two variants of the ``@cCode.global`` annotation, namely ``@cCode.globalUninitialized`` +and ``@cCode.globalExternal``. The first one generates global declarations without initial +values. These global variables are thus initialized according to C semantics, and there can be +a mismatch between the global state instance created by the user, and the initial values in C. +The second one hides the global declarations, which can be useful when interacting with C code +that declares global variables outside of the Stainless program. + + +Custom Conversion +----------------- + +When it comes to function using system calls, such as I/Os, no automated conversion is possible. In +those situations the user can define his own implementation for functions, add manual conversion +from Scala types to C types or even drop some functions and types from the translation, with +``@cCode.function``, ``@cCode.typedef`` and ``@cCode.drop`` annotations from the package +``stainless.annotation``. Their usage is described below. + + +Custom Function Implementation +****************************** + +In order to circumvent some current limitations of GenC, one can use ``@cCode.function(code, +includes)`` to define the corresponding implementation of any top-level function or method, usually +accompanied by ``@extern``. Its usage is as follows: + + * For convenience, the C implementation generated by ``code`` is represented using a String and + not an Abstract Syntax Tree. The user is responsible for the correctness of the provided C99 + code. Because GenC might rename the function, e.g. to deal with overloading, the special + ``__FUNCTION__`` token should be used instead of the original name. Furthermore, the parameters + and return type should match the signature automatically generated by GenC. + + * The optional parameter ``includes`` can hold a colon separated list of required C99 include + header files. + +Here is a typical example: + +.. code-block:: scala + + // Print a 32-bit integer using the *correct* + // format for printf in C99 + @cCode.function( + code = """ + | void __FUNCTION__(int32_t x) { + | printf("%"PRIi32, x); + | } + """, + includes = "inttypes.h:stdio.h" + ) + def myprint(x: Int): Unit = { + print(x) + } + + +Custom Type Translation +*********************** + +When a whole type need to be represented using a special C type, the ``@cCode.typedef(alias, +include)`` annotation can be used. Here the ``include`` parameter is also optional, however it can +only refer to one header, as it is not expected to have a type defined in several headers. The +``alias`` string must represent an existing and valid type. + +Using an aliasing from ``S`` to ``C`` implies that every function that accept a ``S`` in the input +program must accept a ``C`` in the generated C code. Usually, using this annotation implicates +manually defining the implementation of functions using this type with ``@cCode.function``. + +Here is an example: + +.. code-block:: scala + + @cCode.typedef(alias = "FILE*", include = "stdio.h") + case class MyFile( ... + + +Ignore Function or Type +*********************** + +It is also possible to skip the translation of some functions or types that are only used as +implementation details in proofs, for example, using the ``@cCode.drop()`` annotation. + + +API For Safe Low Level Programs +------------------------------- + +In this section we describe the APIs that can be used to make the bridge between some Scala +programming facilities and their low level, equivalent, C features. + + +I/Os +**** + +Similarly to Scala's ``scala.io.StdIn`` and ``scala.io.StdOut``, Stainless provides ``stainless.io.StdIn`` and +``stainless.io.StdOut``. These two APIs are provided with equivalent C code for easy translation with +GenC, but are also shaped to allow users to write proofs in a non-deterministic environment. + + +Furthermore, Stainless provides ``stainless.io.FileInputStream`` to read data and +``stainless.io.FileOutputStream`` to write data to a file with a C99 compatible API. + +.. NOTE:: + + It is important that you close the stream after it was created or your C + application might leak resources. diff --git a/_sources/gettingstarted.rst.txt b/_sources/gettingstarted.rst.txt new file mode 100644 index 0000000000..7758004303 --- /dev/null +++ b/_sources/gettingstarted.rst.txt @@ -0,0 +1,105 @@ +.. _gettingstarted: + +Verifying and Compiling Examples +================================ + +Verifying Examples +------------------ + +Stainless is currently available as either: + +* a command line tool, which exposes most of the functionality, available as a ZIP file (recommended) or via Docker. +* via an SBT plugin. + +See the :doc:`installation documentation ` for more information. + +It is henceforth assumed that there exists a ``stainless`` script in in your ``PATH``. + +To see the main options, use + +.. code-block:: bash + + $ stainless --help + +in your command line shell. +You may also wish to consult the :doc:`available command-line options `. + +You can try some of the examples from ``frontends/benchmarks`` +distributed with Stainless: + +.. code-block:: bash + + $ stainless --solvers=smt-cvc5 frontends/benchmarks/verification/invalid/InsertionSort.scala + +and get something like this (some output cropped) + +.. code-block:: text + + [ Info ] Starting verification... + [ Info ] Verified: 3 / 19 + [Warning ] - Result for 'postcondition' VC for buggySortedIns @37:38: + [Warning ] l.isInstanceOf[Nil] || !(l.head <= e) || { + [Warning ] val res: List = Cons(l.head, buggySortedIns(e, l.tail)) + [Warning ] assume({ + [Warning ] val e: List = Cons(l.head, buggySortedIns(e, l.tail)) + [Warning ] true + [Warning ] }) + [Warning ] contents(res) == contents(l) ++ Set(e) && isSorted(res) && size(res) == size(l) + BigInt("1") + [Warning ] } + [Warning ] frontends/benchmarks/verification/invalid/InsertionSort.scala:37:38: => INVALID + case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l) + ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + [Warning ] Found counter-example: + [Warning ] l: List -> Cons(-770374653, Cons(-771685886, Nil())) + [Warning ] e: Int -> 1376322050 + [ Info ] Verified: 3 / 19 + [Warning ] - Result for 'postcondition' VC for buggySortedIns @37:73: + [Warning ] l.isInstanceOf[Nil] || l.head <= e || { + [Warning ] val res: List = Cons(e, l) + [Warning ] contents(res) == contents(l) ++ Set(e) && isSorted(res) && size(res) == size(l) + BigInt("1") + [Warning ] } + [Warning ] frontends/benchmarks/verification/invalid/InsertionSort.scala:37:73: => INVALID + case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l) + ^^^^^^^^^^ + [Warning ] Found counter-example: + [Warning ] l: List -> Cons(691483681, Cons(512, Nil())) + [Warning ] e: Int -> -1263292350 + [ Info ] Verified: 17 / 19 + [ Info ] ┌───────────────────┐ + [ Info ] ╔═╡ stainless summary ╞══════════════════════════════════════════════════════════════════════════════════════════════╗ + [ Info ] ║ └───────────────────┘ ║ + [ Info ] ║ InsertionSort.scala:33:7: buggySortedIns non-negative measure valid U:smt-z3 0,1 ║ + [ Info ] ║ InsertionSort.scala:35:5: buggySortedIns body assertion: match exhaustiveness trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:35:5: buggySortedIns postcondition trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:36:21: buggySortedIns postcondition valid U:smt-z3 0,1 ║ + [ Info ] ║ InsertionSort.scala:37:38: buggySortedIns postcondition invalid U:smt-z3 0,3 ║ + [ Info ] ║ InsertionSort.scala:37:45: buggySortedIns measure decreases valid U:smt-z3 0,1 ║ + [ Info ] ║ InsertionSort.scala:37:73: buggySortedIns postcondition invalid U:smt-z3 0,1 ║ + [ Info ] ║ InsertionSort.scala:20:7: contents non-negative measure valid from cache 0,0 ║ + [ Info ] ║ InsertionSort.scala:20:37: contents body assertion: match exhaustiveness trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:22:24: contents measure decreases valid U:smt-z3 0,0 ║ + [ Info ] ║ InsertionSort.scala:25:7: isSorted non-negative measure valid U:smt-z3 0,0 ║ + [ Info ] ║ InsertionSort.scala:25:36: isSorted body assertion: match exhaustiveness trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:28:44: isSorted measure decreases valid U:smt-z3 0,1 ║ + [ Info ] ║ InsertionSort.scala:15:7: size non-negative measure valid from cache 0,0 ║ + [ Info ] ║ InsertionSort.scala:15:34: size body assertion: match exhaustiveness trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:15:34: size postcondition trivial 0,0 ║ + [ Info ] ║ InsertionSort.scala:16:19: size postcondition valid U:smt-z3 0,0 ║ + [ Info ] ║ InsertionSort.scala:17:25: size postcondition valid U:smt-z3 0,0 ║ + [ Info ] ║ InsertionSort.scala:17:29: size measure decreases valid from cache 0,0 ║ + [ Info ] ╟┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄╢ + [ Info ] ║ total: 19 valid: 17 (3 from cache, 6 trivial) invalid: 2 unknown: 0 time: 0,81 ║ + [ Info ] ╚════════════════════════════════════════════════════════════════════════════════════════════════════════════════════╝ + [ Info ] Verification pipeline summary: + [ Info ] cache, anti-aliasing, smt-z3 + [ Info ] Shutting down executor service. + + +Compiling and Executing Examples +-------------------------------- + +Scala code written with Stainless library dependencies can be compiled and run using the +library sources available on the `Stainless github repository `_, +along with the scala compiler and runner script. + +See the :ref:`installation documentation ` for more information. \ No newline at end of file diff --git a/_sources/ghost.rst.txt b/_sources/ghost.rst.txt new file mode 100644 index 0000000000..220d0cdecc --- /dev/null +++ b/_sources/ghost.rst.txt @@ -0,0 +1,153 @@ +.. _ghost: + +Ghost Context +============= + +Introduction +------------ + +When verifying code, one often needs to introduce lemmas, auxiliary functions, +additional fields and parameters, and contracts, whose only function is to specify +and prove that some properties are satisfied by the program. + +.. code-block:: scala + + import stainless.lang._ + import stainless.lang.collection._ + import stainless.lang.annotation._ + + def isSorted(list: List[BigInt]): Boolean = list match { + case Nil() => true + case Cons(_, Nil()) => true + case Cons(x1, Cons(x2, _)) if x1 > x2 => false + case Cons(_, xs) => isSorted(xs) + } + + def sort(list: List[BigInt]): List[BigInt] = { + /* ... */ + } ensuring { res => + res.contents == list.contents && + isSorted(res) && + res.size == l.size + } + +One can alleviate this issue by adding the following import: + + +.. code-block:: scala + + import stainless.lang.StaticChecks._ + + +Ghost annotation +---------------- + +Correctness check +----------------- + +As part of the verification pipeline, Stainless will check that it never +encounters a *ghost expression* outside of a *ghost context*. Should +the check fail, verification will fail and compilation will be aborted. + +A *ghost expression* is any of: + +- Call to a ghost method +- Selection of a ghost field +- Instantiation of a ghost class +- Reference to a ghost variable + +A *ghost context* as any of: + +- Body of a ghost method +- Argument to a ghost parameter (method or class constructor) +- Assignment to a ghost variable +- Anywhere where a value of type ``Unit`` is expected + +Ghost expression elimination +---------------------------- + +If the correctness check described in the previous section succeeds, the sbt plugin +will then proceed to eliminate ghost methods and expressions from the programs. + +Case study +---------- + +.. code-block:: scala + + import stainless.lang._ + import stainless.lang.StaticChecks._ + import stainless.collection._ + import stainless.annotation._ + + import java.util.ArrayDeque + + object MessageQueue { + + case class MsgQueue[A]( + @extern @pure + queue: ArrayDeque[A], + @ghost + var msgs: List[A] + ) { + def put(msg: A): Unit = { + + msgs = msg :: msgs + _put(msg) + } + + @extern @pure + private def _put(msg: A): Unit = { + queue.addFirst(msg) + } + + def take(): Option[A] = { + val result = _take() + msgs = msgs.tailOption.getOrElse(Nil()) + result + } ensuring { res => + res == old(this).msgs.headOption + } + + @extern @pure + private def _take(): Option[A] = { + Option(queue.pollFirst()) + } ensuring { res => + res == msgs.headOption + } + + @extern @pure + def isEmpty: Boolean = { + queue.size() == 0 + } ensuring { res => + res == msgs.isEmpty + } + } + + object MsgQueue { + @extern @pure + def empty[A]: MsgQueue[A] = { + MsgQueue(new ArrayDeque(), Nil()) + } ensuring { res => + res.isEmpty && res.msgs.isEmpty + } + } + + def test = { + val queue = MsgQueue.empty[String] + + queue.put("World") + queue.put("Hello") + + assert(!queue.isEmpty) + + val a = queue.take() + assert(a == Some("Hello")) + + val b = queue.take() + assert(b == Some("World")) + assert(queue.isEmpty) + + val c = queue.take() + assert(!c.isDefined) + } + } diff --git a/_sources/imperative.rst.txt b/_sources/imperative.rst.txt new file mode 100644 index 0000000000..819ea74877 --- /dev/null +++ b/_sources/imperative.rst.txt @@ -0,0 +1,545 @@ +.. _imperative: + +Imperative +========== + +To complement the core :doc:`Pure Scala ` language, Stainless +proposes a few extensions to that core language. + +On the technical side, these extensions do not have specific treatment in the +back-end of Stainless. Instead, they are desugared into :doc:`Pure Scala ` +constructs during a preprocessing phase in the Stainless front-end. + +These transformations are partly documented in the `EPFL PhD thesis of Régis Blanc `_. + +Imperative Code +--------------- + +Stainless lets you introduce local variables in functions, and use Scala assignments +syntax. + +.. code-block:: scala + + def foo(x: Int): Int = { + var a = x + var b = 42 + a = a + b + b = a + b + } + +The above example illustrates three new features introduced by imperative support: + +1. Declaring a variable in a local scope + +2. Blocks of expressions + +3. Assignments + +You can use Scala variables with a few restrictions. The variables can only be +declared and used locally, no variable declaration outside of a function body. +There is also support for variables in case classes constructors. Imperative support +introduces the possibility to use sequences of expressions (blocks) -- a +feature not available in :doc:`Pure Scala `, where your only +option is a sequence of ``val`` which essentially introduce nested ``let`` +declarations. + + +While loops +----------- + +You can use the ``while`` keyword. While loops usually combine the ability to +declare variables and make a sequence of assignments in order to compute +something useful: + +.. code-block:: scala + + def foo(x: Int): Int = { + var res = 0 + var i = 0 + while(i < 10) { + res = res + i + i = i + 1 + } + res + } + +Stainless will automatically generate a postcondition to the ``while`` loop, using +the negation of the loop condition. It will automatically prove that +verification condition and you should see an ``invariant postcondition`` marked +as ``valid``. + +Stainless internally handles loops as a function with a postcondition. For the end-user, it +means that Stainless is only going to rely on the postcondition of the loop to prove properties +of code relying on loops. Usually that invariant is too weak to prove anything remotely +useful and you will need to annotate the loop with a stronger invariant. + +You can annotate a loop with an invariant as follows: + +.. code-block:: scala + + var res = 0 + var i = 0 + (while(i < 10) { + res = res + i + i = i + 1 + }) invariant(i >= 0 && res >= i) + +The strange syntax comes from some Scala magic in order to make the keyword +``invariant`` a valid keyword. Stainless is defining an implicit conversion from +``Unit`` to an ``InvariantFunction`` object that provides an ``invariant`` +method. The ``invariant`` method takes a boolean expression as a parameter and +its semantics is to hold at the following points during the execution of the loop: + +1. When first entering the loop: initialization. +2. After each complete execution of the body. +3. On exiting the loop. + +Stainless will generate verification conditions ``invariant inductive`` and +``invariant postcondition`` to verify points (2) and (3) above. It will also +generate a ``precondition`` corresponding to the line of the while loop. This +verification condition is used to prove the invariant on initialization of the +loop. + +Arrays +------ + +PureScala supports functional arrays, that is, the operations ``apply`` and +``updated`` which do not modify an array but only returns some result. In +particular, ``updated`` returns a new copy of the array. + +.. code-block:: scala + + def f(a: Array[Int]): Array[Int] = { + a.updated(0, a(1)) + } + +However, using functional arrays is not the most natural way to work with +arrays, and arrays are often used in imperative implementations of algorithms. +We add the usual ``update`` operation on arrays: + +.. code-block:: scala + + val a = Array(1,2,3,4) + a(1) //2 + a(1) = 10 + a(1) //10 + +Stainless simply rewrite arrays using ``update`` operation as the assignment of function arrays +using ``updated``. This leverages the built-in algorithm for functional arrays +and relies on the elimination procedure for assignments. Concretely, it would +transform the above on the following equivalent implementation: + +.. code-block:: scala + + var a = Array(1,2,3,4) + a(1) //2 + a = a.updated(1, 10) + a(1) //10 + +Stainless also has a ``swap`` operation in ``stainless.lang``, which is equivalent to two updates. + +.. code-block:: scala + + def swap[@mutable T](a1: Array[T], i1: Int, a2: Array[T], i2: Int): Unit + + +Mutable Objects +--------------- + +A restricted form of mutable classes is supported via case classes with ``var`` +arguments: + +.. code-block:: scala + + case class A(var x: Int) + def f(): Int = { + val a = new A(10) + a.x = 13 + a.x + } + +Mutable case classes are behaving similarly to ``Array``, and are handled with a +rewriting, where each field updates becomes essentially a copy of the object with +the modified parameter changed. + +Aliasing +-------- + +With mutable data structures comes the problem of aliasing. In Stainless, we +maintain the invariant that in any scope, there is at most one pointer to some +mutable structure. Stainless will issue an error if you try to create an alias to +some mutable structure in the same scope: + +.. code-block:: scala + + val a = Array(1,2,3,4) + val b = a //error: illegal aliasing + b(0) = 10 + assert(a(0) == 10) + +However, Stainless correctly supports aliasing mutable structures when passing it +as a parameter to a function (assuming its scope is not shared with the call +site, i.e. not a nested function). Essentially you can do: + +.. code-block:: scala + + case class A(var x: Int) + def updateA(a: A): Unit = { + a.x = 14 + } + def f(): Unit = { + val a = A(10) + updateA(a) + assert(a.x == 14) + } + +The function ``updateA`` will have the side effect of updating its argument +``a`` and this will be visible at the call site. + +Annotations for Imperative Programming +-------------------------------------- + +We introduce the special function ``old`` that can be used in postconditions to +talk about the value of a variable before the execution of the block. When you refer to a variable +or mutable structure in a post-condition, Stainless will always consider the current value of +the object, so that in the case of a post-condition this would refer to the final value of the +object. Using ``old``, you can refer to the original value of the variable and check some +properties: + +.. code-block:: scala + + case class A(var x: Int) + def inc(a: A): Unit = { + a.x = a.x + 1 + } ensuring(_ => a.x == old(a).x + 1) + +``old`` can be wrapped around any identifier that is affected by the body. You can also use +``old`` for variables in scope, in the case of nested functions: + +.. code-block:: scala + + def f(): Int = { + var x = 0 + def inc(): Unit = { + x = x + 1 + } ensuring(_ => x == old(x) + 1) + + inc(); inc(); + assert(x == 2) + } + +Another useful and similar construct is ``snapshot`` that semantically makes a deep copy of a mutable object. +Contrarily to ``old``, ``snapshot`` allows to refer to the state of an object prior to its mutation within +the body of the function, as long as it is used in a :doc:`ghost context `. + +For instance: + +.. code-block:: scala + + def updateArray(a: Array[BigInt], i: Int, x: BigInt): Unit = { + require(0 <= i && i < a.length - 1) + require(a(i) == 0 && a(i + 1) == 0) + @ghost val a0 = snapshot(a) + a(i) = x + // a0 is unaffected by the update of a + // Note: using StaticChecks assert, which introduces a ghost context + assert(a0(i) == 0 && a(i) == x) + @ghost val a1 = snapshot(a) + a(i + 1) = 2 * x + assert(a1(i + 1) == 0 && a(i + 1) == 2 * x) + } + + +Extern functions and abstract methods +------------------------------------- + +``@extern`` functions and abstract methods of non-sealed trait taking mutable objects as parameters are treated as-if +they were applying arbitrary modifications to them. +For instance, the assertions in the following snippet are invalid: + +.. code-block:: scala + + @extern + def triple(mc: MutableClass): BigInt = ??? + + trait UnsealedTrait { + def quadruple(mc: MutableClass): BigInt + } + + def test1(mc: MutableClass): Unit = { + val i = mc.i + triple(mc) + assert(i == mc.i) // Invalid, mc.i could be anything + } + + def test2(ut: UnsealedTrait, mc: MutableClass): Unit = { + val i = mc.i + ut.quadruple(mc) + assert(i == mc.i) // Invalid as well + } + +Annotating such methods or functions with ``@pure`` tells Stainless to assume the parameters are not mutated: + +.. code-block:: scala + + case class MutableClass(var i: BigInt) + + @pure @extern + def triple(mc: MutableClass): BigInt = ??? + + trait UnsealedTrait { + @pure + def quadruple(mc: MutableClass): BigInt + } + + def test1(mc: MutableClass): Unit = { + val i = mc.i + triple(mc) + assert(i == mc.i) // Ok + } + + def test2(ut: UnsealedTrait, mc: MutableClass): Unit = { + val i = mc.i + ut.quadruple(mc) + assert(i == mc.i) // Ok + } + +Note that Stainless will enforce purity for visible implementations of ``quadruple``. + +Sometimes, a method or ``@extern`` function may mutate some parameters but not all of them. +In such cases, the untouched parameters can be annotated with ``@pure``: + +.. code-block:: scala + + case class MutableClass(var i: BigInt) + + @extern + def sum(@pure mc1: MutableClass, mc2: MutableClass): BigInt = ??? + + trait UnsealedTrait { + def doubleSum(@pure mc1: MutableClass, mc2: MutableClass): BigInt + } + + def test1(mc1: MutableClass, mc2: MutableClass): Unit = { + val i1 = mc1.i + val i2 = mc2.i + sum(mc1, mc2) + assert(i1 == mc1.i) // Ok + assert(i2 == mc2.i) // Invalid, mc2.i may have any value + } + + def test2(ut: UnsealedTrait, mc1: MutableClass, mc2: MutableClass): Unit = { + val i1 = mc1.i + val i2 = mc2.i + ut.doubleSum(mc1, mc2) + assert(i1 == mc1.i) // Ok + assert(i2 == mc2.i) // Invalid + } + +Trait Variables +--------------- + +Traits are allowed to declare variables, with the restriction that these cannot be +assigned a default value. + +.. code-block:: scala + + trait MutableBox[A] { + var value: A + } + +Such abstract variables must be overridden at some point by either: + +a) a mutable field of a case class + +.. code-block:: scala + + case class Box[A](var value: A) extends MutableBox[A] + +b) a pair of getter/setter + +.. code-block:: scala + + case class WriteOnceBox[A]( + var underlying: A, + var written: Boolean = false + ) extends MutableBox[A] { + + def value: A = underlying + + def value_=(newValue: A): Unit = { + if (!written) { + underlying = newValue + written = true + } + } + } + +Note: a setter is not required to actually perform any mutation, and the following +is a perfectly valid sub-class of `MutableBox`: + +.. code-block:: scala + + case class ImmutableBox[A](underlying: A) extends MutableBox[A] { + def value: A = underlying + def value_=(newValue: A): Unit = () + } + + +Return keyword +-------------- + +Stainless partially supports the `return` keyword. For verification, an internal +phase of Stainless (called `ReturnElimination`) injects a data-structure named +`ControlFlow` to simulate the control flow of programs with returns. + +.. code-block:: scala + + sealed abstract class ControlFlow[Ret, Cur] + case class Return[Ret, Cur](value: Ret) extends ControlFlow[Ret, Cur] + case class Proceed[Ret, Cur](value: Cur) extends ControlFlow[Ret, Cur] + +Here is a function taken from `ControlFlow2.scala `_: + +.. code-block:: scala + + def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = { + if (a && b) { + return 1 + } + + val y = x match { + case None() => return 0 + case Some(x) if a => return x + 1 + case Some(x) if b => return x + 2 + case Some(x) => x + }; + + -y + } + +The program transformation can be inspected by running: + + .. code-block:: bash + + stainless ControlFlow2.scala --batched --debug=trees --debug-objects=foo --debug-phases=ReturnElimination + +We get the following output (with ``cf`` identifiers renamed for clarity; you can +use the ``--print-ids`` option so that Stainless expressions get displayed with +unique identifiers, at the cost of readability): + + .. code-block:: scala + + def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = { + val cf0: ControlFlow[BigInt, Unit] = if (a && b) { + Return[BigInt, Unit](1) + } else { + Proceed[BigInt, Unit](()) + } + cf0 match { + case Return(retValue) => + retValue + case Proceed(proceedValue) => + val cf1: ControlFlow[BigInt, BigInt] = x match { + case None() => Return[BigInt, BigInt](0) + case Some(x) if a => Return[BigInt, BigInt](x + 1) + case Some(x) if b => Return[BigInt, BigInt](x + 2) + case Some(x) => Proceed[BigInt, BigInt](x) + } + cf1 match { + case Return(retValue) => + retValue + case Proceed(proceedValue) => + -proceedValue + } + } + } + +Stainless also supports ``return`` in while loops, and transforms them to local functions, also in +the ``ReturnElimination`` phase. Here is a function taken from `ReturnInWhile.scala `_. + + .. code-block:: scala + + def returnN(n: Int): Int = { + require(n >= 0) + var i = 0 + (while (true) { + decreases(n - i) + if (i == n) return i + i += 1 + }).invariant(0 <= i && i <= n) + + assert(false, "unreachable code") + 0 + }.ensuring((res: Int) => res == n) + +After transformation, we get a recursive (local) function named ``returnWhile`` +that returns a control flow element to indicate whether the loop terminated +normally or returned. We check that the invariant clause of the while loop is +indeed an invariant by adding it to the pre and postconditions of the generated +``returnWhile`` function. When the while loop returns, we check in addition that +the postcondition of the top-level holds (see comment). + + .. code-block:: scala + + def returnN(n: Int): Int = { + require(n >= 0) + + var i: Int = 0 + val cf0: ControlFlow[Int, Unit] = { + def returnNWhile: ControlFlow[Int, Unit] = { + require(0 <= i && i <= n) + decreases(n - i) + { + val cf1: ControlFlow[Int, Unit] = if (i == n) { + Return[Int, Unit](i) + } else { + Proceed[Int, Unit](()) + } + cf1 match { + case Return(retValue) => Return[Int, Unit](retValue) + case Proceed(proceedValue) => + Proceed[Int, Unit]({ + i = (i + 1) + () + }) + } + } match { + case Return(retValue) => + Return[Int, Unit](retValue) + case Proceed(proceedValue) => + if (true) { + returnNWhile + } else { + Proceed[Int, Unit](()) + } + } + } ensuring { + (cfWhile: ControlFlow[Int, Unit]) => cfWhile match { + case Return(retValue) => + // we check the postcondition `retValue == n` of the top-level function + retValue == n && + 0 <= i && i <= n + case Proceed(proceedValue) => + ¬true && 0 <= i && i <= n + } + } + if (true) { + returnNWhile + } else { + Proceed[Int, Unit](()) + } + } + cf0 match { + case Return(retValue) => retValue + case Proceed(proceedValue) => + assert(false, "unreachable code") + 0 + } + } ensuring { + (res: Int) => res == n + } + +Finally, ``return`` is also supported for local function definitions, with the same transformation. +It is however not supported for anonymous functions. diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 0000000000..38ded73814 --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,36 @@ +.. Stainless documentation master file, created by + sphinx-quickstart on Fri Feb 27 13:23:31 2015. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Stainless documentation +======================= + +Contents: + +.. toctree:: + :maxdepth: 2 + + intro + installation + gettingstarted + tutorial + options + verification + laws + imperative + equivalence + ghost + wrap + purescala + library + genc + neon + limitations + casestudies + coq + faq + references + internals + +* :ref:`search` diff --git a/_sources/installation.rst.txt b/_sources/installation.rst.txt new file mode 100644 index 0000000000..63e5cf670e --- /dev/null +++ b/_sources/installation.rst.txt @@ -0,0 +1,402 @@ +.. _installation: + +Installing Stainless +==================== + +.. _requirements: + +General Requirement +------------------- + +- Java 17 JRE + It suffices to have headless OpenJDK JRE 17 (e.g. one that one gets with ``apt install openjdk-17-jre-headless`` on Debian/Ubuntu). + Make sure that ``java -version`` reports a version starting with 1.17, such as ``openjdk version "1.17`` or ``java version "1.17``. + +Stainless bundles Scala compiler front-end and runs it before it starts compilation. We recommend using the Scala 3 front end (originally named dotty), though Scala 2 is also available. + +.. _standalone-release: + +Use Standalone Release (recommended) +------------------------------------ + +1. Download the latest Stainless release from the `Releases page on GitHub `_, under the **Assets** section. Make sure to pick the appropriate ZIP for your operating system. This release is bundled with Z3 4.12.2 and cvc5 1.0.8. + +2. Unzip the the file you just downloaded to a directory. + +3. (Optional) Add this directory to your ``PATH``. This will let you invoke Stainless via the ``stainless`` command instead of its fully qualified path in step 5. + +4. Paste the following code in a file named ``HelloStainless.scala``: + +.. code-block:: scala + + import stainless.collection._ + + object HelloStainless { + def myTail(xs: List[BigInt]): BigInt = { + require(xs.nonEmpty) + xs match { + case Cons(h, _) => h + // Match provably exhaustive + } + } + } + +5. In a terminal, type the following command, substituting the proper path to the directory where you unzipped the latest release: + +.. code-block:: bash + + $ /path/to/unzipped/directory/stainless HelloStainless.scala + +6. The output should read: + +.. code-block:: text + + [ Debug ] Generating VCs for functions: myTail + [ Debug ] Finished generating VCs + [ Info ] Starting verification... + [ Info ] Verified: 0 / 1 + [ Debug ] - Checking cache: 'body assertion: match exhaustiveness' VC for myTail @6:5... + [ Debug ] Cache miss: 'body assertion: match exhaustiveness' VC for myTail @6:5... + [ Debug ] - Now solving 'body assertion: match exhaustiveness' VC for myTail @6:5... + [ Debug ] + [ Debug ] - Original VC: + [ Debug ] nonEmpty[BigInt](xs) ==> { + [ Debug ] val scrut: List[BigInt] = xs + [ Debug ] !scrut.isInstanceOf[Cons] ==> false + [ Debug ] } + [ Debug ] + [ Debug ] - Simplified VC: + [ Debug ] !nonEmpty[BigInt](xs) || xs.isInstanceOf[Cons] + [ Debug ] + [ Debug ] Solving with: nativez3 + [ Debug ] - Result for 'body assertion: match exhaustiveness' VC for myTail @6:5: + [ Debug ] => VALID + [ Info ] Verified: 1 / 1 + [ Info ] ┌───────────────────┐ + [ Info ] ╔═╡ stainless summary ╞═════════════════════════════════════════════════════════════════════════════════╗ + [ Info ] ║ └───────────────────┘ ║ + [ Info ] ║ HelloStainless.scala:6:5: myTail body assertion: match exhaustiveness valid nativez3 0,2 ║ + [ Info ] ╟┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄╢ + [ Info ] ║ total: 1 valid: 1 (0 from cache, 0 trivial) invalid: 0 unknown: 0 time: 0,17 ║ + [ Info ] ╚═══════════════════════════════════════════════════════════════════════════════════════════════════════╝ + [ Info ] Verification pipeline summary: + [ Info ] cache, nativez3 + [ Info ] Shutting down executor service. + +Note: If the warning above says something about falling back on the Princess solver, you might be missing the ``libgomp1`` library, +which you can install with your favorite package manager. For example, on Debian/Ubuntu, just run ``apt-get install libgomp1``. + + +.. _sbt-project: + +Usage Within An Existing Project +******************************** + +Stainless can also be used within an existing SBT 1.7.x project. + +1. Start by installing an external solver (see Section ":ref:`smt-solvers`"). + +2. Download ``sbt-stainless`` from the `GitHub releases `_, and move it to the directory of the project. You should have the following project structure: + +.. code-block:: + + MyProject + ├── build.sbt + ├── project + │ └── build.properties + ├── sbt-stainless.zip <-------- + └── src/ + +3. Unzip ``sbt-stainless.zip``: + +.. code-block:: + + MyProject + ├── build.sbt + ├── project + │ ├── build.properties + │ └── lib <-------- + │ └── sbt-stainless.jar <-------- + ├── sbt-stainless.zip + ├── src/ + └── stainless/ <-------- + +4. In your project's build file, enable the ``StainlessPlugin`` on the modules that should be verified by Stainless. Below is an example: + +.. code-block:: scala + + // build.sbt + lazy val algorithm = project + .in(file("algorithm")) + .enablePlugins(StainlessPlugin) // <-- Enabling Stainless verification on this module! + .settings(...) + +Note that if you are using ``.scala`` build files you need to use the fully qualified name ``ch.epfl.lara.sbt.stainless.StainlessPlugin``. Also, because Stainless accepts a subset of the Scala language, you may need to refactor your build a bit and code to successfully use Stainless on a module. + +5. After modifying the build, type ``reload`` if inside the sbt interactive shell. From now on, when executing ``compile`` on a module where the ``StainlessPlugin`` is enabled, Stainless will check your Scala code and report errors in the shell (just like any other error that would be reported during compilation). + +That's all there is to it. However, the ``sbt-stainless`` plugin is a more recent addition to Stainless compared to command-line script. Furthermore, there incremental compilation is not supported. All sources (included the stainless-library sources) are recompiled at every ``compile`` execution.ub + +Also, note that the plugin offers a ``stainlessEnabled`` setting that can help experimenting with Stainless. The ``stainlessEnabled`` setting is set to ``true`` by default, but you can flip the flag to false by typing ``set every stainlessEnabled := false`` while inside the sbt interactive shell. + +6. It is possible to specify extra source dependencies to be added to the set of files processed by Stainless via the ``stainlessExtraDeps`` setting. For example, to add both the ``stainless-algebra`` and ``stainless-actors`` packages, along with the latter's dependency on Akka, + one can add the following settings to their build: + +.. code-block:: scala + + stainlessExtraDeps ++= Seq( + "ch.epfl.lara" %% "stainless-algebra" % "0.1.2", + "ch.epfl.lara" %% "stainless-actors" % "0.1.1", + ) + + libraryDependencies += "com.typesafe.akka" %% "akka-actor" % "2.5.21" + +Note that the dependencies specified in ``stainlessExtraDeps`` must be available as a source JAR from any of the resolvers configured in the build. + +.. _running-code: + +Running Code with Stainless dependencies +---------------------------------------- + +Using sources: + +1. Clone the sources from https://github.com/epfl-lara/stainless + +2. Create a folder to put compiled Scala objects: ``mkdir -p ~/.scala_objects`` + +3. Compile your code (here in ``MyFile.scala``, though you can have more than one file) while referring to the Stainless library sources: ``scalac -d ~/.scala_objects $(find /path/to/stainless/frontends/library/stainless/ -name "*.scala") MyFile.scala`` + +4. Run your code (replace ``MyMainClass`` with the name of your main object): ``scala -cp ~/.scala_objects MyMainClass`` + +Using jar: + +You can package the Stainless library into a jar to avoid the need to compile it every time: + +.. code-block:: bash + + $ cd path/to/stainless/ + $ sbt stainless-library/packageBin + +Add the generated Stainless library jar file when invoking the compiler with ``scalac`` and the JVM with ``scala`` or ``java``. For instance: + +.. code-block:: bash + + $ mkdir -p ~/.scala_objects + $ scalac -d ~/.scala_objects -cp /path/to/stainless/frontends/library/target/scala-2.13/stainless-library_2.13-X.Y.Z-A-BCDEFGHI.jar MyFile1.scala MyFile2.scala # and so on + $ scala -cp ~/.scala_objects:/path/to/stainless/frontends/library/target/scala-2.13/stainless-library_2.13-X.Y.Z-A-BCDEFGHI.jar MyMainClass + +where ``X.Y.Z`` is the Stainless version and ``A-BCDEFGHI`` is some hash (which can be autocompleted by the terminal). + +.. _smt-solvers: + +External Solver Binaries +------------------------ + +If no external SMT solvers (such as Z3 or cvc5) are found, Stainless will use the bundled Scala-based `Princess solver `_ + +To improve performance, we highly recommend that you install the following two additional external SMT solvers as binaries for your platform: + +* cvc5 1.0.8, https://cvc5.github.io/ +* Z3 4.12.2, https://github.com/Z3Prover/z3 + +You can enable these solvers using ``--solvers=smt-z3`` and ``--solvers=smt-cvc5`` flags. + +Solver binaries that you install should match your operating system and your architecture. We recommend that you install these solvers as a binary and have their binaries available in the ``$PATH`` (as ``z3`` or ``cvc5``). + +Note that somewhat lower version numbers of solvers should work as well and might even have different sets of soundness-related issues. + +You can use multiple solvers in portfolio mode, as with the options ``--timeout=15 --solvers=smt-z3,smt-cvc5``, where verification succeeds if at least one of the solvers proves (within the given number of seconds) each the verification conditions. We suggest to order the solvers starting from the one most likely to succeed quickly. + +For final verification runs of highly critical software, we recommend that (instead of the portfolio mode) you obtain several solvers and their versions, then try a single solver at a time and ensure that each verification run succeeds (thus applying N-version programming to SMT solver implementations). + +Install Z3 4.12.2 +***************** + +1. Download Z3 4.12.2 from https://github.com/Z3Prover/z3/releases/tag/z3-4.12.2 +2. Unzip the downloaded archive +3. Copy the ``z3`` binary found in the ``bin/`` directory of the inflated archive to a directory in your ``$PATH``, eg., ``/usr/local/bin``. +4. Make sure ``z3`` can be found, by opening a new terminal window and typing: + +.. code-block:: bash + + $ z3 --version + +5. The output should read: + +.. code-block:: text + + Z3 version 4.12.2 - 64 bit` + + +Install cvc5 1.0.8 +****************** + +1. Download cvc5 1.0.8 from https://github.com/cvc5/cvc5/releases/tag/cvc5-1.0.8 for your platform. + +2. Copy or link the downloaded binary under name ``cvc5`` to a directory in your ``$PATH``, eg., ``/usr/local/bin``. + +4. Make sure ``cvc5`` can be found, by opening a new terminal window and typing: + +.. code-block:: bash + + $ cvc5 --version | head + +5. The output should begin with: + +.. code-block:: text + + This is cvc5 version 1.0.8 + + +Build from Source on Linux & macOS +---------------------------------- + +To build Stainless, we use ``sbt``. In a typical configuration, ``sbt universal:stage`` in the root of the source tree should work, yet, +in an attempt to be more reproducible and independent from SBT cache and path, the instructions below assume that the directory called ``stainless`` does not exist, they instruct ``sbt`` to use a relative path for its bootstrap, and do not require adding ``sbt`` to your path. + +**Install SBT** + +Follow the instructions at http://www.scala-sbt.org/ to install ``sbt`` 1.7.3 (or somewhat later version). + +**Check out sources** + +Get the sources of Stainless by cloning the official Stainless repository: + +.. code-block:: bash + + $ git clone https://github.com/epfl-lara/stainless.git + Cloning into 'stainless'... + +**Run SBT** + +The following instructions will invoke SBT while using a stainless sub-directory to download files. + +.. code-block:: bash + + $ cd stainless + $ sbt universal:stage + +**Where to find generated files** + +The compilation will automatically generate the bash script ``stainless-dotty`` (and the Scala2 one ``stainless-scalac``). + +You may want to introduce a soft-link from to a file called ``stainless``: + +.. code-block:: bash + + $ ln -s frontends/dotty/target/universal/stage/bin/stainless-dotty stainless + +and, for the Scala2 version of the front end, + + $ ln -s frontends/scalac/target/universal/stage/bin/stainless-scalac stainless-scalac-old + +Analogous scripts work for various platforms and allow additional control over the execution, such as passing JVM arguments or system properties: + +.. code-block:: bash + + $ stainless -Dscalaz3.debug.load=true -J-Xmx6G --help + +Note that Stainless is organized as a structure of several projects. The main project lives in ``core`` while the two available frontends can be found in ``frontends/dotty`` (and ``frontends/scalac``). From a user point of view, this should most of the time be transparent and the build command should take care of everything. + +Build from Source on Windows 10 +------------------------------- + +Before following the infrequently updated instructions in this section, considering running Ubuntu on Windows 10 (through e.g. WSL) and following the instructions for Linux. + +Get the sources of Stainless by cloning the official Stainless repository. You will need a Git shell for windows, e.g. `Git for Windows `_. +On Windows, please do not use ``sbt universal:stage`` as this generates a Windows batch file which is unusable, because it contains commands that are too long for Windows. +Instead, please use ``sbt stainless-scalac-standalone/assembly`` as follows: + +.. code-block:: bash + + $ git clone https://github.com/epfl-lara/stainless.git + Cloning into 'stainless'... + // ... + $ cd stainless + $ sbt stainless-scalac-standalone/assembly + // takes about 1 minutes + +Running Stainless can then be done with the command: ``java -jar frontends\stainless-dotty-standalone\target\scala-3.3.3\stainless-dotty-standalone-{VERSION}.jar``, where ``VERSION`` denotes Stainless version. + +Running Tests +------------- + +Stainless comes with a test suite. Use the following commands to +invoke different test suites: + +.. code-block:: bash + + $ sbt test + $ sbt it:test + +It's also possible to run tests in isolation, for example, the following command runs ``Extraction`` tests on all files in ``termination/looping``: + +.. code-block:: bash + + $ sbt 'it:testOnly *ExtractionSuite* -- -z "in termination/looping"' + +Building Stainless Documentation +-------------------------------- + +Stainless documentation is available at https://epfl-lara.github.io/stainless/ . +To build the documentation locally, you will need Sphinx ( +http://sphinx-doc.org/ ), a restructured text toolkit that +was originally developed to support Python documentation. + +* On Ubuntu 18, you can use ``sudo apt install sphinx-common`` + +The documentation resides in the ``core/src/sphinx/`` directory and can be built using the provided ``Makefile``. To do this, in a Linux shell, +type ``make html``, and open in your web browser the generated top-level local HTML file, by default stored in +``core/src/sphinx/_build/html/index.html``. Also, you can open the ``*.rst`` documentation files in a text editor, as they are human-readable in their source form as well. + +Note for project maintainers: to build documentation on GitHub Pages, use ``make gh-pages`` in the same Makefile, or adapt it to you needs. + +Using IDEs with --no-colors option. Emacs illustration +------------------------------------------------------ + +Using command line option ``--no-colors`` asks stainless to produce clear 7-bit ASCII output with error messages in a standardized format: + +.. code-block:: bash + + FileName.scala:LineNo:ColNo: text of the error message + +This helps IDEs to pick up line numbers and show error location in the source file. + +In ``emacs`` editor, you can invoke ``ansi-term`` and ``compilation-shell-minor-mode``. Then, run + +.. code-block:: bash + + stainless --no-colors + +You may also consider using the ``--watch`` option. + +You should now be able to click on a message for verification condition to jump to the appropriate position in the appropriate file, as well as to use emacs commands ``previous-error`` and ``next-error`` to navigate through errors and other verification-condition outcomes. + +Here is a very simple illustration that introduces an interactive ``comp-ansi-term`` command that creates new window with ansi-term and minor compilation mode: + +.. code-block:: lisp + + (setq comp-terminal-current-number 1) + (defun create-numbered-comp-terminal () + (ansi-term "/bin/bash") + (rename-buffer (concat "q" (number-to-string comp-terminal-current-number)) 1) + (setq comp-terminal-current-number (+ comp-terminal-current-number 1)) + (compilation-shell-minor-mode) + ) + (defun comp-ansi-term (arg) + "Run ansi-term with bash and compilation-shell-minor-mode in buffer named q_N for increasing N" (interactive "P") + (create-numbered-comp-terminal) + (split-window-vertically) + (previous-buffer) + (other-window 1) + ) + +The following globally binds the above command to the F3 key and binds F7 and F8 to commands for navigating reports: + +.. code-block:: lisp + + (global-set-key [f3] 'comp-ansi-term) + (global-set-key [f7] 'previous-error) + (global-set-key [f8] 'next-error) + +For more information, please consult the documentation for ``emacs``. diff --git a/_sources/internals.rst.txt b/_sources/internals.rst.txt new file mode 100644 index 0000000000..106113f3f0 --- /dev/null +++ b/_sources/internals.rst.txt @@ -0,0 +1,12 @@ +.. _internals: + +Stainless' Internals +==================== + +The main component of Stainless and the dataflow in its pipeline: + +.. image:: static/images/pipeline.svg + :width: 90% + + + diff --git a/_sources/intro.rst.txt b/_sources/intro.rst.txt new file mode 100644 index 0000000000..3203e7f894 --- /dev/null +++ b/_sources/intro.rst.txt @@ -0,0 +1,135 @@ +Introduction +============ + +The Stainless verification framework aims to help developers build +verified Scala software. It encourages using a small set of core +Scala features and provides unique verification functionality. +In particular, Stainless can + +* verify statically that your program conforms to a given + specification and that it cannot crash at run-time + +* provide useful counterexamples when an implementation does + not satisfy its specification + +* verify that your program will terminate on all inputs + + +Stainless and Scala +------------------- + +Stainless attempts to strike a delicate balance between the +convenience of use on the one hand and the simplicity of +reasoning on the other hand. Stainless supports verification +of Scala programs by applying a succession of semantic-preserving +transformations to the :doc:`Pure Scala ` fragment until +it fits into the fragment supported by +`Inox `_. +The Pure Scala fragment is at the core of +the functional programming paradigm and should sound familiar to +users of Scala, Haskell, ML, and fragments +present in interactive theorem provers such as Isabelle and Coq. Thus, +if you do not already know Scala, learning the Stainless subset should +be easier as it is a smaller language. Moreover, thanks to the use of +a Scala front end, Stainless supports implicits and ``for`` +comprehensions (which also serve as a syntax for monads in Scala). +Stainless also comes with a simple library of useful data types, which +are designed to work well with automated reasoning and Stainless's +language fragment. + +In addition to this pure fragment, Stainless supports certain +:doc:`imperative ` features. +Features thus introduced are handled by +a translation into Pure Scala concepts. They are often more +than just syntactic sugar, because some of them require +significant modification of the original program, such as +introducing additional parameters to a set of functions. As +an intended aspect of its current design, Stainless's language +currently does not provide a default encoding of +e.g. concurrency with a shared mutable heap, though it might +support more manageable forms of concurrency in the future. + +If you would like to use Stainless now, check the +:doc:`installation` section and follow :doc:`gettingstarted` and :doc:`Tutorial `. +To learn more about the functionality that Stainless provides, read on below. + +Software Verification +--------------------- + +The Stainless program verifier collects a list of top-level functions, +and verifies the *validity* of their *contracts*. Essentially, for each function, +it will (try to) prove that the postcondition always holds, assuming a given +precondition does hold. A simple example: + +.. code-block:: scala + + def factorial(n: BigInt): BigInt = { + require(n >= 0) + if(n == 0) { + BigInt(1) + } else { + n * factorial(n - 1) + } + } ensuring(res => res >= 0) + +Stainless generates a ``postcondition`` verification condition for the above +function, corresponding to the predicate parameter to the ``ensuring`` +expression. It attempts to prove it using a combination of an internal +algorithm and external automated theorem proving. Stainless will return one of the +following: + +* The postcondition is ``valid``. In that case, Stainless was able to prove that for **any** + input to the function satisfying the precondition, the postcondition will always hold. +* The postcondition is ``invalid``. It means that Stainless disproved the postcondition and + that there exists at least one input satisfying the precondition such that the + postcondition does not hold. Stainless will always return a concrete counterexample, very + useful when trying to understand why a function is not satisfying its contract. +* The postcondition is ``unknown``. It means Stainless is unable to prove or find a + counterexample. It usually happens after a timeout or an internal error occurring in + the external theorem prover. + +Stainless will also verify for each call site that the precondition of the invoked +function cannot be violated. + +Stainless supports verification of a significant part of the Scala language, described in +:doc:`purescala` and :doc:`imperative`. + +Program Termination +------------------- + +A "verified" function in stainless is guaranteed to never crash, however, it can +still lead to an infinite evaluation. Stainless therefore provides a termination +checker that complements the verification of safety properties. + +For each function in the program, Stainless will try to automatically infer a +decreasing metric associated with this function to prove termination. The +termination checker will then report one of the following: + +* The function ``terminates``. In this case, Stainless was able to prove that for + all inputs (satisfying the function's precondition), evaluation of the function + under those inputs is guaranteed to terminate. +* The function ``loops``. In this case, Stainless was able to construct an input + to the function such that evaluation under that input will be looping. +* The function ``maybe loops``. In the case where recursive functions are passed + around as first-class functions, Stainless will sometimes over-approximate the + potential call sites and report loops that may never occur. +* Termination of the function is ``unknown``. In this case, Stainless was neither + able to prove nor disprove termination of the relevant function. Automated + termination proving is a *hard* problem and such cases are thus to be expected. + +In cases where automated termination checking fails, Stainless provides the user +with the ability to manually specify a measure under which termination should +occur through the ``decreases`` construct. For example, the +`McCarthy 91 function `_ +can be shown terminating as follows: + +.. code-block:: scala + + def M(n: BigInt): BigInt = { + decreases(stainless.math.max(101 - n, 0)) + if (n > 100) n - 10 else M(M(n + 11)) + } ensuring (_ == (if (n > 100) n - 10 else BigInt(91))) + + +It is also possible to add a pre-condition (``require(...)``) *before* ``decreases``. + diff --git a/_sources/laws.rst.txt b/_sources/laws.rst.txt new file mode 100644 index 0000000000..06d5a5f713 --- /dev/null +++ b/_sources/laws.rst.txt @@ -0,0 +1,605 @@ +.. _laws: + +Specifying Algebraic Properties +=============================== + +Introduction +------------ + +Many datatypes that programmers deal with on a day-to-day basis often provide +the same set of operations, for example: + +- They can be tested for equality to some other value +- They can be ordered (partially or totally) +- They can be composed together +- They can be added or multiplied together +- They have an inverse with respect to some operation + +Because those are very common properties, it is often useful to be able to +abstract over them. In fact, each of these properties corresponds to an +algebraic structure, and is governed by the set of laws which allow the +programmer to reason at a higher level of abstraction, and to be able +to rely on the behavior specified by the laws associated with the structure. + +While these properties can be modeled and implemented using Java interfaces, +modern programming languages such as Scala or Haskell provide a better +mechanism for expressing the properties: typeclasses. + +Typeclasses +----------- + +Typeclasses were introduced by Wadler & Blott [WB89]_ as an extension +to the Hindley/Milner type system to implement a certain kind of overloading, +known as *ad-hoc* polymorphism. + +A typeclass is identified by its name, and is associated with a set of +(usually polymorphic) functions signatures, its *methods*. + +It can then be *instantiated* at various types, given that the user is able +to provide a concrete implementation for each method. A user can then apply +these methods to any type for which there is a corresponding instance, which +essentially corresponds to *overloading*. + +Using typeclasses, one can model algebraic properties of datatypes in a fairly natural way. +Here is for example, the definition and implementation of a ``Monoid``, ie. a typeclass +for datatypes which can be mashed together associatively, and which have an +identity element w.r.t. to this operation: + +.. code-block:: scala + + abstract class Monoid[A] { + def empty: A + def append(x: A, y: A): A + + @law + def law_leftIdentity(x: A) = { + append(empty, x) == x + } + + @law + def law_rightIdentity(x: A) = { + append(x, empty) == x + } + + @law + def law_associativity(x: A, y: A, z: A) = { + append(x, append(y, z)) == append(append(x, y), z) + } + } + + implicit val bigIntAdditiveMonoid: Monoid[BigInt] = new Monoid[BigInt] { + override def empty: BigInt = 0 + override def append(x: BigInt, y: BigInt): BigInt = x + y + } + +Here, the abstract class specifies the two abstract operations which are required, +but also the associated laws that the implementation of these operations must +satisfy for the datatype to form a valid monoid. + +Stainless will then ensure that the implementation of ``Monoid`` for the ``BigInt`` type satisfy +those laws. In this case, the above definition of ``bigIntAdditiveMonoid`` will generate the +following verification conditions:: + + ┌───────────────────┐ + ╔═╡ stainless summary ╞══════════════════════════════════════════════════════════════════════╗ + ║ └───────────────────┘ ║ + ║ law_associativity law valid nativez3 ../../test.scala:25:3 0.052 ║ + ║ law_leftIdentity law valid nativez3 ../../test.scala:25:3 0.037 ║ + ║ law_rightIdentity law valid nativez3 ../../test.scala:25:3 0.029 ║ + ╟--------------------------------------------------------------------------------------------╢ + ║ total: 9 valid: 9 (0 from cache) invalid: 0 unknown: 0 time: 0.729 ║ + ╚════════════════════════════════════════════════════════════════════════════════════════════╝ + +Armed with the knowledge that our ``Monoid`` will always be lawful, one can now fearlessly write +the ``foldMap`` function, and get the expected result: + +.. code-block:: scala + + def foldMap[A, M](xs: List[A])(f: A => M)(implicit M: Monoid[M]): M = xs match { + case Nil() => M.empty + case Cons(y, ys) => M.append(f(y), foldMap(ys)(f)) + } + + def sumBigInt(xs: List[BigInt]): BigInt = { + foldMap(xs)(x => x) + } + +Sometimes, Stainless will not be able to automatically prove that an instance is lawful, +for example when the property of interest involves a recursive definition over an inductive +data type, as in the following code: + +.. code-block:: scala + + sealed abstract class Nat { + def +(m: Nat): Nat = this match { + case Zero => m + case Succ(n) => Succ(n + m) + } + + def *(m: Nat): Nat = this match { + case Zero => Zero + case Succ(n) => n * m + m + } + } + + final case object Zero extends Nat + final case class Succ(prev: Nat) extends Nat + + final val One = Succ(Zero) + + implicit def natAdditiveMonoid: Monoid[Nat] = new Monoid[Nat] { + def empty: nat = Zero + def append(x: Nat, y: Nat): Nat = x + y + } + +To help Stainless out, one needs to prove that ``Zero`` indeed the right identity of ``+``, +as well as the associativity of the latter. + +.. code-block:: scala + + @induct + def lemma_rightIdentity_plus(x: Nat): Boolean = { + x + Zero == x + }.holds + + @induct + def lemma_associativity_plus(x: Nat, y: Nat, z: Nat): Boolean = { + x + (y + z) == (x + y) + z + }.holds + +One can then override the law of interest, and instantiate the lemma over the relevant parameters: + +.. code-block:: scala + + implicit def natAdditiveMonoid: Monoid[Nat] = new Monoid[Nat] { + def empty: nat = Zero + def append(x: Nat, y: Nat): Nat = x + y + + override def law_rightIdentity(x: Nat) = { + super.law_rightIdentity(x) because lemma_rightIdentity_plus(x) + } + + override def law_associativity(x: Nat, y: Nat, z: Nat) = { + super.law_associativity(x, y, z) because lemma_associativity_plus(x, y, z) + } + } + +With these modifications, the example goes through without a hitch. + +Typeclass inheritance +--------------------- + +Some algebraic structures can be defined as some other algebraic structure plus some additional +operations and/or laws, eg. a monoid can be seen as a semigroup with identity. + +In Scala, typeclasses allow to represent such relationship between algebraic structures by mean of inheritance. + +Let's take for example the ``Ord`` typeclass, which describes totally ordered datatypes. + +This class is defined as follows: + +.. code-block:: scala + + trait Eq[A] { + def equals(x: A, y: A): Boolean + } + + trait Ord[A] extends Eq[A] { + def lessThanEq(x: A, y: A): Boolean + + def lessThan(x: A, y: A): Boolean = lessThanEq(x, y) && !equals(x, y) + } + +This can also be read as: if ``A`` is an instance of ``Ord``, then it also is a instance of ``Eq``. + +Associated methods +------------------ + +On top of abstract operations, a typeclass can also introduces concrete methods which +do not need to (but can) be re-defined by the programmer at instance declaration time, +just like the ``lessThan`` method of the ``Ord`` class above. + +While such methods could be defined as a standalone function with an ``Ord`` constraint, +having it be a part of the class allows users to override it with e.g. a more efficient +implementation specific to the datatype they are instantiating the class for, as shown below: + +.. code-block:: scala + + case object BigIntOrd extends Ord[BigInt] { + def equal(x: BigInt, y: BigInt) = x == y + def lessThanEq(x: BigInt, y: BigInt) = x <= y + + override def lessThan(x: BigInt, y: BigInt) x < y + } + +Coherence +--------- + +Let's now look at an issue that might arise when working with typeclasses in Scala. + +.. code-block:: scala + + abstract class Monoid[A] { + def empty: A + def combine(x: A, y: A): A + } + + implicit val bigIntAddMonoid: Monoid[BigInt] = new Monoid[BigInt] { + override def empty: BigInt = 0 + override def combine(x: BigInt, y: BigInt): BigInt = x + y + } + + implicit val bigIntProdMonoid: Monoid[BigInt] = new Monoid[BigInt] { + override def empty: BigInt = 1 + override def combine(x: BigInt, y: BigInt): BigInt = x * y + } + + def fold[A](list: List[A])(implicit M: Monoid[A]): A = { + list.foldRight(M.empty)(M.combine) + } + + val list: List[BigInt] = List(2, 3) + val res: BigInt = fold(list) // ? + +Here, the Scala compiler bails out with an *ambiguous implicits* error but for good reasons this time. +Indeed, depending on which instance of ``Monoid[BigInt]`` it picks, ``res`` can either be equal to 5 or 6. +This issue arise because the two instances above are *overlapping*, which has the effect of making the +type system *incoherent*. For a type system to be coherent, "every valid typing derivation for a program +must lead to a resulting program that has the same dynamic semantics", which is clearly not the case here. +While in this specific example, the compiler will rightfully reject the program, this might always be +possible as one could import a different instance in scope in two different modules, and then a third module +might assume that these modules actually make use of the same instance, silently breaking the program. +Imagine trying to merge two ``Sets`` that have been created with two different ``Ord`` instances in scope. + +Haskell partially solves this problem by enforcing that instances defined in the same module do not overlap, +that is to say that the compiler would reject the program above. We deem Haskell's approach only partial as +it allows the programmer to define two or more overlapping instances, provided that they are not defined in the same module. +A program is then only rejected when the programmer makes imports such overlapping instances in scope and +attempts to make use of them. This decision stems from the will to allow linking together two different +libraries which both define a class instance for the same type. + +Because Stainless operates under a closed-world assumption, we could go further and disallow overlapping +instances altogether, but this has not been implemented yet. + +One might still want to provide both an additive and multiplicative ``Monoid`` instance for integers. +To this end, one can wrap values of type ``BigInt`` with two different wrapper classes for which +we will define the respective instances: + +.. code-block:: scala + + case class Sum(value: BigInt) extends AnyVal + case class Product(value: BigInt) extends AnyVal + + implicit val bigIntSumMonoid: Monoid[Sum] = new Monoid[Sum] { + override def empty: Sum = Sum(0) + override def combine(x: Int, y: Int): Sum = Sum(x.value + y.value) + } + + implicit val bigIntProductMonoid: Monoid[Product] = new Monoid[Product] { + override def empty: Product = Product(1) + override def combine(x: Int, y: Int): Product = Product(x.value * y.value) + } + +.. code-block:: scala + + def foldMap[A, B](list: List[A])(f: A => B)(implicit M: Monoid[B]): B = { + list.map(f).foldRight(M.empty)(M.combine) + } + +It then becomes possible to unambiguously pick which instance to use depending on the semantics one wants: + +.. code-block:: scala + + val list: List[BigInt] = List(2, 3) + + val sum: BigInt = foldMap(list)(Sum(_)).value // 5 + val product: BigInt = foldMap(list)(Product(_)).value // 6 + +Under the hood +-------------- + +In this section we describe how laws are encoded within Stainless. + +Let's take as an example the Semigroup+Monoid hierarchy, slightly +amended to exercise at once all the features described above. + +.. code-block:: scala + + abstract class Semigroup[A] { + def append(x: A, y: A): A + + @law + def law_associativity(x: A, y: A, z: A): Boolean = { + append(x, append(y, z)) == append(append(x, y), z) + } + } + + abstract class Monoid[A] extends Semigroup[A] { + def empty: A + + @law + def law_leftIdentity(x: A): Boolean = { + append(empty, x) == x + } + + @law + def law_rightIdentity(x: A): Boolean = { + append(x, empty) == x + } + + override def law_associativity(x: A, y: A, z: A): Boolean = { + // We refine the Semigroup associativity law with a dummy + // predicate `refineLaw` to demonstrate this feature. + super.law_associativity(x, y, z) && refineLaw(x, y, z) + } + } + + def refineLaw[A](x: A, y: A, z: A): Boolean = true + +Together with a simple implementation for ``BigInt``: + +.. code-block:: scala + + def bigIntAdditiveMonoid: Monoid[BigInt] = new Monoid[BigInt] { + def empty: BigInt = 0 + def append(x: BigInt, y: BigInt): BigInt = x + y + + override def law_rightIdentity(x: BigInt): Boolean = { + // no manual proof is needed in this case, but we include + // a dummy one for the sake of this example. + someProof + } + } + + def someProof: Boolean = true + +Here is the internal Stainless AST pretty much right after extraction +from the Scala compiler. + +Each symbol (class, method, variable) is annotated with its internal identifier +(ie. the number after the ``$`` sign at the end of its name) which will prove useful +for reading the code after the next phase, as it introduces new symbols with the same +name but different identifiers. + +.. code-block:: scala + + abstract class Semigroup$0[A$85] { + + @abstract + def append$3(x$108: A$85, y$24: A$85): A$85 = [A$85] + + @law + def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = { + this.append$3(x$109, this.append$3(y$25, z$11)) == + this.append$3(this.append$3(x$109, y$25), z$11) + } + } + + abstract class Monoid$0[A$86] extends Semigroup$0[A$86] { + + @abstract + def empty$6: A$86 = [A$86] + + @law + def law_leftIdentity$0(x$110: A$86): Boolean = + this.append$3(this.empty$6, x$110) == x$110 + + @law + def law_rightIdentity$0(x$111: A$86): Boolean = + this.append$3(x$111, this.empty$6) == x$111 + + def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean = + super.law_associativity$0(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12) + } + + def refineLaw$0[A$87](x$113: A$87, y$27: A$87, z$13: A$87): Boolean = true + + case class $anon$0() extends Monoid$0[BigInt] { + def empty$7: BigInt = 0 + def append$4(x$112: BigInt, y$26: BigInt): BigInt = x$112 + y$26 + + def law_rightIdentity$1(x$113: BigInt): Boolean = someProof$0 + } + + def bigIntAdditiveMonoid$0: Monoid$0[BigInt] = $anon$0() + + def someProof$0: Boolean = true + +The code above maps in straightforward way to the original code. + +Let's now take a look at the output of the ``Laws`` phase. This is +the phase which desugars the law definitions and their overrides +into methods with explicit postconditions. + +.. code-block:: scala + + abstract class Semigroup$0[A$85] { + + @abstract + def append$3(x$108: A$85, y$24: A$85): A$85 = [A$85] + + @final + @inlineOnce + @derived(law_associativity$0) + def law_associativity$2(x$120: A$85, y$30: A$85, z$14: A$85): Boolean = { + this.append$3(x$120, this.append$3(y$30, z$14)) == + this.append$3(this.append$3(x$120, y$30), z$14) + } + + @abstract + def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = { + [Boolean] + } ensuring { + (res$82: Boolean) => res$82 && this.law_associativity$2(x$109, y$25, z$11) + } + } + + abstract class Monoid$0[A$86] extends Semigroup$0[A$86] { + + @abstract + def empty$6: A$86 = [A$86] + + @final + @inlineOnce + @derived(law_leftIdentity$0) + def law_leftIdentity$1(x$116: A$86): Boolean = + this.append$3(this.empty$6, x$116) == x$116 + + @abstract + def law_leftIdentity$0(x$110: A$86): Boolean = { + [Boolean] + } ensuring { + (res$77: Boolean) => res$77 && this.law_leftIdentity$1(x$110) + } + + @final + @inlineOnce + @derived(law_rightIdentity$0) + def law_rightIdentity$2(x$117: A$86): Boolean = + this.append$3(x$117, this.empty$6) == x$117 + + @abstract + def law_rightIdentity$0(x$111: A$86): Boolean = { + [Boolean] + } ensuring { + (res$80: Boolean) => res$80 && this.law_rightIdentity$2(x$111) + } + + @law + def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean = { + this.law_associativity$2(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12) + } ensuring { + (res$84: Boolean) => res$84 && this.law_associativity$2(x$112, y$26, z$12) + } + } + + @derived(bigIntAdditiveMonoid$0) + case class $anon$0() extends Monoid$0[BigInt] { + + def empty$7: BigInt = 0 + def append$4(x$114: BigInt, y$27: BigInt): BigInt = x$114 + y$27 + + @law + @derived(law_leftIdentity$0) + def law_leftIdentity$2(x$119: BigInt): Boolean = { + true + } ensuring { + (res$84: Boolean) => this.law_leftIdentity$1(x$119) + } + + @law + def law_rightIdentity$1(x$115: BigInt): Boolean = { + someProof$0 + } ensuring { + (res$79: Boolean) => res$79 && this.law_rightIdentity$2(x$115) + } + + @law + @derived(law_associativity$0) + def law_associativity$2(x$120: BigInt, y$29: BigInt, z$13: BigInt): Boolean = { + true + } ensuring { + (res$85: Boolean) => this.law_associativity$1(x$120, y$29, z$13) + } + } + + def bigIntAdditiveMonoid$0: Monoid$0[BigInt] = $anon$0() + + def someProof$0: Boolean = true + +There are a few things going on here: + +1. First of all, each method marked ``@law`` introduces a new method which + holds the original body of the law. The law's body is then rewritten to + be empty, and is provided with a postcondition which refers to the newly + introduced method. This desugaring step basically turns the laws + into abstract methods which must be overridden at some point with + methods whose body can be proven to be true, while also satisfying the law + itself. + + The helper method will be used in subsequent steps to refer to the + law's body, without having to inline it or call the law itself, + which is disallowed since it is conceptually an abstract method, as + evidenced by its newly added ``@abstract`` flag. + + .. code-block:: scala + + // In class `Semigroup`... + + // This is the helper method. + @final + @inlineOnce + @derived(law_associativity$0) + def law_associativity$2(x$120: A$85, y$30: A$85, z$14: A$85): Boolean = { + this.append$3(x$120, this.append$3(y$30, z$14)) == + this.append$3(this.append$3(x$120, y$30), z$14) + } + + // This is the original law definition, which now became an abstract method. + @abstract + def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = { + [Boolean] + } ensuring { + (res$82: Boolean) => res$82 && this.law_associativity$2(x$109, y$25, z$11) + } + +2. Laws which are overridden into abstract subclasses, are provided with a + postcondition that ensures that their body can be proven true, + while still satisfying the original law via a call to the helper + method introduced in the previous step. This step ensures that laws + cannot be fully redefined, and thus potentially weakened, in subclasses. + + .. code-block:: scala + + // In class `Monoid`... + + @law + def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean = { + this.law_associativity$2(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12) + } ensuring { + (res$84: Boolean) => res$84 && this.law_associativity$2(x$112, y$26, z$12) + } + +3. In the typeclass implementations (eg. class ``$anon$0``), methods which override laws + are provided with a postcondition which again ensures that their body holds, + while still satisfying the law they override, again via a call to the helper + method introduced in step 1. + + .. code-block:: scala + + // In class `$anon$0`... + + @law + def law_rightIdentity$1(x$115: BigInt): Boolean = { + someProof$0 + } ensuring { + (res$79: Boolean) => res$79 && this.law_rightIdentity$2(x$115) + } + +4. If a law is not overridden in a typeclass implementation, a stub override is + automatically defined by Stainless, to ensure that a verification condition + will be generated. Those stubs just have ``true`` as a body, and a postcondition + which calls to the appropriate law helper introduced in step 1. + This expresses the fact that the law holds on its own, without any additional proof steps. + + .. code-block:: scala + + // In class `$anon$0` + + @law + @derived(law_leftIdentity$0) + def law_leftIdentity$2(x$119: BigInt): Boolean = { + true + } ensuring { + (res$84: Boolean) => this.law_leftIdentity$1(x$119) + } + +.. note:: + + As can be seen above, calling the super method when refining (such as in ``law_associativity``) + or proving (such as in ``law_rightIdentity``) a law is superfluous, since it is done anyway + during the encoding as to ensure that laws cannot be weakened. Doing so can nonetheless help + readability, since it makes the code match more closely to the semantics of Scala. + +.. [WB89] P. Wadler and S. Blott. 1989. How to make ad-hoc polymorphism less ad hoc. + diff --git a/_sources/library.rst.txt b/_sources/library.rst.txt new file mode 100644 index 0000000000..a78ce33add --- /dev/null +++ b/_sources/library.rst.txt @@ -0,0 +1,388 @@ +.. _library: + +Stainless Library +================= + +Stainless defines its own library with some core data types and +operations on them, which work with the fragment supported +by Stainless, available in ``frontends/library/stainless``, which +we encourage the reader to consult as it is always up to date. + +One of the reasons for a separate library is to +ensure that these operations can be correctly mapped to +mathematical functions and relations inside of SMT solvers, +largely defined by the SMT-LIB standard (see +http://www.smt-lib.org/). Thus for some data types, such as +``BigInt``, Stainless provides a dedicated mapping to support reasoning. +(If you are a fan +of growing the language only through libraries, keep in mind that +growing operations together with the ability to reason about them +is what the development of mathematical theories is all about, and +is a process slower than putting together +libraries of unverified code--efficient automation of reasoning about a +single decidable theory generally results in multiple research papers.) +For other operations (e.g., `List[T]`), the library +is much like Stainless user-defined code, but specifies some +useful preconditions and postconditions of the operations, thus +providing reasoning abilities using mechanisms entirely available +to the user. + +.. note:: + + The ScalaDoc for the library is `available online <_static/stainless-library/index.html>`_. + + For the most up-to-date version of the source code of library, + please consult the ``library/`` directory in your Stainless distribution. + +To use Stainless' libraries, you need to use the appropriate +`import` directive at the top of Stainless' compilation units. +Here is a quick summary of what to import. + + ++--------------------------------+-----------------------------------------------------------------+ +| Package to import | What it gives access to | ++================================+=================================================================+ +| `stainless.annotation._` | Stainless annotations, e.g. @induct | ++--------------------------------+-----------------------------------------------------------------+ +| `stainless.lang._` | `Map`, `Set`, `PartialFunction`, `holds`, `passes`, `invariant` | ++--------------------------------+-----------------------------------------------------------------+ +| `stainless.collection._` | List[T] and subclasses, Option[T] and subclasses | ++--------------------------------+-----------------------------------------------------------------+ + +To learn more, we encourage you to look in the `library/` subdirectory of Stainless distribution. + +Annotations +----------- + +Stainless provides some special annotations in the package ``stainless.annotation``, +which instruct Stainless to handle some functions or objects in a specialized way. + ++-------------------+----------------------------------------------------------------+ +| Annotation | Meaning | ++===================+================================================================+ +| ``@library`` | Treat this object/function as library, don't try | +| | to verify its specification. Can be overridden by | +| | including a function name in the ``--functions`` | +| | command line option. | ++-------------------+----------------------------------------------------------------+ +| ``@induct`` | Use the inductive tactic when generating | +| | verification conditions. | ++-------------------+----------------------------------------------------------------+ +| ``@invariant`` | Treat the annotated method as an invariant of the enclosing | +| | class. Can be used instead of ``require`` within a value class | +| | body. For soundness, invariants can only refer to fields of | +| | their class, and thus cannot call methods on ``this``. | ++-------------------+----------------------------------------------------------------+ +| ``@ghost`` | Drop the annotated field or method during compilation. | +| | See the :doc:`corresponding section ` for more | +| | information. | ++-------------------+----------------------------------------------------------------+ +| ``@extern`` | Only extract the contracts of a function, replacing | +| | its body by a ``choose`` expression. | ++-------------------+----------------------------------------------------------------+ +| ``@opaque`` | Used to hide a function ``f``'s body when doing verification | +| | of functions (``f`` itself, or others) invoking ``f``. Does | +| | not hide pre and postconditions. | ++-------------------+----------------------------------------------------------------+ +| ``@dropVCs`` | Do not generate verification conditions for this function. | ++-------------------+----------------------------------------------------------------+ +| ``@pure`` | Specify that this function is pure, which will then | +| | be checked. If the function is also annotated with | +| | ``@extern``, it will not be checked, but assumed pure. | ++-------------------+----------------------------------------------------------------+ +| ``@ignore`` | Ignore this definition when extracting Stainless trees. | +| | This annotation is useful to define functions | +| | that are not in Stainless's language but will be | +| | hard-coded into specialized trees, or to include | +| | code written in full Scala which is not verifiable | +| | by Stainless. Can also be used on class fields whose type | +| | cannot be understood by Stainless, eg. because it comes from | +| | an external library, the JDK, or some other code which | +| | does not understand. | +| | See the corresponding :doc:`documentation page `. | ++-------------------+----------------------------------------------------------------+ +| ``@inline`` | Inline this function. Stainless will refuse to inline | +| | (mutually) recursive functions. | ++-------------------+----------------------------------------------------------------+ +| ``@inlineOnce`` | Inline this function but only once, which is allowed | +| | even on (mutually) recursive functions. | +| | Note: A recursive function will not be inlined within itself. | ++-------------------+----------------------------------------------------------------+ +| ``@partialEval`` | Partially evaluate calls to this function. | +| | Note: ``stainless.lang.partialEval`` can also be used to | +| | partially evaluate an expression. | ++-------------------+----------------------------------------------------------------+ + +Stainless also has some special keywords defined in ``stainless.lang`` that can be used around +function calls. `Here `_ is an example for ``unfold``. + ++-------------------+----------------------------------------------------------------+ +| Annotation | Meaning | ++===================+================================================================+ +| ``inline`` | Call-site inlining | ++-------------------+----------------------------------------------------------------+ +| ``unfold`` | Inject an equality assumption between a function call and its | +| | unfolded version. Can be useful to locally override an | +| | ``@opaque`` annotation. | ++-------------------+----------------------------------------------------------------+ + +List[T] +------- + +As there is no special support for Lists in SMT solvers, Stainless Lists are encoded +as an ordinary algebraic data type: + +.. code-block:: scala + + sealed abstract class List[T] + case class Cons[T](h: T, t: List[T]) extends List[T] + case class Nil[T]() extends List[T] + + +List API +******** + +Stainless Lists support a rich and strongly specified API. + ++---------------------------------------------------+---------------------------------------------------+ +| Method signature for ``List[T]`` | Short description | ++===================================================+===================================================+ +| ``size: BigInt`` | Number of elements in this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``content: Set[T]`` | The set of elements in this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``contains(v: T): Boolean`` | Returns true if this List contains ``v``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``++(that: List[T]): List[T]`` | Append this List with ``that``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``head: T`` | Returns the head of this List. Can only be called | +| | on a nonempty List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``tail: List[T]`` | Returns the tail of this List. Can only be called | +| | on a nonempty List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``apply(index: BigInt): T`` | Return the element in index ``index`` in this | +| | List (0-indexed). | ++---------------------------------------------------+---------------------------------------------------+ +| ``::(t:T): List[T]`` | Prepend an element to this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``:+(t:T): List[T]`` | Append an element to this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``reverse: List[T]`` | The reverse of this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``take(i: BigInt): List[T]`` | Take the first ``i`` elements of this List, or | +| | the whole List if it has less than ``i`` elements.| ++---------------------------------------------------+---------------------------------------------------+ +| ``drop(i: BigInt): List[T]`` | This List without the first ``i`` elements, | +| | or the Nil() if this List has less than ``i`` | +| | elements. | ++---------------------------------------------------+---------------------------------------------------+ +| ``slice(from: BigInt, to: BigInt): List[T]`` | Take a sublist of this List, from index ``from`` | +| | to index ``to``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``replace(from: T, to: T): List[T]`` | Replace all occurrences of ``from`` in this List | +| | with ``to``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``chunks(s: BigInt): List[List[T]]`` | | ++---------------------------------------------------+---------------------------------------------------+ +| ``zip[B](that: List[B]): List[(T, B)]`` | Zip this list with ``that``. In case the Lists | +| | do not have equal size, take a prefix of the | +| | longer. | ++---------------------------------------------------+---------------------------------------------------+ +| ``-(e: T): List[T]`` | Remove all occurrences of ``e`` from this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``--(that: List[T]): List[T]`` | Remove all occurrences of any element in ``that`` | +| | from this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``&(that: List[T]): List[T]`` | A list of all elements that occur both in | +| | ``that`` and this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``pad(s: BigInt, e: T): List[T]`` | Add ``s`` instances of ``e`` at the end of this | +| | List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``find(e: T): Option[BigInt]`` | Look for the element ``e`` in this List, and | +| | optionally return its index if it is found. | ++---------------------------------------------------+---------------------------------------------------+ +| ``init: List[T]`` | Return this List except for the last element. | +| | Can only be called on nonempty Lists. | ++---------------------------------------------------+---------------------------------------------------+ +| ``last: T`` | Return the last element of this List. | +| | Can only be called on nonempty Lists. | ++---------------------------------------------------+---------------------------------------------------+ +| ``lastOption: Option[T]`` | Optionally return the last element of this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``headOption: Option[T]`` | Optionally return the first element of this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``unique: List[T]`` | Return this List without duplicates. | ++---------------------------------------------------+---------------------------------------------------+ +| ``splitAt(e: T): List[List[T]]`` | Split this List to chunks separated by an | +| | occurrence of ``e``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``split(seps: List[T]): List[List[T]]`` | Split this List in chunks separated by an | +| | occurrence of any element in ``seps``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``count(e: T): BigInt`` | Count the occurrences of ``e`` in this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``evenSplit: (List[T], List[T])`` | Split this List in two halves. | ++---------------------------------------------------+---------------------------------------------------+ +| ``insertAt(pos: BigInt, l: List[T]): List[T]`` | Insert an element after index ``pos`` in this | +| | List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``replaceAt(pos: BigInt, l: List[T]): List[T]`` | Replace the ``l.size`` elements after index | +| | ``pos``, or all elements after index ``pos`` | +| | if there are not enough elements, | +| | with the elements in ``l``. | ++---------------------------------------------------+---------------------------------------------------+ +| ``rotate(s: BigInt): List[T]`` | Rotate this list by ``s`` positions. | ++---------------------------------------------------+---------------------------------------------------+ +| ``isEmpty: Boolean`` | Returns whether this List is empty. | ++---------------------------------------------------+---------------------------------------------------+ +| ``map[R](f: T => R): List[R]`` | Builds a new List by applying a predicate ``f`` | +| | to all elements of this list. | ++---------------------------------------------------+---------------------------------------------------+ +| ``foldLeft[R](z: R)(f: (R,T) => R): R`` | Applies the binary operator ``f`` to a start value| +| | ``z`` and all elements of this List, going left | +| | to right. | ++---------------------------------------------------+---------------------------------------------------+ +| ``foldRight[R](f: (T,R) => R)(z: R): R`` | Applies a binary operator ``f`` to all elements of| +| | this list and a start value ``z``, going right to | +| | left. | ++---------------------------------------------------+---------------------------------------------------+ +| ``scanLeft[R](z: R)(f: (R,T) => R): List[R]`` | Produces a List containing cumulative results | +| | of applying the operator ``f`` going left to | +| | right. | ++---------------------------------------------------+---------------------------------------------------+ +| ``scanRight[R](f: (T,R) => R)(z: R): List[R]`` | Produces a List containing cumulative results | +| | of applying the operator ``f`` going right to | +| | left. | ++---------------------------------------------------+---------------------------------------------------+ +| ``flatMap[R](f: T => List[R]): List[R]`` | Builds a new List by applying a function ``f`` | +| | to all elements of this list and using the | +| | elements of the resulting Lists. | ++---------------------------------------------------+---------------------------------------------------+ +| ``filter(p: T => Boolean): List[T]`` | Selects all elements of this List | +| | which satisfy the predicate ``p`` | ++---------------------------------------------------+---------------------------------------------------+ +| ``forall(p: T => Boolean): Boolean`` | Tests whether predicate ``p`` holds | +| | for all elements of this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``exists(p: T => Boolean): Boolean`` | Tests whether predicate ``p`` holds for some of | +| | the elements of this List. | ++---------------------------------------------------+---------------------------------------------------+ +| ``find(p: T => Boolean): Option[T]`` | Finds the first element of this List satisfying | +| | predicate ``p``, if any. | ++---------------------------------------------------+---------------------------------------------------+ +| ``takeWhile(p: T => Boolean): List[T]`` | Takes longest prefix of elements that satisfy | +| | predicate ``p`` | ++---------------------------------------------------+---------------------------------------------------+ + +Additional operations on Lists +****************************** + +The object ``ListOps`` offers this additional operations: + ++--------------------------------------------------------+---------------------------------------------------+ +| Function signature | Short description | ++========================================================+===================================================+ +| ``flatten[T](ls: List[List[T]]): List[T]`` | Converts the List of Lists ``ls`` into a List | +| | formed by the elements of these Lists. | ++--------------------------------------------------------+---------------------------------------------------+ +| ``isSorted(ls: List[BigInt]): Boolean`` | Returns whether this list of mathematical integers| +| | is sorted in ascending order. | ++--------------------------------------------------------+---------------------------------------------------+ +| ``sorted(ls: List[BigInt]): List[BigInt]`` | Sorts this list of mathematical integers | +| | is sorted in ascending order. | ++--------------------------------------------------------+---------------------------------------------------+ +| ``insSort(ls: List[BigInt], v: BigInt): List[BigInt]`` | Sorts this list of mathematical integers | +| | is sorted in ascending order using insertion sort.| ++--------------------------------------------------------+---------------------------------------------------+ + +Theorems on Lists +***************** + +The following theorems on Lists have been proven by Stainless and are included +in the object ``ListSpecs``: + ++---------------------------------------------------------------+--------------------------------------------------------+ +| Theorem signature | Proven Claim | ++===============================================================+========================================================+ +| ``snocIndex[T](l: List[T], t: T, i: BigInt)`` | ``(l :+ t).apply(i) == (if (i < l.size) l(i) else t)`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``reverseIndex[T](l: List[T], i: BigInt)`` | ``l.reverse.apply(i) == l.apply(l.size - 1 - i)`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``appendIndex[T](l1: List[T], l2: List[T], i: BigInt)`` | ``(l1 ++ l2).apply(i) ==`` | +| | ``(if (i < l1.size) l1(i) else l2(i - l1.size))`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``appendAssoc[T](l1: List[T], l2: List[T], l3: List[T])`` | ``((l1 ++ l2) ++ l3) == (l1 ++ (l2 ++ l3))`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``snocIsAppend[T](l: List[T], t: T)`` | ``(l :+ t) == l ++ Cons[T](t, Nil())`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``snocAfterAppend[T](l1: List[T], l2: List[T], t: T)`` | ``(l1 ++ l2) :+ t == (l1 ++ (l2 :+ t))`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``snocReverse[T](l: List[T], t: T)`` | ``(l :+ t).reverse == Cons(t, l.reverse)`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``reverseReverse[T](l: List[T])`` | ``l.reverse.reverse == l`` | ++---------------------------------------------------------------+--------------------------------------------------------+ +| ``scanVsFoldRight[A,B](l: List[A], z: B, f: (A,B) => B)`` | ``l.scanRight(f)(z).head == l.foldRight(f)(z)`` | ++---------------------------------------------------------------+--------------------------------------------------------+ + +Set[T], Map[T] +-------------- + +Stainless uses its own Sets and Maps, which are defined in the ``stainless.lang`` package. +However, these classes are not implemented within Stainless. +Instead, they are parsed into specialized trees. +Methods of these classes are mapped to specialized trees within SMT solvers. +For code generation, we rely on Java Sets and Maps. + +The API of these classes is a subset of the Scala API and can be found +in the :doc:`purescala` section. + +Additionally, the following functions for Sets are provided in the +``stainless.collection`` package: + + ++-----------------------------------------------------------+-------------------------------------------+ +| Function signature | Short description | ++===========================================================+===========================================+ +| ``setToList[A](set: Set[A]): List[A]`` | Transforms the Set ``set`` into a List. | ++-----------------------------------------------------------+-------------------------------------------+ +| ``setForall[A](set: Set[A], p: A => Boolean): Boolean`` | Tests whether predicate ``p`` holds | +| | for all elements of Set ``set``. | ++-----------------------------------------------------------+-------------------------------------------+ +| ``setExists[A](set: Set[A], p: A => Boolean): Boolean`` | Tests whether predicate ``p`` holds | +| | for all elements of Set ``set``. | ++-----------------------------------------------------------+-------------------------------------------+ + + +PartialFunction[A, B] +--------------------- + +To define anonymous functions with preconditions, Stainless has a ``PartialFunction[A, B]`` type +with the corresponding annotation ``A ~> B``. To construct a partial function, you must use +``PartialFunction.apply`` as in the ``unOpt`` function below. The precondition written in the +``require`` becomes the ``pre`` field of the partial function (as in the call to ``f.pre`` in ``map1``). + +.. code-block:: scala + + def map1[A, B](l: List[A], f: A ~> B): List[B] = { + require(l.forall(f.pre)) + l match { + case Cons(x, xs) => Cons[B](f(x), map1(xs, f)) + case Nil() => Nil[B]() + } + } + + def unOpt[T](l: List[Option[T]]): List[T] = { + require(l.forall(_.nonEmpty)) + map1(l, PartialFunction {(x:Option[T]) => require(x.nonEmpty); x.get}) + } + +Partial functions can also be written using pattern matching: + +.. code-block:: scala + + def unOptCase[T](l: List[Option[T]]): List[T] = { + require(l.forall { case Some(_) => true; case _ => false }) + map1(l, PartialFunction[Option[T], T] { case Some(v) => v }) + } diff --git a/_sources/limitations.rst.txt b/_sources/limitations.rst.txt new file mode 100644 index 0000000000..4f332629fd --- /dev/null +++ b/_sources/limitations.rst.txt @@ -0,0 +1,40 @@ +.. _limitations: + +Limitations of Verification +--------------------------- + +A goal of Stainless is to ensure that proven properties hold in +all program executions so that, for example, verified programs +do not crash and all of the preconditions and postconditions +are true in all executions. +For this to be the case, there needs +to be a precise correspondence between runtime execution +semantics and the semantics used in verification, including +the SMT solvers invoked. + +Below we document several cases where we are aware that the +discrepancy exists and provide suggested workarounds. + +Out of Memory Errors +^^^^^^^^^^^^^^^^^^^^ + +By default, Stainless assumes that unbounded data types can +be arbitrarily large and that all well-founded recursive +functions have enough stack space to finish their computation. +Thus a verified program may crash at run-time due to: + + * stack overflow + * heap overflow + +The set of values for recursive algebraic data types is assumed to be infinite. +In any given execution, there will be actual bounds on the +total available memory. The program could thus crash +with an out-of-memory error when trying to allocate another +value of algebraic data type. + +For a safety critical application you may wish to resort to +tail-recursive programs only, and also write preconditions +and postconditions that enforce a bound on the maximum size +of the data structures that your application +manipulates. For this purpose, you can define size functions +that return `BigInt` data types. diff --git a/_sources/neon.rst.txt b/_sources/neon.rst.txt new file mode 100644 index 0000000000..866dbfe454 --- /dev/null +++ b/_sources/neon.rst.txt @@ -0,0 +1,1039 @@ +.. _neon: + +Proving Theorems +================ + +Verifying the contract of a function is really proving a mathematical +theorem. Stainless can be seen as a (mostly) automated theorem prover. It is +automated in the sense that once the property stated, Stainless will proceed with searching +for a proof without any user interaction. In practice, however, many theorems will be fairly +difficult to prove, and it is possible for the user to provide hints to Stainless. + +Hints typically take the form of simpler properties that combine in order to prove +more complicated ones. In the remaining subsections, we provide code patterns and introduce +simple domain-specific language operators that can help in constructing complex Stainless proofs. + +A practical introduction to proofs +---------------------------------- + +When writing logical propositions such as preconditions or +postconditions in Stainless, one is basically writing Boolean +predicates. They can be as simple as testing whether a list is empty +or not, to more complex combinations of properties. Lemmas or +theorems are simply logical tautologies, that is, propositions that +always hold. They can be expressed using Boolean-valued methods that +return ``true`` for all their inputs. + +To make this more concrete, let's take a simple lemma as an +example [#example-dir]_. Here we want to prove that the append operation (``++``) on +lists preserves the content of the two lists being concatenated. This +proposition is relatively straightforward and Stainless is able to verify +that it always holds. + +.. code-block:: scala + + import stainless.collection._ // for List + import stainless.lang._ // for holds + + object Example { + def appendContent[A](l1: List[A], l2: List[A]): Boolean = { + l1.content ++ l2.content == (l1 ++ l2).content + }.holds + } + +Here we wrote ``.holds`` which is a method implicitly available on ``Boolean`` +that ensure the returned value is ``true``. It is equivalent to writing +``ensuring { res => res }``. + +Now let's look at another example that looks trivial but for which Stainless +needs some help with the proof: we want to prove that adding ``Nil`` +at the end of a list has no effect. + +.. code-block:: scala + + import stainless.collection._ // for List + import stainless.lang._ // for holds + + object Example { + def rightUnitAppend[T](l1: List[T]): Boolean = { + l1 ++ Nil() == l1 + }.holds + } + +If you try to verify this last example you'll face a delicate +situation: Stainless runs indeterminately until it is either killed or +times out. But why does this happen? The proposition doesn't seem +more complicated than ``appendContent``. Perhaps even more +surprisingly, Stainless *is* able to verify the following: + +.. code-block:: scala + + def leftUnitAppend[T](l1: List[T]): Boolean = { + Nil() ++ l1 == l1 + }.holds + +How is this possible? The two propositions are completely symmetric! +The problem is that Stainless doesn't know anything about lists, a priori. +It can only reason about lists thanks to their definition in terms of +the case classes ``Cons`` and ``Nil`` and associated methods such as +``++``. In particular, Stainless doesn't know that ``Nil`` represents the +empty list, and hence that appending it to some other list is a no-op. +What then, is the difference between the two examples above? To +answer this question, we need to have a look at the definition of the +``++`` method: + +.. code-block:: scala + + def ++(that: List[T]): List[T] = (this match { + case Nil() => that + case Cons(x, xs) => Cons(x, xs ++ that) + }) ensuring { res => /* ... */ } + +Note that the implementation of ``++`` is recursive in its first +argument ``this`` but *not* in its second argument ``that``. This is +why Stainless was able to verify ``leftUnitAppend`` easily: it is true *by +definition*, i.e. ``Nil() ++ l1`` is actually defined to be ``l1``. +What about the symmetric case? How is ``l1 ++ Nil()`` defined? Well, +it depends on whether ``l1`` is the empty list or not. So in order to +prove ``rightUnitAppend``, we need to proceed with a case analysis. The +resulting proof has a recursive (i.e. inductive) structure reminiscent +of the definition of ``++``: + +.. code-block:: scala + + import stainless.collection._ // for List + import stainless.lang._ // for holds + import stainless.proof._ // for because + + object Example { + def rightUnitAppend[T](l1: List[T]): Boolean = { + (l1 ++ Nil() == l1) because { + l1 match { + case Nil() => true + case Cons(x, xs) => rightUnitAppend(xs) + } + } + }.holds + } + +With this new implementation of the ``rightUnitAppend`` lemma, Stainless is capable +of verifying that it holds. If you look closely at it, you can distinguish three +parts: + +1. the claim we want to prove ``l1 ++ Nil() == l1``; +2. ``because``, which is just some syntactic sugar for conjunction -- remember, + every proposition is a Boolean formula; +3. and a recursion on ``l1`` that serves as a hint for Stainless to perform + induction. + +The recursion is based here on pattern matching, which Stainless will also check for +exhaustiveness. It has essentially the same structure as +the implementation of ``++``: the base case is when ``l1`` is the empty list +and the inductive case is performed on ``Cons`` objects. + + +Techniques for proving non-trivial propositions +----------------------------------------------- + +In the previous section, we saw that "proof hints" can improve the odds +of Stainless successfully verifying a given proposition. In this section, +we will have a closer look at what constitutes such a proof and +discuss a few techniques for writing them. + +As mentioned earlier, propositions are represented by Boolean +expressions in Stainless. But how are proofs represented? They are just +Boolean expressions as well [#props-not-types]_. The difference +between propositions and proofs is not their representation, but how +they are used by Stainless. Intuitively, a proof ``p: Boolean`` for a +proposition ``x: Boolean`` is an expression such that + + 1. Stainless is able to verify ``p``, and + 2. Stainless is able to verify that ``p`` implies ``x``. + +This is what we mean when we say that proofs are "hints". Typically, +a proof ``p`` of a proposition ``x`` is a more complex-looking but +equivalent version of ``x``, i.e. an expression such that ``p == x``. +This might seem a bit counter-intuitive: why should it be easier for +Stainless to verify an equivalent but more complex expression? The answer +is that the more complex version may consist of sub-expressions that +more closely resemble the definitions of functions used in ``x``. We +have already seen an example of this principle in the previous +section: let's have another look at the proof of ``rightUnitAppend``: + +.. code-block:: scala + + def rightUnitAppend[T](l1: List[T]): Boolean = { + val x = l1 ++ Nil() == l1 + val p = l1 match { + case Nil() => true + case Cons(x, xs) => rightUnitAppend(xs) + } + x because p + }.holds + +Here, we have rewritten the example to make the distinction between +the proposition ``x`` and its proof ``p`` more explicit. It's easy to +check that indeed ``x == p``, and hence the overall result of +``rightUnitAppend`` is equivalent to ``x`` (recall that ``because`` is +just an alias of ``&&``, so ``(x because p) == (x && x) == x``). +However, the proof term ``p`` closely resembles the definition of +``++`` and its sub-expressions are easier to verify for Stainless than +``x`` itself. The only non-trivial expression is the recursive call +to ``rightUnitAppend(xs)``, which serves as the inductive hypothesis. +We will discuss induction in more detail in Section +":ref:`induction`". + + +Divide and Conquer +****************** + +Before we delve into the details of particular proof techniques, it is +worth revisiting a guiding principle for writing proofs -- whether it +be in Stainless, by hand, or using some other form of mechanized proof +checker -- namely to *modularize* proofs, i.e. to split the proofs of +complex propositions into manageable *sub-goals*. This can be +achieved in various ways. + + * Use *helper lemmas* -- these are propositions that are lemmas on + their own, i.e. they state and prove simple but self-contained + propositions that can be reused elsewhere. As such, they play a + role akin to helper methods in normal programming, and indeed, are + implemented in the same way, except that they carry a ``.holds`` + suffix. + + * Use *case analysis* to split complex propositions into simpler + sub-cases. This is especially helpful in the presence of + recursion, where it leads to inductive proofs (see Section + ":ref:`induction`"). + + * Use *relational reasoning* to split complex relationships into + conjunctions of elementary ones. This often requires one to make + use of relational properties such as transitivity (e.g. to break a + single equation ``a == b`` into a chain of equations ``a == x1 && + x1 == x2 && ... && xN == b``), symmetry (e.g. to use a previously + proven inequality ``a <= b`` where ``b >= a`` is expected), + anti-symmetry (to unify variables), and so on (see Section + ":ref:`rel-reasoning`"). + + * Separate specification form implementation. It is sometimes easier + to prove the fact that a given function fulfills its specification + as a separate lemma (although the proof techniques are roughly the + same, see Section ":ref:`post-cond`"). + + * Generalize (or specialize) propositions. Sometimes, propositions + are more easily proved in a stronger (or weaker) form and + subsequently instantiated (or combined with other propositions) to + yield a proof of the original proposition. + +While it is good practice to factor common propositions into helper +lemmas, one sometimes wants to verify simple, specific sub-goals in a +proof without going through the trouble of introducing an additional +method. This is especially true while one is exploring the branches +of a case analysis or wants to quickly check whether Stainless is able to +prove a seemingly trivial statement automatically (we will see +examples of such situations in the coming sections). For such cases, +one can use the ``check`` function from ``stainless.proof``. The ``check`` +function behaves as the identity function on Booleans but additionally +assumes its argument in its precondition. As a result, Stainless will +check that ``x`` holds while verifying the call to ``check(x)``. +For example, when verifying the following function: + +.. code-block:: scala + + import stainless.proof.check + + def foo(x: BigInt): Boolean = { + check(x >= 0 || x < 0) && check(x + 0 == 0) + } + +Stainless will check (separately) that ``x >= 0 || x < 0`` and ``x + 0 == +0`` hold for all ``x``, even though the function ``foo`` does not +specify any pre or postconditions, and report a counter example for +the second case:: + + [ Info ] - Now considering 'precond. (call check(x >= 0 || x < 0))' VC for foo @40:5... + [ Info ] => VALID + [ Info ] - Now considering 'precond. (call check(x + 0 == 0))' VC for foo @40:31... + [ Error ] => INVALID + [ Error ] Found counter-example: + [ Error ] x -> 1 + +This is especially helpful when "debugging" proofs. + + +.. _proofcontrol: + +Proof control using ``assert`` and ``check`` +******************************************** + +Both the ``assert`` and ``check`` keywords generate a verification condition for +the corresponding formula in the current context. The difference in these +keywords is in how they affect the context of other verification conditions. As +a rule of thumb, assertions do not affect the context of verification conditions +outside the block of the assertion, while ``check`` does. Thus you can use +assertions to prove local properties, and use ``check`` to have the property +(checked and) visible outside the block. + +.. code-block:: scala + + def foo(): Unit = { + val x = { + assert(b1) // verification condition: b1 + check(b2) // verification condition: b1 ==> b2 + } + assert(b3) // verification condition: b2 ==> b3 (b1 not visible to the solver) + } + +Similarly, ``assert``'s are not guaranteed to be visible when generating +verification conditions for postconditions, while ``check``'s are. + +.. code-block:: scala + + def foo(): Unit = { + assert(b1) // verification condition: b1 + check(b2) // verification condition: b1 ==> b2 + }.ensuring(_ => b3) // verification condition b2 ==> b3 (b1 might not be visible to the solver) + + +.. _induction: + +Induction +********* + +The vast majority of functional programs are written as functions over +:ref:`ADTs `, and consequently, Stainless comes with some special +support for verifying properties of ADTs. Among other things, Stainless +provides an annotation ``@induct``, which can be used to automatically +prove postconditions of recursive functions defined on ADTs by way of +*structural induction*. We have already seen an example of such an +inductive property, namely ``rightUnitAppend``. In fact, using +``@induct``, Stainless is able to prove ``rightUnitAppend`` directly: + +.. code-block:: scala + + import stainless.annotation._ // for @induct + + @induct + def rightUnitAppend[T](l1: List[T]): Boolean = { + l1 ++ Nil() == l1 + }.holds + +This is possible because the inductive step follows (more or less) +directly from the inductive hypothesis and Stainless can verify the base +case automatically. However, Stainless may fail to verify more complex +functions with non-trivial base cases or inductive steps. In such +cases, one may still try to provide proof hints by performing *manual +case analysis*. Consider the following lemma about list reversal: + +.. code-block:: scala + + import stainless.collection._ // for List + import stainless.lang._ // for holds + + object Example { + def reverseReverse[T](l: List[T]): Boolean = { + l.reverse.reverse == l + }.holds + } + +Stainless is unable to verify ``reverseReverse`` even using ``@induct``. +So let's try and prove the lemma using manual case analysis. We start +by adding an "unrolled" version of the proposition and inserting calls +to ``check`` in each branch of the resulting pattern match: + +.. code-block:: scala + + def reverseReverse[T](l: List[T]): Boolean = { + l.reverse.reverse == l because { + l match { + case Nil() => check { Nil[T]().reverse.reverse == Nil[T]() } + case Cons(x, xs) => check { (x :: xs).reverse.reverse == (x :: xs) } + } + } + }.holds + +Clearly, the two versions of the lemma are equivalent: all we did was +expand the proposition using a pattern match and add some calls to +``check`` (remember ``check`` acts as the identity function on its +argument). Let's see what output Stainless produces for the expanded +version:: + + [ Info ] - Now considering 'postcondition' VC for reverseReverse @615:5... + [Warning ] => UNKNOWN + [ Info ] - Now considering 'precond. (call check(List[T]().reverse().reverse() ...)' VC for reverseReverse @617:28... + [ Info ] => VALID + [ Info ] - Now considering 'precond. (call check({val x$27 = l.h; ...)' VC for reverseReverse @618:28... + [Warning ] => UNKNOWN + [ Info ] - Now considering 'match exhaustiveness' VC for reverseReverse @616:7... + [ Info ] => VALID + +As expected, Stainless failed to verify the expanded version. However, we +get some additional information due to the extra pattern match and the +calls to ``check``. In particular, Stainless tells us that the match is +exhaustive, which means we covered all the cases in our case analysis +-- that's certainly a good start. Stainless was also able to automatically +verify the base case, so we can either leave the call to ``check`` as +is, or replace it by ``trivial``. Unfortunately, Stainless wasn't able to +verify the inductive step, something is missing. Let's try to +manually reduce the inductive case and see where we get. + +.. code-block:: scala + + def reverseReverse[T](l: List[T]): Boolean = { + l.reverse.reverse == l because { + l match { + case Nil() => trivial + case Cons(x, xs) => check { (xs.reverse :+ x).reverse == (x :: xs) } + } + } + }.holds + +And now we're stuck. We can't apply the inductive hypothesis here, +nor can we reduce the inductive case further, unless we perform +case analysis on ``xs``, which would grow the term further without +changing its shape. To make any headway, we need to use an additional +property of ``reverse``, given by the following lemma (which Stainless *is* +able to prove using ``@induct``): + +.. code-block:: scala + + @induct + def snocReverse[T](l: List[T], t: T): Boolean = { + (l :+ t).reverse == t :: l.reverse + }.holds + +The lemma states that appending an element ``t`` to a list ``l`` and +reversing it is equivalent to first reversing ``l`` and then +prepending ``t``. Using this lemma, we can write the proof of +``reverseReverse`` as + +.. code-block:: scala + + def reverseReverse[T](l: List[T]): Boolean = { + l.reverse.reverse == l because { + l match { + case Nil() => trivial + case Cons(x, xs) => check { + (xs.reverse :+ x).reverse == x :: xs.reverse.reverse && + x :: xs.reverse.reverse == (x :: xs) because + snocReverse(xs.reverse, x) && reverseReverse(xs) + } + } + } + }.holds + +Stainless is able to verify this version of the lemma. Note that Stainless +doesn't actually require us to include the two equations as they are +equivalent to the applications ``snocReverse(xs.reverse, x)`` and +``reverseReverse(xs)``. Similarly, the call to ``check`` is somewhat +redundant now that Stainless is able to verify the entire proof. We could +thus "simplify" the above to + +.. code-block:: scala + + def reverseReverse[T](l: List[T]): Boolean = { + l.reverse.reverse == l because { + l match { + case Nil() => trivial + case Cons(x, xs) => snocReverse(xs.reverse, x) && reverseReverse(xs) + } + } + }.holds + +However, the previous version is arguably more readable for a human +being, and therefore preferable. In Section ":ref:`rel-reasoning`" we +will see how readability can be improved even further through the use +of a DSL for equational reasoning. + +So far, we have only considered structurally inductive proofs. +However, Stainless is also able to verify proofs using *natural induction* +-- the form of induction that is perhaps more familiar to most +readers. Consider the following definition of the exponential +function :math:`exp(x, y) = x^y` over integers: + +.. code-block:: scala + + def exp(x: BigInt, y: BigInt): BigInt = { + require(y >= 0) + if (x == 0) 0 + else if (y == 0) 1 + else x * exp(x, y - 1) + } + +The function ``exp`` is again defined recursively, but this time using +``if`` statements rather than pattern matching. Let's try and prove +some properties of this function using natural induction. One such +property is that for any pair of positive numbers :math:`x, y \geq 0`, +the exponential :math:`x^y` is again a positive number. + +.. code-block:: scala + + def positive(x: BigInt, y: BigInt): Boolean = { + require(y >= 0 && x >= 0) + exp(x, y) >= 0 + } + +Since Stainless doesn't know anything about exponentials, it isn't able to +verify the lemma without hints. As with the previous example, we +start writing our inductive proof by expanding the top-level ``if`` +statement in the definition of ``exp``. + +.. code-block:: scala + + def positive(x: BigInt, y: BigInt): Boolean = { + require(y >= 0 && x >= 0) + exp(x, y) >= 0 because { + if (x == 0) check { exp(x, y) >= 0 } // <-- valid + else if (y == 0) check { exp(x, y) >= 0 } // <-- valid + else check { exp(x, y) >= 0 } // <-- unknown + } + }.holds + +Stainless was able to verify the first two (base) cases, but not the +inductive step, so let's continue unfolding ``exp`` for that case. + +.. code-block:: scala + + def positive(x: BigInt, y: BigInt): Boolean = { + require(y >= 0 && x >= 0) + exp(x, y) >= 0 because { + if (x == 0) trivial + else if (y == 0) trivial + else check { x * exp(x, y - 1) >= 0 } + } + }.holds + +Although Stainless still isn't able to verify the lemma, we now see a way +to prove the inductive step: ``x`` is positive (by the second +precondition) and so is ``exp(x, y - 1)`` (by the inductive +hypothesis). Hence the product ``x * exp(x, y - 1)`` is again +positive. + +.. code-block:: scala + + def positive(x: BigInt, y: BigInt): Boolean = { + require(y >= 0 && x >= 0) + exp(x, y) >= 0 because { + if (x == 0) trivial + else if (y == 0) trivial + else check { + x >= 0 && exp(x, y - 1) >= 0 because positive(x, y - 1) + } + } + }.holds + +With these hints, Stainless is able to verify the proof. Again, we could +shorten the proof by omitting inequalities that Stainless can infer +directly, albeit at the expense of readability. + +.. code-block:: scala + + def positiveShort(x: BigInt, y: BigInt): Boolean = { + require(y >= 0 && x > 0) + exp(x, y) >= 0 because { + if (x == 0) trivial + else if (y == 0) trivial + else positiveShort(x, y - 1) + } + }.holds + +We conclude the section with the inductive proof of another, somewhat +more interesting property of the exponential function, namely that +:math:`(x y)^z = x^z y^z`. + +.. code-block:: scala + + def expMultCommute(x: BigInt, y: BigInt, z: BigInt): Boolean = { + require(z >= 0) + exp(x * y, z) == exp(x, z) * exp(y, z) because { + if (x == 0) trivial + else if (y == 0) trivial + else if (z == 0) trivial + else check { + x * y * exp(x * y, z - 1) == + x * exp(x, z - 1) * y * exp(y, z - 1) because + expMultCommute(x, y, z - 1) + } + } + }.holds + +.. _rel-reasoning: + +Relational reasoning +******************** + +The majority of the example propositions we have seen so far related +some expression (e.g. ``l.reverse ++ Nil()`` or ``exp(x, y)``) to some +other expression (e.g. ``... == l1`` or ``... >= 0``). This is +certainly a common case among the sorts of propositions about +functions and data structures one might wish to prove. The proofs of +such propositions typically involve some form of *relational +reasoning*, i.e. reasoning involving properties (such as transitivity, +reflexivity or symmetry) of the relations in question. Stainless knows +about these properties for built-in relations such as ``==`` or orders +on numbers. For user-defined relations, they first need to be +established as lemmas. In this section, we discuss how to make +effective use of built-in relations, but the general principles extend +to their user-defined counterparts. + +When working with simple structural equality, we can rely on the default ``==`` +operator and Stainless will happily understand when the reflexivity, symmetry and +transitivity properties apply and use them to conclude bigger proofs. Similarly, +when working on ``BigInt``, Stainless knows about reflexivity, antisymmetry and +transitivity over ``>=`` or ``<=``, and also antireflexivity, antisymmetry +and transitivity of ``>`` and ``<``. + +However, even for relatively simple proofs about ADTs, Stainless needs +hints when combining, say equality, with user-defined operations, such +as ``++`` or ``reverse`` on lists. For example, Stainless is not able to +verify that the following holds for arbitrary pairs of lists ``l1`` +and ``l2``: + +.. code-block:: scala + + (l1 ++ l2).reverse == l2.reverse ++ l1.reverse + +The hard part of giving hints to Stainless is often to find them in the +first place. Here we can apply a general principle on top of +structural induction (as discussed in the previous section): we start +from the left-hand side of an equation and build a chain of +intermediate equations to the right-hand side. Using ``check`` +statements we can identify where Stainless times out and hence potentially +needs hints. + +.. code-block:: scala + + def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = { + ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because { + l1 match { + case Nil() => + /* 1 */ check { (Nil() ++ l2).reverse == l2.reverse } && + /* 2 */ check { l2.reverse == l2.reverse ++ Nil() } && + /* 3 */ check { l2.reverse ++ Nil() == l2.reverse ++ Nil().reverse } + case Cons(x, xs) => + /* 4 */ check { ((x :: xs) ++ l2).reverse == (x :: (xs ++ l2)).reverse } && + /* 5 */ check { (x :: (xs ++ l2)).reverse == (xs ++ l2).reverse :+ x } && + /* 6 */ check { (xs ++ l2).reverse :+ x == (l2.reverse ++ xs.reverse) :+ x } && + /* 7 */ check { (l2.reverse ++ xs.reverse) :+ x == l2.reverse ++ (xs.reverse :+ x) } && + /* 8 */ check { l2.reverse ++ (xs.reverse :+ x) == l2.reverse ++ (x :: xs).reverse } + } + } + }.holds + +If we run the above code with a decent timeout, Stainless reports four +*UNKNOWN* cases: the postcondition of the ``reverseAppend`` function itself and +checks number 2, 6 and 7. + + * Check #2 fails because, as we saw earlier, Stainless is not capable of + guessing the ``rightUnitAppend`` lemma by itself. We fix this case + by simply instantiating the lemma, i.e. by appending ``&& + rightUnitAppend(l2.reverse)`` to the base case. + + * Check #6 fails because, at this point, we need to inject the + induction hypothesis on ``xs`` and ``l2`` by adding ``&& + reverseAppend(xs, l2)``. + + * Finally, check #7 fails for a similar reason as check #2: we need + an additional "associativity" lemma to prove that ``(l1 ++ l2) :+ t + == l1 ++ (l2 :+ t)`` holds for any ``l1``, ``l2`` and ``t``. We + call this lemma ``snocAfterAppend`` and leave it as an exercise for + the reader. + +Once we have a valid proof, we can try to optimize it for readability. +As it stands, the resulting code is rather verbose because both sides +of most equations are duplicated. One option is to completely remove +the equations (they are implied by the instantiations of the lemmas) +and simply write + +.. code-block:: scala + + def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = { + ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because { + l1 match { + case Nil() => + rightUnitAppend(l2.reverse) + case Cons(x, xs) => + reverseAppend(xs, l2) && snocAfterAppend(l2.reverse, xs.reverse, x) + } + } + }.holds + +Or we can employ the equational reasoning DSL provided by the +``stainless.proofs`` package to remove the duplicate expressions and +interleave the equations with their associated proofs. This has the +advantage of not losing information that is still useful for a human +being reading the proof later on: + +.. code-block:: scala + + def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = { + ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because { + l1 match { + case Nil() => { + (Nil() ++ l2).reverse ==| trivial | + l2.reverse ==| rightUnitAppend(l2.reverse) | + l2.reverse ++ Nil() ==| trivial | + l2.reverse ++ Nil().reverse + }.qed + case Cons(x, xs) => { + ((x :: xs) ++ l2).reverse ==| trivial | + (x :: (xs ++ l2)).reverse ==| trivial | + (xs ++ l2).reverse :+ x ==| reverseAppend(xs, l2) | + (l2.reverse ++ xs.reverse) :+ x ==| + snocAfterAppend(l2.reverse, xs.reverse, x) | + l2.reverse ++ (xs.reverse :+ x) ==| trivial | + l2.reverse ++ (x :: xs).reverse + }.qed + } + } + }.holds + +The idea is to group statements in a block +(``{ }``) and call ``qed`` on it. Then, instead of writing ``a == b && b == c +&& hint1 && hint2`` we write ``a ==| hint1 | b ==| hint2 | c``. And when no +additional hint is required, we can use ``trivial`` which simply stands for +``true``. + +Additionally, by using this DSL, we get the same feedback granularity from Stainless +as if we had used ``check`` statements. This way we can construct proofs based +on equality more easily and directly identify where hints are vital. + +One shortcoming of the relational reasoning DSL is that it relies on +Stainless' knowledge of the relational properties of the built-in +relations, and in particular those of equality. Consequently it works +badly (if at all) with user-defined relations. However, since the DSL +is defined as a library (in ``library/proof/package.scala``), it can +in principle be extended and modified to include specific user-defined +relations on a case-by-case basis. + +.. TODO add a word about requirement in ctor (e.g. Rational) + +.. TODO Footnote linking to Etienne's answer on SO. + + +Limits of the approach: HOFs, quantifiers and termination +********************************************************* + +While the techniques discussed in this section are useful in general, +their applicability has, of course, its limitations in practice. These +limitations are mostly due to Stainless' limited support for certain +language constructs, such as higher-order functions (HOFs) or +quantifiers (which in turn is due, mostly, to the limited support of +the corresponding theories in the underlying SMT solvers). + +Still, even using these "experimental" features, one manages to prove +some interesting propositions. Here is another list example, which +relates the ``foldLeft``, ``foldRight`` and ``reverse`` operations +defined on lists and makes crucial use of HOFs: + +.. code-block:: scala + + import stainless.collection._ + import stainless.lang._ + import stainless.proof._ + + def folds[A, B](xs: List[A], z: B, f: (B, A) => B): Boolean = { + val f2 = (x: A, z: B) => f(z, x) + xs.foldLeft(z)(f) == xs.reverse.foldRight(z)(f2) because { + xs match { + case Nil() => true + case Cons(x, xs) => { + (x :: xs).foldLeft(z)(f) ==| trivial | + xs.foldLeft(f(z, x))(f) ==| folds(xs, f(z, x), f) | + xs.reverse.foldRight(f(z, x))(f2) ==| trivial | + xs.reverse.foldRight(f2(x, z))(f2) ==| + snocFoldRight(xs.reverse, x, z, f2) | + (xs.reverse :+ x).foldRight(z)(f2) ==| trivial | + (x :: xs).reverse.foldRight(z)(f2) + }.qed + } + } + }.holds + +A rather different, more general issue that arises when proving +propositions using Stainless is related to *termination checking*. When +verifying inductive proofs (and more generally the postconditions of +recursive methods), Stainless assumes that the corresponding proofs are +*well-founded*, or equivalently, that the corresponding recursive +methods terminate on all inputs. It is thus possible -- and indeed rather +easy -- to write bogus proofs (intentionally or accidentally) which +Stainless recognizes as valid, but which are not well-founded. Consider +the following lemma, which apparently establishes that all lists are +empty: + +.. code-block:: scala + + import stainless.collection._ + import stainless.lang._ + import stainless.proof._ + + object NotWellFounded { + + // This proof is not well-founded. Since Stainless doesn't run the + // termination checker by default, it will accept the proof as + // valid. + def allListsAreEmpty[T](xs: List[T]): Boolean = { + xs.isEmpty because { + xs match { + case Nil() => trivial + case Cons(x, xs) => allListsAreEmpty(x :: xs) + } + } + }.holds + } + +Stainless hences performs termination checking by default to minimize +the risk of accidentally writing bogus proofs such as the one above. +It will thus emit a warning if it cannot prove that a function terminates, or +if it can show that its measure (inferred or user-defined) does not decreases between +recursive calls. + +.. TODO example: folds + future work (alt. version of folds) + +.. _post-cond: + +Techniques for proving non-trivial postconditions +------------------------------------------------- + +When proving a mathematical lemma, the return type of the +corresponding function is most of +the time, if not always, ``Boolean``. For those proofs it is rather easy to +write a postcondition: using ``holds`` is generally enough. + +But when it comes to writing postconditions for more general functions, such as +the addition of rational numbers, we are no longer dealing with ``Boolean`` so +we need a strategy to properly write ``ensuring`` statements. + + +Rationals: a simple example +*************************** + +Let's take rational numbers as an example: we define them as a case class with +two attributes, `n` for the numerator and `d` for the denominator. We also +define three simple properties on them: ``isRational``, ``isNonZero`` and +``isPositive``. + +.. code-block:: scala + + case class Rational(n: BigInt, d: BigInt) { + def isRational = d != 0 + def isPositive = isRational && (n * d >= 0) + def isNonZero = isRational && (n != 0) + + // ... + } + +And on top of that, we want to support addition on ``Rational`` in a way that +the rationality and positiveness properties are correctly preserved: + +.. code-block:: scala + + def +(that: Rational): Rational = { + require(isRational && that.isRational) + Rational(n * that.d + that.n * d, d * that.d) + } ensuring { res => + res.isRational && + (this.isPositive == that.isPositive ==> res.isPositive == this.isPositive) + } + +In this simple case, things work nicely and we can write the +multiplication in a similar fashion: + +.. code-block:: scala + + def *(that: Rational): Rational = { + require(isRational && that.isRational) + Rational(n * that.n, d * that.d) + } ensuring { res => + res.isRational && + (res.isNonZero == (this.isNonZero && that.isNonZero)) && + (res.isPositive == (!res.isNonZero || this.isPositive == that.isPositive)) + } + + +Measures: a slightly more complex example +***************************************** + +Now let's look at a slightly more complex example: measures on +discrete probability spaces. We represent such measures using a +``List``-like recursive data structure: a generic abstract class +``Meas[A]`` that has two subclasses, ``Empty[A]`` and ``Cons[A]``. +The constructor of the class ``Empty[A]`` takes no arguments; it +represents an "empty" measure that evaluates to 0 when applied to any +set of values of type ``A``. The constructor of ``Cons[A]``, on the +other hand, takes three parameters: a value ``x``, its associated +weight ``w`` expressed as a ``Rational`` (since Stainless doesn't quite yet +support real numbers out of the box), and another measure ``m`` on +``A``. The value ``Cons(x, w, m)`` represents the measure obtained by +adding to ``m`` the "single-point" measure that evaluates to ``w`` at +``x`` and to 0 everywhere else. We also define an ``isMeasure`` +property -- similar to the ``isRational`` property presented above -- +which recursively checks that all the weights in a measure are +positive rationals (note that all our measures have finite support). + +.. code-block:: scala + + /** Measures on discrete probability spaces. */ + sealed abstract class Meas[A] { + + /** All weights must be positive. */ + def isMeasure: Boolean = this match { + case Empty() => true + case Cons(x, w, m) => w.isPositive && m.isMeasure + } + + // ... + } + + /** The empty measure maps every subset of the space A to 0. */ + case class Empty[A]() extends Meas[A] + + /** + * The 'Cons' measure adjoins an additional element 'x' of type 'A' + * to an existing measure 'm' over 'A'. Note that 'x' might already + * be present in 'm'. + */ + case class Cons[A](x: A, w: Rational, m: Meas[A]) extends Meas[A] + + +The defining operation on a measure ``m`` is its evaluation ``m(xs)`` +(or equivalently ``m.apply(xs)``) on some set ``xs: Set[A]``, i.e. on a +subset of the "space" ``A``. The value of ``m`` should be a positive +rational for any such set ``xs``, provided ``m.isMeasure`` holds. +This suggests ``_.isPositive`` as the postcondition for ``apply``, +but simply claiming that the result is positive is not enough for Stainless +to verify this postcondition. + +We can provide the necessary hint to Stainless by performing structural +induction on ``this`` inside the postcondition as follows: + +.. code-block:: scala + + /** Compute the value of this measure on a subset of the space 'A'. */ + def apply(xs: Set[A]): Rational = { + require (isMeasure) + this match { + case Empty() => Rational(0, 1) + case Cons(x, w, m) => if (xs contains x) w + m(xs) else m(xs) + } + } ensuring { res => + res.isPositive because { + this match { + case Empty() => trivial + case Cons(x, w, m) => m(xs).isPositive + } + } + } + +Notice the similarity between the pattern match in the body of the +``apply`` function and that in the postcondition. With this hint, +Stainless is able to verify the postcondition. + + +A complex example: additivity of measures +----------------------------------------- + +Using the principles and techniques discussed so far, one can prove +quite advanced propositions using Stainless. Returning to the +measure-theoretic example from the previous section, we would like to +prove that our implementation of measures is properly *additive*. +Formally, a measure :math:`\mu \colon A \to \mathbb{R}` on a countable +set :math:`A` must fulfill the following additivity property +[#dicrete-meas]_: + +.. math:: + + \forall A_1, A_2 \subseteq A . A_1 \cap A_2 = \emptyset \Rightarrow + \mu(A_1 \cup A_2) = \mu(A_1) + \mu(A_2) + +which we can express in Stainless as + +.. code-block:: scala + + def additivity[A](m: Meas[A], xs: Set[A], ys: Set[A]): Boolean = { + require(m.isMeasure && (xs & ys).isEmpty) + m(xs ++ ys) == m(xs) + m(ys) + }.holds + +We can prove this property using structural induction on the parameter +``m``, case analysis on the parameters ``xs`` and ``ys``, equational +reasoning, and properties of rational numbers (in the form of +user-defined lemmas) as well as sets (using Stainless's built-in support). + +.. code-block:: scala + + def additivity[A](m: Meas[A], xs: Set[A], ys: Set[A]): Boolean = { + require(m.isMeasure && (xs & ys).isEmpty) + m(xs ++ ys) == m(xs) + m(ys) because { + m match { + case Empty() => trivial + case Cons(x, w, n) => if (xs contains x) { + w + n(xs ++ ys) ==| additivity(n, xs, ys) | + w + (n(xs) + n(ys)) ==| plusAssoc(w, n(xs), n(ys)) | + (w + n(xs)) + n(ys) ==| !(ys contains x) | + m(xs) + m(ys) + }.qed else if (ys contains x) { + w + n(xs ++ ys) ==| additivity(n, xs, ys) | + w + (n(xs) + n(ys)) ==| plusComm(w, (n(xs) + n(ys))) | + (n(xs) + n(ys)) + w ==| plusAssoc(n(xs), n(ys), w) | + n(xs) + (n(ys) + w) ==| plusComm(n(ys), w) | + n(xs) + (w + n(ys)) ==| !(xs contains x) | + m(xs) + m(ys) + }.qed else { + n(xs ++ ys) ==| additivity(n, xs, ys) | + n(xs) + n(ys) + }.qed + } + } + }.holds + +The full proof (including the proofs of all helper lemmas) as well as +its generalization to *sub-additivity* can be found in the +``testcases/verification/proof/measure/`` directory of the Stainless +distribution [#example-dir]_. + + +Quick Recap +----------- + +Let's summarize what we've learned here. To write proofs efficiently, +it's good to keep the following in mind: + +1. Always use a proper timeout and ask Stainless for more information about + what he tries to verify, e.g. ``--timeout=5 --debug=verification``. + +2. Use ``@induct`` when working on structurally inductive proofs to + get a more precise feedback from Stainless: this will decompose the + proof into a base case and an inductive case for the first argument + of the function under consideration. + + If Stainless isn't able to verify the proof using ``@induct``, try + performing manual case analysis. + +3. Modularize your proofs and verify *sub-goals*! + + - use plenty of helper lemmas; + - use ``check`` abundantly; + - if possible use the relational reasoning DSL presented above. + + This is especially handy when you can connect the two sides of a relational + claim with sub-statements. + + +.. rubric:: Footnotes + +.. [#example-dir] The source code of this example and all others in + this chapter is included in the Stainless distribution. Examples about + lists can be found in ``library/collection/List.scala``, other + examples are located in the ``testcases/verification/proof/`` + directory. + +.. [#props-not-types] Propositions and proofs + live in the same universe in Stainless. This is contrary to + e.g. type-theoretic proof assistants where propositions are + represented by types and proofs are terms inhabiting such types. + +.. [#dicrete-meas] To be precise, we are assuming here the underlying + measurable space :math:`(A, \mathcal{P}(A))`, where :math:`A` is + countable and :math:`\mathcal{P}(A)` denotes its discrete σ-algebra + (i.e. the power set of :math:`A`). diff --git a/_sources/options.rst.txt b/_sources/options.rst.txt new file mode 100644 index 0000000000..ec5017e56e --- /dev/null +++ b/_sources/options.rst.txt @@ -0,0 +1,399 @@ +.. _cmdlineoptions: + +Specifying Options +================== + +Stainless's command line options have the form ``--option`` or ``--option=value``. +To enable a flag option, use ``--option=true`` or ``on`` or ``yes``, +or just ``--option``. To disable a flag option, use ``--option=false``. + +Additionally, if you need to pass options to the ``scalac`` frontend of Stainless, +you can do it by using a single dash ``-``. For example, try ``-Ybrowse:typer``. + +The rest of this section presents some of the command-line options that Stainless recognizes. +For a short (but always up-to-date) summary, you can also invoke ``stainless --help``. + +Choosing which Stainless feature to use +--------------------------------------- + +The first group of options determines which feature of Stainless will be used. +By default, ``--verification`` is chosen. + +* ``--verification`` + + Proves or disproves function contracts, as explained in the :doc:`verification` section. + +* ``--eval`` + + Evaluate parameterless functions and report their body's value and whether + or not their postcondition holds. + +* ``--genc`` + + Convert stainless code to C (implies --batched, default: false). + See documentation section for generating C code. + +* ``--coq`` + + Transform the program into a Coq program, and let Coq generate subgoals automatically + +* ``--type-checker`` + + Use type checker inspired by System FR to generate verification conditions. + Default is ``true`` and is strongly recommended; using ``false`` reverts to + an old verification-condition generator. + +* ``--infer-measures=[yes|no|only] (default: yes)`` + + Infers measures for recursive functions which do not already have one. + +* ``--check-measures=[true|false] (default: true)`` + + Check termination of functions with measures, ie. whether measures decrease between recursive calls. + +* ``--testgen`` + + Proves or disproves function contracts (like ``--verification``) and attempts to create Scala test cases from reported counter-examples. + +* ``--genc-testgen`` + + Like ``--testgen``, but generates C test cases using GenC. + +* ``--help`` + + Prints a helpful message, then exits. + + +Additional top-level options +---------------------------- + +These options are available to all Stainless components: + +* ``--watch`` + + Re-run the selected analysis components upon file changes, making the program analysis + interactive and significantly more efficient than restarting stainless manually. + +* ``--no-colors`` + + Disable colored output and non-ascii characters (consider this option for better support in IDEs) + +* ``--compact`` + + Reduces the components' summaries to only the invalid elements (e.g. invalid VC). + +* ``--debug=d1,d2,...`` + + Enables printing detailed messages for the components d1,d2,... . + Available components include: + + * ``solver`` (SMT solvers and their wrappers) + + * ``termination`` (Termination analysis) + + * ``timers`` (Timers, timer pools) + + * ``trees`` (Manipulation of trees) + + * ``verification`` (Verification) + + * ``full-vc`` (Display VCs before and after simplification) + + * ``type-checker`` (Type checking of the final program for VC generation) + + * ``type-checker-vcs`` (Generation of VCs by the type-checker) + + * ``derivation`` (Dump typing derivations) + +* ``--functions=f1,f2,...`` + + Only consider functions f1, f2, ... . This applies to all functionalities + where Stainless manipulates the input in a per-function basis. + + Stainless will match against suffixes of qualified names. For instance: + ``--functions=List.size`` will match the method ``stainless.collection.List.size``, + while ``--functions=size`` will match all methods and functions named ``size``. + This option supports ``_`` as wildcard: ``--functions=List._`` will + match all ``List`` methods. + +* ``--solvers=s1,s2,...`` + + Use solvers s1, s2,... . If more than one solver is chosen, all chosen + solvers will be used in parallel, and the best result will be presented. + By default, the ``nativez3`` solver is picked. + + Some solvers are specialized in proving verification conditions + and will have a hard time finding a counterexample in the case of an invalid + verification condition, whereas some are specialized in finding + counterexamples, and some provide a compromise between the two. + Also, some solvers do not as of now support higher-order functions. + + Available solvers include: + + * ``nativez3`` + + Native Z3 with z3-templates for unfolding recursive functions (default). + + * ``smt-cvc5`` + + cvc5 through SMT-LIB. An algorithm within Stainless takes up the unfolding + of recursive functions, handling of lambdas etc. To use this or any + of the following cvc5-based solvers, you need to have the ``cvc5`` + executable in your system path (the latest unstable version is recommended). + + * ``smt-z3`` + + Z3 through SMT-LIB. To use this or the next solver, you need to + have the ``z3`` executable in your program path (the latest stable version + is recommended). Inductive reasoning happens on the Stainless side + (similarly to ``smt-cvc5``). + + * ``unrollz3`` + + Native Z3, but inductive reasoning happens within Stainless (similarly to ``smt-z3``). + + * ``princess`` + + Princess solver through its native interface (uses princess-templates) during + unfolding. This is a full-stack JVM solver and enables Stainless to run without + external solver dependencies. + +* ``--timeout=t`` + + Set a timeout for each attempt to prove one verification condition/ + repair one function (in sec.) When using the ``--eval`` component, one + should use ``--max-calls`` instead. + +* ``--cache`` + + Use persistent cache on disk to save the state of the verification and/or + termination analyses. + +* ``--cache-dir=`` + + Specify in which directory the cache files generated by ``--cache`` and other + options should be stored. Defaults to ``.stainless-cache/``. + +* ``--json=`` + + Export the verification and/or termination analyses to the given file. + +* ``--extra-deps=org:name_scalaVersion:version,...`` + + Fetch the specified dependencies, and add their sources to the set of files + processed by Stainless. Each dependency must be available as a source JAR + from MavenCentral, the EPFL-LARA bintray organization, your local Ivy database, + or through another resolver specified via ``--extra-resolvers``. + + Note: Stainless will not pull transitive dependencies, so one has to specify + all transitive dependencies explicitely via this option. + + Example: ``--extra-deps=ch.epfl.lara:stainless-algebra_2.12:0.1.2`` + +* ``--extra-resolvers=URL,...`` + + Specify additional resolvers to be used to fetch the dependencies specified via + the ``--extra-deps`` option. + + Note: The full URL of the resolver must be used. + + Example: ``--extra-resolvers=https://oss.sonatype.org/content/repositories/snapshots/`` + + See the `Coursier source code `_ for the list of most common repositories URLs. + + +Additional Options (by component) +--------------------------------- + +The following options relate to specific components in Stainless. + + +Verification +************ + +* ``--strict-aritmetic`` + + Check arithmetic operations for unintended behaviour and + overflows. Note that reasoning about bitvectors is sound + even if this option is false, but in that case no warnings + are generated for overflows and underflows because these + have well-defined semantics in Scala. + +* ``--vc-cache`` + + Use a persistent cache mechanism to speed up verification; on by default. + +* ``--fail-early`` + + Aborts verification as soon as a VC cannot be proven to be correct. + +* ``--fail-invalid`` + + Aborts verification as soon as an invalid VC is found. + + + +Termination +*********** + +* ``--ignore-posts`` + + Ignore postconditions during termination verification. + + + +Unrolling Solver +**************** + +* ``--check-models`` + + Double-check counterexamples with the evaluator. + +* ``--feeling-lucky`` + + Use evaluator to find counterexamples early. + +* ``--unroll-assumptions`` + + Use unsat-assumptions to drive unrolling while remaining fair. + +* ``--silent-errors`` + + Don't crash on errors, simply return ``Unknown``. + +* ``--unroll-factor=n`` + + Speeds up unrolling by a factor ``n``. + +* ``--model-finding=n`` + + Boosts model-finding capabilities by a factor ``n``. This may come at + the cost of proof construction. + +* ``--no-simplifications`` + + Disables program simplification heuristics. + + + +cvc5 Solver +*********** + +* ``--solver:cvc5=`` + + Pass extra command-line arguments to cvc5. + + + +Evaluators +********** + +* ``--codegen`` + + Use compiled evaluator instead of an interpreter. + +* ``--small-arrays`` + + Assume all arrays can fit into memory during compiled evaluation. + +* ``--instrument`` + + Instrument ADT field access during code generation. + +* ``--max-calls=n`` + + Bounds the total number of function call evaluations (before crashing). + +* ``--ignore-contracts`` + + Ignores function contracts during evaluation. + + + +Tests generation +**************** + +* ``testgen-file=`` + + Specifies the output file for the generated tests. + +* ``genc-testgen-includes=header1.h,header2,...`` + + Only applies for ``--genc-testgen``. Indicates the headers to ``#include`` in the generated test file. + +Configuration File +------------------ + +Stainless supports setting default values for command line options configuration files. +To specify configuration file you can use the option ```--config-file=FILE``. The default is +``stainless.conf`` or ``.stainless.conf``. The file should be a valid HOCON file. + +For example, consider the config file containin the following lines: + +.. code-block:: text + + vc-cache = false + debug = [verification, trees] + timeout = 5 + check-models = true + print-ids = true + + +The file will translate to the following command line options: + +``--vc-cache=false --debug=verification,trees --timeout=5 --print-ids`` + +Stainless searches for a configuration file recursively +starting from the current directory and walking up the +directory hierarchy. For example, if one runs stainless +from ``/a/b/c`` and there is a config file in any of `c`, +`b` or `a`, the first of those is going to be loaded. + +Library Files +------------- + +Purpose of library files +************************ + +Stainless contains library source Scala files that define types and functions that are meant to be always available +via import statements such as ``import stainless.lang._``, ``import stainless.annotation._``, +``import stainless.collection._``, and so on. Many of these types have special treatment inside the extraction +pipeline and will map directly to mathematical data types of the underlying SMT solvers. +At build time, the ``build.sbt`` script computes the list of these files by traversing the ``frontends/library/`` directory. + +Changing the list of library files +********************************** + +To support further customization, if at run time stainless finds +a file ``libfiles.txt`` in the current directory, it replaces the list of library files files with the list contained +in this file, one file per line, with paths relative to the directory ``frontends/library/``. For example, ``libfiles.txt`` +may contain: + +.. code:: text + + stainless/util/Random.scala + stainless/lang/Option.scala + stainless/lang/StaticChecks.scala + stainless/lang/Real.scala + stainless/lang/Either.scala + stainless/lang/Set.scala + stainless/lang/MutableMap.scala + stainless/lang/package.scala + stainless/lang/Bag.scala + stainless/lang/Map.scala + stainless/collection/List.scala + stainless/math/BitVectors.scala + stainless/math/Nat.scala + stainless/math/package.scala + stainless/io/StdIn.scala + stainless/io/package.scala + stainless/annotation/annotations.scala + stainless/annotation/isabelle.scala + stainless/annotation/cCode.scala + stainless/proof/Internal.scala + stainless/proof/package.scala + +Shortening this list may reduce the startup time, but also cause Stainless to not work propertly, so +using the ``--watch`` and ``--functions`` options is the first option to try. + +For further customization by advanced users, please examine the ``build.sbt`` file. diff --git a/_sources/purescala.rst.txt b/_sources/purescala.rst.txt new file mode 100644 index 0000000000..290e13ce03 --- /dev/null +++ b/_sources/purescala.rst.txt @@ -0,0 +1,856 @@ + .. _purescala: + +Pure Scala +========== + +The input to Stainless is a purely functional **subset** of `Scala +`_, which we call +**Pure Scala**. Constructs specific for Stainless are defined inside +Stainless's libraries in package `stainless` and its subpackages. +Stainless invokes standard `scalac` compiler on the input file, then +performs additional checks to ensure that the given program +belongs to Pure Scala. + +Pure Scala supports two kinds of top-level declarations: + +1. Algebraic Data Type (ADT) definitions in the form of an + abstract class and case classes/objects + +.. code-block:: scala + + abstract class MyList + case object MyEmpty extends MyList + case class MyCons(elem: BigInt, rest: MyList) extends MyList + +2. Objects/modules, for grouping classes and functions + +.. code-block:: scala + + object Specs { + def increment(a: BigInt): BigInt = { + a + 1 + } + + case class Identifier(id: BigInt) + } + +Booleans +-------- + +Booleans are used to express truth conditions in Stainless. +Unlike some proof assistants, there is no separation +at the type level between +Boolean values and the truth conditions of conjectures +and theorems. + +Typical propositional operations are available using Scala +notation, along +with a new shorthand for implication. The `if` expression +is also present. + +.. code-block:: scala + + a && b + a || b + a == b + !a + a ==> b // Stainless syntax for boolean implication + +Stainless uses short-circuit interpretation of `&&`, `||`, and `==>`, +which evaluates the second argument only when needed: + +.. code-block:: scala + + a && b === if (a) b else false + + a || b === if (a) true else b + + a ==> b === if (a) b else true + +This aspect is important because of: + +1. evaluation of expressions, which is kept compatible with Scala + +2. verification condition generation for safety: arguments of Boolean operations +may be operations with preconditions; these preconditions apply only in case +that the corresponding argument is evaluated. + +3. termination checking, which takes into account that only one of the paths in an if expression is evaluated for a given truth value of the condition. + +.. _adts: + +Algebraic Data Types +-------------------- + +Abstract Classes +**************** + +ADT roots need to be defined as abstract, unless the ADT is defined with only one case class/object. Unlike in Scala, abstract classes cannot define fields or constructor arguments. + +.. code-block:: scala + + abstract class MyType + +An abstract class can be extended by other abstract classes. + +Case Classes +************ + +The abstract root can also be extended by a case-class, defining several fields: + +.. code-block:: scala + + case class MyCase1(f: Type, f2: MyType) extends MyType + case class MyCase2(f: Int) extends MyType + +.. note:: + You can also define single case-class, for Tuple-like structures. + +You can add invariants to case classes using a ``require`` clause, as follows: + +.. code-block:: scala + + case class Positive(value: BigInt = 0) { + require(value >= 0) + } + +For classes without type parameters, when all fields have a default value, Stainless generates a +verification condition to check that the default instance respects the invariant. In this example, +the verification condition will be seen as coming from an internal function called +``PositiveRequireForDefault``. + +.. note:: + + Invariants are only allowed to refer to fields of their class, and + cannot call any methods on ``this`` (but calls to methods on their + fields are allowed). + +Case Objects +************ + +It is also possible to defined case objects, without fields: + +.. code-block:: scala + + case object BaseCase extends MyType + +Value Classes +************* + +One can define a value class just like in standard Scala, +by extending the ``AnyVal`` class. + +.. code-block:: scala + + case class Positive(value: BigInt) extends AnyVal { + @invariant + def isPositive: Boolean = value >= 0 + } + +In the code block above, we also specify an invariant of the value +class, using the ``@invariant`` annotation. Such invariants are +subsequently lifted into a refinement type of the underlying type. + +.. note:: + + Same remark as above: invariants are only allowed to refer to fields of their class. + +Generics +-------- + +Stainless supports type parameters for classes and functions. + +.. code-block:: scala + + object Test { + abstract class List[T] + case class Cons[T](hd: T, tl: List[T]) extends List[T] + case class Nil[T]() extends List[T] + + def contains[T](l: List[T], el: T) = { ... } + } + + +.. note:: + Type parameters can also be marked as co- or contra-variant, eg. + + .. code-block:: scala + + abstract class List[+T] + case class Cons[T](hd: T, tl: List[T]) extends List[T] + case object Nil extends List[Nothing] + +Methods +------- + +You can define methods in classes. + +.. code-block:: scala + + abstract class List[T] { + def contains(e: T) = { .. } + } + + case class Cons[T](hd: T, tl: List[T]) extends List[T] + case object Nil extends List[Nothing] + + def test(a: List[Int]) = a.contains(42) + +It is possible to define abstract methods in abstract classes and implement them in case classes. +Multiple layers of inheritance are allowed, as is the ability to override concrete methods. + +.. code-block:: scala + + abstract class A { + def x(a: Int): Int + } + + abstract class B extends A { + def x(a: Int) = { + require(a > 0) + 42 + } ensuring { _ >= 0 } + } + + case class C(c: Int) extends B { + override def x(i: Int) = { + require(i >= 0) + if (i == 0) 0 + else c + x(i-1) + } ensuring ( _ == c * i ) + } + + case class D() extends B + +It is also possible to call methods of a superclass with the ``super`` keyword. + +.. code-block:: scala + + sealed abstract class Base { + def double(x: BigInt): BigInt = x * 2 + } + + case class Override() extends Base { + override def double(x: BigInt): BigInt = { + super.double(x + 1) + 42 + } + } + +Abstract methods may have contracts in terms of pre- and postconditions. The +syntax uses ``???`` and is as follows: + +.. code-block:: scala + + abstract class Set[T] { + def contains[T](t: T): Boolean + + def add[T](t: T): Set[T] = { + require(!this.contains(t)) + (??? : Set[T]) + }.ensuring(res => res.contains(t)) + } + +You can then extend such abstract classes by concrete implementations, and +Stainless will generate verification conditions to make sure that the +implementation respects the specification. + +You can also add implementations and assume that they are correct with respect +to the specification of the abstract class, without having Stainless check the +specification (e.g. if you want to use existing Scala data-structures inside). +In that case, mark the concrete class with ``@extern`` (see Section :doc:`wrap` +for more info on ``@extern``) or place the concrete implementation in files +which are not inspected by Stainless (see e.g. +https://github.com/epfl-lara/stainless-project.g8 for an example of how to setup +such a hybrid project). + + +Copy Method +*********** + +The ``copy`` method of classes with immutable fields is extracted as well, +and ensures that the class invariant (if any) is maintained by requiring it +to be satisfied as a precondition. + +.. code-block:: scala + + case class Foo(x: BigInt) { + require(x > 0) + } + + def prop(foo: Foo, y: BigInt) = { + require(y > 1) + foo.copy(x = y) + } + +.. note:: + The example above would not verify without the precondition in function ``prop``, + as ``Foo`` require its field ``x`` to be positive. + + +Initialization +************** + +In Pure Scala, initialization of ``val``'s may not have future or self-references: + +.. code-block:: scala + + object Initialization { + case class C(x: BigInt) { + val y = x // ok + val z = y + x // ok + val a = b // Error: "because field `a` can only refer to previous fields, not to `b`" + val b = z + y // ok + } + } + + +Overriding +********** + +Stainless supports overriding methods with some constraints: +* A ``val`` in an abstract class can only be overridden by a concrete class parameter. +* Methods and ``lazy val``s in abstract classes can be overridden by concrete methods or +``lazy val``'s (interchangably), or by a concrete class parameter, but not by +a ``val``. + +Here are a few examples that are rejected by Stainless: + +.. code-block:: scala + + object BadOverride1 { + sealed abstract class Abs { + require(x != 0) + val x: Int + } + + // Error: "Abstract values `x` must be overridden with fields in concrete subclass" + case class AbsInvalid() extends Abs { + def x: Int = 1 + } + } + +.. code-block:: scala + + object BadOverride2 { + sealed abstract class Abs { + val y: Int + } + + // Error: "Abstract values `y` must be overridden with fields in concrete subclass" + case class AbsInvalid() extends Abs { + val y: Int = 2 + } + } + +.. code-block:: scala + + object BadOverride3 { + sealed abstract class AAA { + def f: BigInt + } + + // Error: "because abstract methods BadOverride3.AAA.f were not overridden by + // a method, a lazy val, or a constructor parameter" + case class BBB() extends AAA { + val f: BigInt = 0 + } + } + + +Default Parameters +****************** + +Functions and methods can have default values for their parameters. + +.. code-block:: scala + + def test(x: Int = 21): Int = x * 2 + + assert(test() == 42) // valid + + + +Type Definitions +---------------- + +Type Aliases +************ + +Type aliases can be defined the usual way: + +.. code-block:: scala + + object testcase { + type Identifier = String + + def newIdentifier: Identifier = /* returns a String */ + } + +Type aliases can also have one or more type parameters: + +.. code-block:: scala + + type Collection[A] = List[A] + + def singleton[A](x: A): Collection[A] = List(x) + +Type Members +************ + +Much like classes can have field members and method members, they can also +define type members. Much like other members, those can also be declared +abstract within an abstract class and overridden in implementations: + +.. code-block:: scala + + case class Grass() + + abstract class Animal { + type Food + val happy: Boolean + def eat(food: Food): Animal + } + + case class Cow(happy: Boolean) extends Animal { + type Food = Grass + def eat(g: Grass): Cow = Cow(happy = true) + } + +Note: Like regular type aliases, type members can also have one or more type parameters. + +Type members then give rise to path-dependent types, where the type of a variable +can depend on another variable, by selecting a type member on the latter: + +.. code-block:: scala + + // Path-dependent type + // vvvvvvvvvvv + def giveFood(animal: Animal)(food: animal.Food): Animal = { + animal.eat(food) + } + + def test = { + val cow1 = Cow(false) + val cow2 = giveFood(cow1)(Grass()) + assert(cow2.happy) // VALID + } + +Specifications +-------------- + +Stainless supports three kinds of specifications to functions and methods: + +Preconditions +************* + +Preconditions constraint the argument and is expressed using `require`. It should hold for all calls to the function. + +.. code-block:: scala + + def foo(a: Int, b: Int) = { + require(a > b) + ... + } + +Postconditions +************** + +Postconditions constraint the resulting value, and is expressed using `ensuring`: + +.. code-block:: scala + + def foo(a: Int): Int = { + a + 1 + } ensuring { res => res > a } + +Body Assertions +*************** + +Assertions constrain intermediate expressions within the body of a function. + +.. code-block:: scala + + def foo(a: Int): Int = { + val b = -a + assert(a >= 0 || b >= 0, "This will fail for -2^31") + a + 1 + } + +The error description (last argument of ``assert``) is optional. + +Expressions +----------- + +Stainless supports most purely-functional Scala expressions: + +Pattern matching +**************** + +.. code-block:: scala + + expr match { + // Simple (nested) patterns: + case CaseClass( .. , .. , ..) => ... + case v @ CaseClass( .. , .. , ..) => ... + case v : CaseClass => ... + case (t1, t2) => ... + case 42 => ... + case _ => ... + + // can also be guarded, e.g. + case CaseClass(a, b, c) if a > b => ... + } + +Custom pattern matching with ``unapply`` methods are also supported: + +.. code-block:: scala + + object :: { + def unapply[A](l: List[A]): Option[(A, List[A])] = l match { + case Nil() => None() + case Cons(x, xs) => Some((x, xs)) + } + } + + def empty[A](l: List[A]) = l match { + case x :: xs => false + case Nil() => true + } + +Values +****** + +.. code-block:: scala + + val x = ... + + val (x, y) = ... + + val Cons(h, _) = ... + +.. note:: + The latter two cases are actually syntactic sugar for pattern matching with one case. + + +Inner Functions +*************** + +.. code-block:: scala + + def foo(x: Int) = { + val y = x + 1 + def bar(z: Int) = { + z + y + } + bar(42) + } + + +Local and Anonymous Classes +*************************** + +Functions and methods can declare local classes, which can close over +the fields of the enclosing class, as well as the parameters of the enclosing +function or method. + +.. code-block:: scala + + abstract class Foo { + def bar: Int + } + + def makeFoo(x: Int): Foo = { + case class Local() extends Foo { + def bar: Int = x + } + Local() + } + +.. note:: Functions and methods which return an instance of a local class + must have an explicit return type, which will typically be that of the parent class. + Otherwise, a structural type will be inferred by the Scala compiler, and those are + currently unsupported. + +Anonymous classes with an explicit parent are supported as well: + +.. code-block:: scala + + abstract class Foo { + def bar: Int + } + + def makeFoo(x: Int): Foo = new Foo { + def bar: Int = x + } + +.. note:: Anonymous classes cannot declare more public members than their parent class, + ie. the following is not supported: + +.. code-block:: scala + + abstract class Foo { + def bar: Int + } + + def makeFoo(x: Int): Foo = new Foo { + def bar: Int = x + def hi: String = "Hello, world" + } + +Predefined Types +---------------- + +TupleX +****** + +.. code-block:: scala + + val x = (1,2,3) + val y = 1 -> 2 // alternative Scala syntax for Tuple2 + x._1 // == 1 + + +Int +*** + +.. code-block:: scala + + a + b + a - b + -a + a * b + a / b + a % b // a modulo b + a < b + a <= b + a > b + a >= b + a == b + +.. note:: + Integers are treated as 32bits integers and are subject to overflows. + +BigInt +****** + +.. code-block:: scala + + val a = BigInt(2) + val b = BigInt(3) + + -a + a + b + a - b + a * b + a / b + a % b // a modulo b + a < b + a > b + a <= b + a >= b + a == b + +.. note:: + BigInt are mathematical integers (arbitrary size, no overflows). + +Real +**** + +``Real`` represents the mathematical real numbers (different from floating points). It is an +extension to Scala which is meant to write programs closer to their true semantics. + +.. code-block:: scala + + val a: Real = Real(2) + val b: Real = Real(3, 5) // 3/5 + + -a + a + b + a - b + a * b + a / b + a < b + a > b + a <= b + a >= b + a == b + +.. note:: + Real have infinite precision, which means their properties differ from ``Double``. + For example, the following holds: + + .. code-block:: scala + + def associativity(x: Real, y: Real, z: Real): Boolean = { + (x + y) + z == x + (y + z) + } holds + + While it does not hold with floating point arithmetic. + + +Set +*** + +.. code-block:: scala + + import stainless.lang.Set // Required to have support for Sets + + val s1 = Set(1,2,3,1) + val s2 = Set[Int]() + + s1 ++ s2 // Set union + s1 & s2 // Set intersection + s1 -- s2 // Set difference + s1 subsetOf s2 + s1 contains 42 + + +Functional Array +**************** + +.. code-block:: scala + + val a = Array(1,2,3) + + a(index) + a.updated(index, value) + a.length + + +Map +*** + +.. code-block:: scala + + import stainless.lang.Map // Required to have support for Maps + + val m = Map[Int, Boolean](42 -> false) + + m(index) + m isDefinedAt index + m contains index + m.updated(index, value) + m + (index -> value) + m + (value, index) + m.get(index) + m.getOrElse(index, value2) + + +Function +******** + +.. code-block:: scala + + val f1 = (x: Int) => x + 1 // simple anonymous function + + val y = 2 + val f2 = (x: Int) => f1(x) + y // closes over `f1` and `y` + val f3 = (x: Int) => if (x < 0) f1 else f2 // anonymous function returning another function + + list.map(f1) // functions can be passed around ... + list.map(f3(1) _) // ... and partially applied + +.. note:: + No operators are defined on function-typed expressions, so specification is + currently quite limited. + + + +Bitvectors +********** + +Bitvectors are currently only supported in GenC and for verification, but +`not for compilation `_. + +These examples are taken from `BitVectors3.scala +`_. + +.. code-block:: scala + + import stainless.math.BitVectors._ + + val x1: UInt8 = 145 + val x2: Int8 = x1.toSigned[Int8] // conversion from unsigned to signed ints + + // Bitvectors can be compared to literal constants, which are encoded as a bitvector of the same + // type as the left-hand-side bitvector. + // In the line below, `-111` get encoded internally as an `Int8`. + assert(x2 == -111) + + // In Stainless internals, `Int8` and `Byte` are the same type, but not for the surface language, + // so `toByte` allows to go from `Int8` to `Byte`. + // Similarly, we support `toShort`, `toInt`, `toLong` for conversions + // respectively from `Int16` to `Short`, `Int32` to `Int`, `Int64` to `Long`, + // and `fromByte`, `fromShort`, `fromInt`, `fromLong` for the other direction + val x3: Byte = x2.toByte + assert(x3 == -111) + + // Unsigned ints can be cast to larger unsigned types + val x4: UInt12 = x1.widen[UInt12] + assert(x4 == 145) + + // or truncated to smaller unsigned types. + val x5: UInt4 = x1.narrow[UInt4] + assert(x5 == 1) // 145 % 2^4 == 1 + + // Signed ints can also be cast to larger signed types (using sign extension) + val x6: Int8 = 120 + val x7: Int12 = x6.widen[Int12] + assert(x7 == 120) + + // and cast to smaller signed types. + // This corresponds to extracting the least significant bits of the representation + // (see `extract` here http://smtlib.cs.uiowa.edu/logics-all.shtml). + val x8: Int4 = x6.narrow[Int4] + assert(x8 == -8) + + // the `toByte`, `toShort`, `toInt`, and `toLong` methods described above + // can be used on any bitvector type. For signed integers, this corresponds + // to a narrowing or a widening operation depending on the bitvector size. + // For unsigned integers, this corresponds to first doing a widening/narrowing + // operation, and then applying `toSigned` + val x9: UInt2 = 3 + assert(x9.toInt == x9.widen[UInt32].toSigned[Int32].toInt) + + // The library also provide constants for maximum and minimum values. + assert(max[Int8] == 127) + assert(min[Int8] == -128) + + +Arrays, which are usually indexed using ``Int``, may also be indexed using the bitvector types. +This is similar to first converting the bitvector index using ``toInt``. + +Bitvector types can be understood as finite intervals of integers +(two's complement representation). For ``X`` an integer larger than ``1`` +(and at most ``256`` in Stainless): + +* ``UIntX`` is the interval :math:`[0, 2^X - 1]`, +* ``IntX`` is the interval :math:`[-2^{X-1}, 2^{X-1} - 1]`. + +Conversions between these types can be interpreted as operations on the +arrays of bits of the bitvectors, or as operations on the integers they +represent. + +* ``widen`` from ``UIntX`` to ``UIntY`` with :math:`Y > X` adds :math:`Y-X` (most significant) 0-bits, and corresponds to the identity transformation on integers. + +* ``widen`` from ``IntX`` to ``IntY`` with :math:`Y > X` copies :math:`Y-X` times the sign bit (sign-extension), and corresponds to the identity transformation on integers. + +* ``narrow`` from ``UIntX`` to ``UIntY`` with :math:`Y < X` removes the :math:`X-Y` most significant bits, + and corresponds to taking the number modulo :math:`2^Y`. + When the ``strict-arithmetic`` option is enabled, narrowing a number ``n`` to ``UIntY`` generates + a check ``n < 2^Y``. + +* ``narrow`` from ``IntX`` to ``IntY`` with :math:`Y < X` removes the :math:`X-Y` most significant bits (including the sign bit), + and corresponds to the identity for integers in the interval :math:`[-2^{Y-1}, 2^{Y-1} - 1]`. Outside this range, + the narrowing operation on a number ``n`` can be described as: 1) (unsigning) adding ``2^X`` if ``n`` is negative, + 2) (unsigned narrowing) taking the result modulo ``2^Y``, 3) (signing) removing ``2^Y`` if the result of (2) is + greater or equal than ``2^{Y-1}``. + In ``strict-arithmetic`` mode, narrowing a number ``n`` to ``IntY`` generates two checks: ``-2^{Y-1} <= n`` and ``n <= 2^{Y-1} - 1``. + +* ``toSigned`` from ``UIntX`` to ``IntX`` does not change the bitvector, and behaves as the identity for integers not larger than :math:`2^{X-1}-1`, + and subtracts :math:`2^{X}` for integers in the interval :math:`[2^{X-1}, 2^{X} - 1]`. + In ``strict-arithmetic`` mode, making a number ``n`` signed generates a check ``n <= 2^{X-1}-1``. + +* ``toUnsigned`` from ``IntX`` to ``UIntX`` does not change the bitvector, and behaves as the identity + for non-negative integers, and adds :math:`2^{X}` for negative integers (in the interval :math:`[-2^{X-1}, 0[`). + In ``strict-arithmetic`` mode, making a number ``n`` unsigned generates a check ``n >= 0``. diff --git a/_sources/references.rst.txt b/_sources/references.rst.txt new file mode 100644 index 0000000000..e27e69c991 --- /dev/null +++ b/_sources/references.rst.txt @@ -0,0 +1,45 @@ +.. _references: + +References +========== + +The Stainless/Inox stack has emerged as a cleaner and leaner version of the Leon +synthesis and verification framework. Leon is documented in several +papers and talks, which provide additional information on the algorithms +and techniques we used in Leon (and now Stainless/Inox). + + +Videos +****** + + - `Verifying and Synthesizing Software with Recursive Functions `_ (ICALP 2014) + - `Executing Specifications using Synthesis and Constraint Solving `_ (RV 2013) + - `Video of Verifying Programs in Leon `_ (2013) + + +Papers +****** + + - `System FR: Formalized Foundations for the Stainless Verifier `_, by *Jad Hamza*, *Nicolas Voirol*, and *Viktor Kuncak*. Object-Oriented Programming, Systems, Languages & Applications (OOPSLA), 2019. + - `Translating Scala Programs to Isabelle/HOL (System Description) `_, by *Lars Hupel* and *Viktor Kuncak*. International Joint Conference on Automated Reasoning (IJCAR), 2016. + - `Counter-example complete verification for higher-order functions `_, by *Nicolas Voirol*, *Etienne Kneuss*, and *Viktor Kuncak*. Scala Symposium, 2015. + - `Sound reasoning about integral data types with a reusable SMT solver interface `_, by *Régis Blanc* and *Viktor Kuncak*. Scala Symposium, 2015. + - `Deductive program repair `_, by *Etienne Kneuss*, *Manos Koukoutos*, and *Viktor Kuncak*. Computer-Aided Verification (CAV), 2015. + - `Symbolic resource bound inference for functional programs `_, by *Ravichandhran Madhavan* and *Viktor Kuncak*. Computer Aided Verification (CAV), 2014. + - `Checking data structure properties orders of magnitude faster `_, by *Emmanouil Koukoutos* and *Viktor Kuncak*. Runtime Verification (RV), 2014 + - `Synthesis Modulo Recursive Functions `_, by *Etienne Kneuss*, *Viktor Kuncak*, *Ivan Kuraj*, and *Philippe Suter*. OOPSLA 2013 + - `Executing specifications using synthesis and constraint solving (invited talk) `_, by Viktor Kuncak, Etienne Kneuss, and Philippe Suter. Runtime Verification (RV), 2013 + - `An Overview of the Leon Verification System `_, by *Régis Blanc*, *Etienne Kneuss*, *Viktor Kuncak*, and *Philippe Suter*. Scala Workshop 2013 + - `Reductions for synthesis procedures `_, by *Swen Jacobs*, *Viktor Kuncak*, and *Phillippe Suter*. Verification, Model Checking, and Abstract Interpretation (VMCAI), 2013 + - `Constraints as Control `_, *Ali Sinan Köksal*, *Viktor Kuncak*, *Philippe Suter*, Principles of Programming Languages (POPL), 2012 + - `Satisfiability Modulo Recursive Programs `_, by *Philippe Suter*, *Ali Sinan Köksal*, *Viktor Kuncak*, Static Analysis Symposium (SAS), 2011 + - `Scala to the power of Z3: Integrating SMT and programming `_, by *Ali Sinan Köksal*, *Viktor Kuncak*, and *Philippe Suter*. Computer-Aideded Deduction (CADE) Tool Demo, 2011 + - `Decision Procedures for Algebraic Data Types with Abstractions `_, by *Philippe Suter*, *Mirco Dotta*, *Viktor Kuncak*. Principles of Programming Languages (POPL), 2010 + - `Complete functional synthesis `_, by *Viktor Kuncak*, *Mikael Mayer*, *Ruzica Piskac*, and *Philippe Suter*. ACM SIGPLAN Conf. Programming Language Design and Implementation (PLDI), 2010. + + + +Books +***** + + - `Concrete Semantics with Isabelle/HOL `_, by *Tobias Nipkow* and *Gerwin Klein*. diff --git a/_sources/tutorial.rst.txt b/_sources/tutorial.rst.txt new file mode 100644 index 0000000000..cc4eb0a501 --- /dev/null +++ b/_sources/tutorial.rst.txt @@ -0,0 +1,448 @@ +.. _tutorial: + +Tutorial: Sorting +================= + +This tutorial shows how to: + + * use `ensuring`, `require`, and `holds` constructs + * learn the difference between `Int` and `BigInt` + * define lists as algebraic data types + * use sets and recursive function to specify data structures + +See :doc:`gettingstarted` about how to setup the command line +tool. + +Warm-up: Max +------------ + +As a warm-up illustrating verification, we define and debug a `max` function +and specify its properties. Stainless uses Scala constructs +`require` and `ensuring` to document preconditions and +postconditions of functions. Note that, in addition to +checking these conditions at run-time (which standard Scala +does), Stainless can analyze the specifications statically and +prove them for *all* executions, or, if they are wrong, automatically find +inputs for which the conditions fail. + +Consider the following definition inside of an object `TestMax`. + +.. code-block:: scala + + object TestMax { + def max(x: Int, y: Int): Int = { + val d = x - y + if (d > 0) x + else y + } ensuring(res => + x <= res && y <= res && (res == x || res == y)) + } + +A Stainless program consists of one or more modules delimited by +`object` and `class` declarations. +The code of `max` attempts to compute the maximum of two given arguments +by subtracting them. If the result is positive, it returns +the first one, otherwise, it returns the second one. + +To specify the correctness of the computed result, we use +the `ensuring` clause. In this case, the clause specifies +that the result is larger than `x` and than `y`, and that it +equals to one of them. The construct `ensuring(res => P)` +denotes that, if we denote by `res` the return value of the +function, then `res` satisfies the boolean-valued expression +`P`. The name `res` we chose is an arbitrary bound variable +(even though we often tend to use `res`). + +We can evaluate this code on some values by writing +parameterless functions and inspecting what they evaluate +to. The web interface will display these results for us. + +.. code-block:: scala + + def test1 = max(10, 5) + def test2 = max(-5, 5) + def test3 = max(-5, -7) + +The code seems to work correctly on the example values. +However, Stainless automatically finds that it is not correct: + +.. code-block:: text + + [ Info ] - Now solving 'postcondition' VC for max @6:16... + [ Info ] - Result for 'postcondition' VC for max @6:16: + [Warning ] => INVALID + [Warning ] Found counter-example: + [Warning ] y: Int -> 2147483647 + [Warning ] x: Int -> -2147483648 + + [ Info ] - Now solving 'postcondition' VC for max @7:10... + [ Info ] - Result for 'postcondition' VC for max @7:10: + [Warning ] => INVALID + [Warning ] Found counter-example: + [Warning ] y: Int -> -2147483648 + [Warning ] x: Int -> 1 + + [ Info ] - Now solving 'body assertion: Subtraction overflow' VC for max @5:13... + [ Info ] - Result for 'body assertion: Subtraction overflow' VC for max @5:13: + [Warning ] => INVALID + [Warning ] Found counter-example: + [Warning ] y: Int -> -2147483648 + [Warning ] x: Int -> 0 + +Here, Stainless emits three distinct verification conditions: + +* One which corresponds to the postcondition of ``max`` when we take the `then` branch + of the ``if`` statement, on line 6. + +* Another one for the postcondition of ``max`` when we take the `else` branch + of the ``if`` statement, on line 7. + +* A last one with an overflow check for the subtraction on line 5. + +Let us look at the first verification condition: + +.. code-block:: text + + - Now solving 'postcondition' VC for max @6:16... + - Result for 'postcondition' VC for max @6:16: + => INVALID + Found counter-example: + y: Int -> 2147483647 + x: Int -> -2147483648 + +Stainless tells us that it found two input for which the ``ensuring`` clause of the +``max`` function evaluates to ``false``. The second verification is similar. + +We may wish to define a test method + +.. code-block:: scala + + def test4 = max(-1639624704, 1879048192) + +whose evaluation indeed results in ``ensuring`` condition being violated. +The problem is due to overflow of 32-bit integers, due to which +the value `d` becomes positive, even though `x` is negative and thus smaller than +the large positive value `y`. + +In fact, Stainless alerts us of this very problem in the third verification condition, +to help us pin point the place where the overflow occured. + +.. note:: + + As in Scala, the `Int` type denotes 32-bit integers with the usual signed arithmetic + operations from computer architecture and the JVM specification. + +To use unbounded integers, we simply change the types to +`BigInt`, obtaining a program that verifies (and, as +expected, passes all the test cases). + +.. code-block:: scala + + def max(x: BigInt, y: BigInt): BigInt = { + val d = x - y + if (d > 0) x + else y + } ensuring(res => + x <= res && y <= res && (res == x || res == y)) + +As a possibly simpler specification, we could have also +defined the reference implementation + +.. code-block:: scala + + def rmax(x: BigInt, y: BigInt) = { + if (x <= y) y else x + } + +and then used as the postcondition of `max` simply + +.. code-block:: scala + + ensuring (res => res == rmax(x,y)) + +In general, Stainless uses both function body and function +specification when reasoning about the function and its +uses. Thus, we need not repeat in the postcondition those +aspects of function body that follow directly through +inlining the function, but we may wish to state those +that require induction to prove. + +The fact that we can use functions in preconditions +and postconditions allows us to state fairly general +properties. For example, the following lemma verifies +a number of algebraic properties of `max`. + +.. code-block:: scala + + def max_lemma(x: BigInt, y: BigInt, z: BigInt): Boolean = { + max(x,x) == x && + max(x,y) == max(y,x) && + max(x,max(y,z)) == max(max(x,y), z) && + max(x,y) + z == max(x + z, y + z) + } holds + +Here `holds` operator on the function body is an +abbreviation for the postcondition stating that the returned +result is always true, that is, for + +.. code-block:: scala + + ensuring(res => res==true) + +As a guideline, we typically use `holds` to express such +algebraic properties that relate multiple invocations of +functions, whereas we use `ensuring` to document property of +an arbitrary single invocation of a function. Stainless is more likely to automatically +use the property of a function if it is associated with it using +`ensuring` than using an external lemma. + +Going back to our buggy implementation of `max` on `Int`-s, +an alternative to using `BigInt`-s is to decide that +the method should only be used under certain conditions, +such as `x` and `y` being non-negative. To specify the +conditions on input, we use the `require` clause. + +.. code-block:: scala + + def max(x: Int, y: Int): Int = { + require(0 <= x && 0 <= y) + val d = x - y + if (d > 0) x + else y + } ensuring (res => + x <= res && y <= res && (res == x || res == y)) + +This program verifies and indeed works correctly on +non-negative 32-bit integers as inputs. + +**Question:** What if we restrict the inputs to `max` to be +`a)` non-positive, or `b)` strictly negative? Modify the +`require` clause for each case accordingly and explain the +behavior of Stainless. See the note below, as well. + +.. note:: + + By default, Stainless will emit verification conditions to + check that arithmetic operations on sized integers such as + `Int` cannot overflow. To opt-out of this behavior, eg. when + such wrapping semantics are desired, one can wrap the offending + expression in a call to `stainless.math.wrapping`: + + .. code-block:: scala + + import stainless.math.wrapping + + def doubleOverflow(x: Int): Int = { + wrapping { x + x } + } + +In the sequel, we will mostly use `BigInt` types. + +Defining Lists and Their Properties +----------------------------------- + +We next consider sorting an unbounded number of elements. +For this purpose, we define a data structure for lists of +integers. Stainless has a built-in data type of parametric +lists, see :doc:`library`, but here we define +our own variant instead. + +Lists +^^^^^ + +We use a recursive algebraic data type +definition, expressed using Scala's **case classes**. + +.. code-block:: scala + + sealed abstract class List + case object Nil extends List + case class Cons(head: BigInt, tail: List) extends List + +We can read the definition as follows: the set of lists is +defined as the least set that satisfies them: + + * empty list `Nil` is a list + * if `head` is an integer and `tail` is a `List`, then + `Cons(head,tail)` is a `List`. + +Each list is constructed by applying the above two rules +finitely many times. A concrete list containing elements 5, +2, and 7, in that order, is denoted + +.. code-block:: scala + + Cons(5, Cons(2, Cons(7, Nil))) + +Having defined the structure of lists, we can move on to +define some semantic properties of lists that are of +interests. For this purpose, we use recursive functions +defined on lists. + +Size of a List +^^^^^^^^^^^^^^ + +As the starting point, we define the size of a list. + +.. code-block:: scala + + def size(l: List) : BigInt = (l match { + case Nil => 0 + case Cons(x, rest) => 1 + size(rest) + }) + +The definition uses *pattern matching* to define size of the +list in the case it is empty (where it is zero) and when it +is non-empty, or, if it's non-empty, then it has a head `x` +and the rest of the list `rest`, so the size is one plus the +size of the rest. Thus `size` is a recursive function. A +strength of Stainless is that it allows using such recursive +functions in specifications. + +It makes little sense to try to write a complete +specification of `size`, given that its recursive definition +is already a pretty clear description of its +meaning. However, it is useful to add a consequence of this +definition, namely that the size is non-negative. The reason +is that Stainless most of the time reasons by unfolding `size`, +and the property of size being non-negative is not revealed +by such unfolding. Once specified, the non-negativity is +easily proven and Stainless will make use of it. + +.. code-block:: scala + + + def isize(l: List) : Int = (l match { + case Nil => 0 + case Cons(x, rest) => { + val rSize = isize(rest) + if (rSize == Int.MaxValue) rSize + else 1 + rSize + } + }).ensuring(res => res >= 0) + +In some cases, it may be helpful to define a size function +that returns a bounded integer type, such as the 32-bit signed integer ```Int``. +One useful way to do this is to define function as follows: + +.. code-block:: scala + + def isize(l: List) : Int = (l match { + case Nil => 0 + case Cons(x, rest) => { + val rSize = isize(rest) + if (rSize == Int.Max) rSize + else 1 + rSize + } + }) ensuring(res => res >= 0) + +The above ``isize`` function satisfies the usual recursive definition for all but a huge +lists, returns a non-negative integer, and ensures that if isize returns a small +number, then the list is indeed small. + +Sorted Lists +^^^^^^^^^^^^ + +We define properties of values simply as executable +predicates that check if the property holds. The following +is a property that a list is sorted in a strictly ascending +order. + +.. code-block:: scala + + def isSorted(l : List) : Boolean = l match { + case Nil => true + case Cons(_,Nil) => true + case Cons(x1, Cons(x2, rest)) => + x1 < x2 && isSorted(Cons(x2,rest)) + } + +Insertion into Sorted List +-------------------------- + +Consider the following specification of insertion into a sorted list. It's a +building block for an insertion sort. + +.. code-block:: scala + + def sInsert(x : BigInt, l : List) : List = { + require(isSorted(l)) + l match { + case Nil => Cons(x, Nil) + case Cons(e, rest) if (x == e) => l + case Cons(e, rest) if (x < e) => Cons(x, Cons(e,rest)) + case Cons(e, rest) if (x > e) => Cons(e, sInsert(x,rest)) + } + } ensuring {(res:List) => isSorted(res)} + +Stainless verifies that the returned list is indeed sorted. Note +how we are again using a recursively defined function to +specify another function. We can introduce a bug into the +definition above and examine the counterexamples that Stainless +finds. + +Being Sorted is Not Enough +-------------------------- + +Note, however, that a function such as this one is also correct. + +.. code-block:: scala + + def fsInsert(x : BigInt, l : List) : List = { + require(isSorted(l)) + Nil + } ensuring {(res:List) => isSorted(res)} + +So, our specification may be considered weak, because it does +not say anything about the elements. + +Using Size in Specification +--------------------------- + +Consider a stronger additional postcondition property: + +.. code-block:: scala + + size(res) == size(l) + 1 + +Does it hold? If we try to add it, we obtain a counterexample. +A correct strengthening, taking into account that the element +may or may not already be in the list, is the following. + +.. code-block:: scala + + size(l) <= size(res) && size(res) <= size(l) + 1 + +Using Content in Specification +------------------------------ + +A stronger specification needs to talk about the `content` +of the list. + +.. code-block:: scala + + def sInsert(x : BigInt, l : List) : List = { + require(isSorted(l)) + l match { + case Nil => Cons(x, Nil) + case Cons(e, rest) if (x == e) => l + case Cons(e, rest) if (x < e) => Cons(x, Cons(e,rest)) + case Cons(e, rest) if (x > e) => Cons(e, sInsert(x,rest)) + } + } ensuring {(res:List) => + isSorted(res) && content(res) == content(l) ++ Set(x)} + +To compute `content`, in this example we use sets (even +though in general, it might be better to use bags +i.e. multisets). + +.. code-block:: scala + + def content(l: List): Set[BigInt] = l match { + case Nil => Set() + case Cons(i, t) => Set(i) ++ content(t) + } + + +This completes the tutorial. To learn more, check the rest of this +documentation and browse the examples provided with Stainless. diff --git a/_sources/verification.rst.txt b/_sources/verification.rst.txt new file mode 100644 index 0000000000..06f05b71b7 --- /dev/null +++ b/_sources/verification.rst.txt @@ -0,0 +1,281 @@ +.. _verification: + +Verification conditions +======================= + +Software verification aims at making software safer. In its typical use case, +it is a tool that takes as input the source code of a program with +specifications as annotations and attempt to prove --- or disprove --- their +validity. + +One of the core modules of Stainless is a verifier for the subset of Scala described +in the sections :doc:`purescala` and :doc:`imperative`. In this +section, we describe the specification language that can be used to declare +properties of programs, as well as the safety properties automatically checked +by Stainless. We also discuss how Stainless can be used to prove mathematical theorems. + + +Given an input program, Stainless generates individual verification conditions +corresponding to different properties of the program. A program is correct if +all of the generated verification conditions are ``valid``. The validity of some +conditions depends on the validity of other conditions --- typically a +postcondition is ``valid`` assuming the precondition is ``valid``. + +For each function, Stainless attempts to verify its contract, if there is one. A +*contract* is the combination of a *precondition* and a *postcondition*. A +function meets its contract if, for any input parameter that passes the +precondition, the postcondition holds after executing the function. +Preconditions and postconditions are annotations given by the user --- they are +the specifications and hence cannot be inferred by a tool and must be provided. + +In addition to user-provided contracts, Stainless will also generate a few safety +verification conditions of its own. It will check that all of the array +accesses are within proper bounds, and that pattern matching always covers all +possible cases, even given complex precondition. The latter is different from +the Scala compiler checks on pattern matching exhaustiveness, as Stainless considers +information provided by (explicit or implicit) preconditions to the ``match`` +expression. + +Postconditions +-------------- + +One core concept in verification is to check the contract of functions. The most +important part of a contract is the postcondition. The postcondition specifies +the behavior of the function. It takes into account the precondition and only +asserts the property of the output when the input satisfies the precondition. + +Formally, we consider a function with a single parameter (one can generalize +the following for any number of parameters): + +.. code-block:: scala + + def f(x: A): B = { + require(prec) + body + } ensuring(r => post) + +where, :math:`\mbox{prec}(x)` is a Boolean expression with free variables +contained in :math:`\{ x \}`, :math:`\mbox{body}(x)` is an expression with +free variables contained in :math:`\{ x \}` and :math:`\mbox{post}(x, r)` is a +Boolean expression with free variables contained in :math:`\{ x, r \}`. The +types of :math:`x` and :math:`r` are respectively ``A`` and ``B``. We write +:math:`\mbox{expr}(a)` to mean the substitution in :math:`\mbox{expr}` of its +free variable by :math:`a`. + +Stainless attempts to prove the following theorem: + +.. math:: + + \forall x. \mbox{prec}(x) \implies \mbox{post}(x, \mbox{body}(x)) + +If Stainless is able to prove the above theorem, it returns ``valid`` for the +function ``f``. This gives you a guarantee that the function ``f`` is correct +with respect to its contract. + +However, if the theorem is not valid, Stainless will return a counterexample to the +theorem. The negation of the theorem is: + +.. math:: + + \exists x. \mbox{prec}(x) \land \neg \mbox{post}(x, \mbox{body}(x)) + +and to prove the validity of the negation, Stainless finds a witness :math:`x` --- a +counterexample --- such that the precondition is verified and the postcondition +is not. + +The general problem of verification is undecidable for a Turing-complete +language, and the Stainless language is Turing-complete. So Stainless has to be +incomplete in some sense. Generally, Stainless will eventually find a counterexample +if one exists. However, in practice, some program structures require too many +unrollings and Stainless is likely to timeout (or being out of memory) before +finding the counterexample. When the postcondition is valid, it could also +happen that Stainless keeps unrolling the program forever, without being able to +prove the correctness. We discuss the exact conditions for this in the +chapter on Stainless's algorithms. + +Preconditions +------------- + +Preconditions are used as part of the contract of functions. They are a way to +restrict the input to only relevant inputs, without having to implement guards +and error handling in the functions themselves. + +Preconditions are contracts that the call sites should respect, and thus are +not checked as part of verifying the function. Given the following definition: + +.. code-block:: scala + + def f(x: A): B = { + require(prec) + body + } + + +For each call site in the whole program (including in ``f`` itself): + +.. code-block:: scala + + ... + f(e) + ... + +where the expression :math:`\mbox{e}(x)` is an expression of type ``A`` with +free variables among :math:`\{ x \}`. Let us define the path condition on :math:`x` +at that program point as :math:`\mbox{pc}(x)`. The path condition is a formula that +summarizes the facts known about :math:`x` at that call site. A typical example is +when the call site is inside an if expression: + +.. code-block:: scala + + if(x > 0) + f(x) + +The path condition on :math:`x` would include the fact that :math:`x > 0`. This +path condition is then used as a precondition of proving the validity of the +call to :math:`\mbox{f}`. Formally, for each such call site, Stainless will attempt +to prove the following theorem: + +.. math:: + + \forall x. \mbox{pc}(x) \implies \mbox{prec}(\mbox{e}(x)) + +Stainless will generate one such theorem for each static call site of a function with +a precondition. + +.. note:: + + Stainless only assumes an open program model, where any function could be called from + outside of the given program. In particular, Stainless will not derive a precondition + to a function based on known information in the context of the calls, such as + knowing that the function is always given positive parameters. Any information needed + to prove the postcondition will have to be provided as part of the precondition + of a function. + + +Sharing bindings between specifications and function body +--------------------------------------------------------- + +The example `ValEnsuring `_ +shows that Stainless supports multiple ``require``'s (in functions, but not for ADT invariants), and +shows how to share a `val` binding between precondition, postcondition, and function body. + + +Loop invariants +--------------- + +Stainless supports annotations for loop invariants in :doc:`imperative`. To +simplify the presentation we will assume a single variable :math:`x` is in +scope, but the definitions generalize to any number of variables. Given the +following program: + +.. code-block:: scala + + (while(cond) { + body + }) invariant(inv) + +where the Boolean expression :math:`\mbox{cond}(x)` is over the free variable +:math:`x` and the expression :math:`\mbox{body}(x, x')` relates the value of +:math:`x` when entering the loop to its updated value :math:`x'` on loop exit. +The expression :math:`\mbox{inv}(x)` is a Boolean formula over the free +variable :math:`x`. + +A loop invariant must hold: + (1) when the program enters the loop initially + (2) after each completion of the body + (3) right after exiting the loop (when the condition turns false) + +Stainless will prove the points (1) and (2) above. Together, and by induction, they imply +that point (3) holds as well. + +Stainless also supports ``noReturnInvariant`` (see `ReturnInWhile3 `_) to describe loop invariants that are allowed to be broken +after a :doc:`return ` (can be combined with ``invariant``). + +Decrease annotation in loops +---------------------------- + +One can also specify that the value of a given expression of numerical type decreases +at each loop iteration by adding a ``decreases`` measure within the loop body: + +.. code-block:: scala + + while(cond) { + decreases(expr) + body + } + +Stainless will then emit a verification condition that checks whether the expression +is strictly positive and decreases at each iteration. + +Array access safety +------------------- + +Stainless generates verification conditions for the safety of array accesses. For +each array variable, Stainless carries along a symbolic information on its length. +This information is used to prove that each expression used as an index in the +array is strictly smaller than that length. The expression is also checked to +be positive. + +ADT invariants +-------------- + +Stainless lets the user write ADT invariants with the ``require`` keyword. +Internally, such invariants are extracted as methods (named ``inv``). Whenever, +an ADT is constructed, and to make sure that the invariant is true, a +verification condition is generated with a call to the corresponding ``inv`` +method. + +The Stainless annotation ``@inlineInvariant`` used on an ADT or one of its +ancestors can be used to inline the call to ``inv`` in the verification +condition, as shown in the following example. This annotation is only +supported when ``--type-checker=true`` (which is the case by default). + +.. code-block:: scala + + import stainless.annotation._ + + object InlineInvariant { + sealed abstract class A + + case class B(x: BigInt) extends A { + require(x >= 50) + } + + @inlineInvariant + case class C(x: BigInt) extends A { + require(x >= 50) + } + + def f(): A = { + B(100) // VC: inv(B(100)) + c(100) // VC: 100 >= 50 (call to `inv` was inlined) + } + } + + + +Pattern matching exhaustiveness +------------------------------- + +Stainless verifies that pattern matching is exhaustive. The regular Scala compiler +only considers the types of expression involved in pattern matching, but Stainless +will consider information such as precondition to formally prove the +exhaustiveness of pattern matching. + +As an example, the following code should issue a warning with Scala: + +.. code-block:: scala + + abstract class List + case class Cons(head: Int, tail: List) extends List + case object Nil extends List + + def getHead(l: List): Int = { + require(!l.isInstanceOf[Nil]) + l match { + case Cons(x, _) => x + } + } + +But Stainless will prove that the pattern matching is actually exhaustive, +relying on the given precondition. diff --git a/_sources/wrap.rst.txt b/_sources/wrap.rst.txt new file mode 100644 index 0000000000..7094bda356 --- /dev/null +++ b/_sources/wrap.rst.txt @@ -0,0 +1,239 @@ +.. _wrap: + +Working With Existing Code +========================== + +While the subset of Scala (namely, PureScala) that is currently supported by Stainless +is already expressive enough to implement a lot of different data structures and algorithms, +it is often the case that one would like to avoid re-implementing a piece of code from scratch +in this fragment, but rather re-use some existing code, whether it is part of the codebase or +pulled in from a Java or Scala library. + +A wrapper for TrieMap +--------------------- + +As a running example, let's write a wrapper for the ``scala.collection.concurrent.TrieMap`` class. +A first attempt to wrap it in a regular Stainless datatype could look like the following: + +.. code-block:: scala + + import stainless.lang._ + import stainless.annotation._ + + import scala.collection.concurrent.TrieMap + + case class TrieMapWrapper[K, V](theMap: TrieMap[K, V]) + +Unfortunately, this will not work as Stainless will complain that it does not +know about the ``TrieMap`` type. In order to work around this, one can annotate +the field with the ``@extern`` annotation, which tells Stainless that the type +should be treated as opaque. + +.. code-block:: scala + + import stainless.lang._ + import stainless.annotation._ + + import scala.collection.concurrent.TrieMap + import scala.collection.concurrent.TrieMap + + case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) + +Extern methods +-------------- + +Let's now define a forwarding method for the ``contains`` method of ``TrieMap``: + +.. code-block:: scala + + import stainless.lang._ + import stainless.annotation._ + + import scala.collection.concurrent.TrieMap + import scala.collection.concurrent.TrieMap + + case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) { + + def contains(k: K): Boolean = { + theMap contains k + } + } + +Once again, this will fail because, from Stainless' point of view, ``theMap`` has an opaque type +and thus has no ``contains`` method. By annotating the method itself with ``@extern``, Stainless will +not attempt to extract the method's body, and we can thus freely refer to any of ``TrieMap``'s methods: + +.. code-block:: scala + + import stainless.lang._ + import stainless.annotation._ + + import scala.collection.concurrent.TrieMap + + case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) { + + @extern + def contains(k: K): Boolean = { + theMap contains k + } + } + +.. note:: + Methods marked ``@extern`` are allowed to mention types which Stainless is not able to extract. + Such types will be replaced by the *unknown type* ``?`` during the recovery phase. + One can inspect which types are replaced during recovery, by supplying the ``--debug=recovery`` flag. + +Contracts +--------- + +Let's also define another extern function, which creates a new empty map: + +.. code-block:: scala + + object TrieMapWrapper { + @extern + def empty[K, V]: TrieMapWrapper[K, V] = { + TrieMapWrapper(TrieMap.empty[K, V]) + } + } + + def prop1 = { + val wrapper = TrieMapWrapper.empty[Int, String] + assert(!wrapper.contains(42)) // invalid + } + +Indeed, because Stainless does not know about ``TrieMap.empty``, it cannot assume +by itself that the result of ``TrieMapWrapper.empty`` does not contain any entries. + +We can remedy to that by adding a postcondition to the ``empty`` function which says that, +for any key ``k`` of type ``K``, the result of ``TrieMapWrapper.empty`` does not contain the key ``k``. + +.. code-block:: scala + + object TrieMapWrapper { + @extern + def empty[K, V]: TrieMapWrapper[K, V] = { + TrieMapWrapper(TrieMap.empty[K, V]) + } ensuring { res => + forall((k: K) => !res.contains(k)) + } + } + +The assertion above now verifies successfully. + +Purity annotations +------------------ + +Let's now see what happens when we call ``contains`` twice: + +.. code-block:: scala + + def prop1 = { + val wrapper = TrieMapWrapper.empty[Int, String] + assert(!wrapper.contains(42)) + assert(!wrapper.contains(42)) + } + +.. code-block:: text + + ┌───────────────────┐ + ╔═╡ stainless summary ╞═══════════════════════════════════════════════════╗ + ║ └───────────────────┘ ║ + ║ prop1 body assertion valid U:smt-z3 ExternField.scala:46:5 0.018 ║ + ║ prop1 body assertion invalid U:smt-z3 ExternField.scala:47:5 0.110 ║ + ╚═════════════════════════════════════════════════════════════════════════╝ + +The second assertion (perhaps surprisingly) fails to verify. This stems from the fact that Stainless assumes +by default that extern functions and methods mutate their arguments. Indeed, because Stainless +does not know about the body of such methods, it cannot know whether such a function is pure or not. +It is thus up to the user to instruct Stainless otherwise, by annotating the function with ``@pure``: + +.. code-block:: scala + + case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) { + + @extern @pure + def contains(k: K): Boolean = { + theMap contains k + } + } + +With the annotation, the two assertions above now verify: + +.. code-block:: text + + ┌───────────────────┐ + ╔═╡ stainless summary ╞═════════════════════════════════════════════════╗ + ║ └───────────────────┘ ║ + ║ prop1 body assertion valid U:smt-z3 ExternField.scala:46:5 0.018 ║ + ║ prop1 body assertion valid U:smt-z3 ExternField.scala:48:5 0.110 ║ + ╚═══════════════════════════════════════════════════════════════════════╝ + +We can now define the other methods of interest, with their appropriate contract: + +.. code-block:: scala + + import stainless.lang._ + import stainless.annotation._ + import scala.annotation.meta.field + + import scala.collection.concurrent.TrieMap + + case class TrieMapWrapper[K, V]( + @extern + theMap: TrieMap[K, V] + ) { + + @extern @pure + def contains(k: K): Boolean = { + theMap contains k + } + + @extern + def insert(k: K, v: V): Unit = { + theMap.update(k, v) + } ensuring { + this.contains(k) && + this.apply(k) == v + } + + @extern @pure + def apply(k: K): V = { + require(contains(k)) + theMap(k) + } + } + + object TrieMapWrapper { + @extern @pure + def empty[K, V]: TrieMapWrapper[K, V] = { + TrieMapWrapper(TrieMap.empty[K, V]) + } ensuring { res => + forall((k: K) => !res.contains(k)) + } + } + +And we can now reason about our wrapper for ``TrieMap``: + +.. code-block:: scala + + def prop2 = { + val wrapper = TrieMapWrapper.empty[BigInt, String] + assert(!wrapper.contains(42)) + wrapper.insert(42, "Hello") + assert(wrapper.contains(42)) + assert(wrapper(42) == "Hello") + } + +.. code-block:: text + + ┌───────────────────┐ + ╔═╡ stainless summary ╞═════════════════════════════════════════════════════════════════════════════════╗ + ║ └───────────────────┘ ║ + ║ prop2 body assertion valid U:smt-z3 ExternField.scala:56:5 0.023 ║ + ║ prop2 body assertion valid U:smt-z3 ExternField.scala:58:5 0.095 ║ + ║ prop2 body assertion valid U:smt-z3 ExternField.scala:59:5 0.080 ║ + ║ prop2 precond. (apply[BigInt, String](wrapper, 42)) valid U:smt-z3 ExternField.scala:59:12 0.200 ║ + ╟-------------------------------------------------------------------------------------------------------╢ + ║ total: 4 valid: 4 (0 from cache) invalid: 0 unknown: 0 time: 0.398 ║ + ╚═══════════════════════════════════════════════════════════════════════════════════════════════════════╝ diff --git a/_static/basic.css b/_static/basic.css new file mode 100644 index 0000000000..603f6a8798 --- /dev/null +++ b/_static/basic.css @@ -0,0 +1,905 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar 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!console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { + this.initOnKeyListeners(); + } + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keydown(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box, textarea, dropdown or button + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' + && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey + && !event.shiftKey) { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + break; + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + break; + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 0000000000..16442b3a64 --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,12 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '0.9.1', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false +}; \ No newline at end of file diff --git a/_static/file.png b/_static/file.png new file mode 100644 index 0000000000..a858a410e4 Binary files /dev/null and b/_static/file.png differ diff --git a/_static/images/pipeline.svg b/_static/images/pipeline.svg new file mode 100644 index 0000000000..b9be3c3556 --- /dev/null +++ b/_static/images/pipeline.svg @@ -0,0 +1 @@ +Stainless PipelineUserFrontendCompilerCallBackRegistryComponentUse ICG: Incremental Computational GraphVerification and/orTermination;Run in threadsVerification and/orTerminationdotc, scalac, ...Update Code;Run FrontendRun CompilerTypecheckCompilation Unit(xlang.Trees)Register newFunDef & ClassDefUse ICG to identifywhat is ready orneed to be recomputed.Option[self-containedprogram]transform trees, generate VCs, send to the solvers, ...The "loop" is executed once more to trigger the verification ofnon-sealed classes now that all the overridden functions are known.wait for Component's ReportsReports...Reports...Reports...All ReportsDisplay reportsunder --watch modethe process restart.The Registry's ICG is the center piece thatenables stainless to verify modified functionswhen the code is updated.loop[for each compilation unit]opt[solve] \ No newline at end of file diff --git a/_static/images/pipeline.txt b/_static/images/pipeline.txt new file mode 100644 index 0000000000..95d10166ae --- /dev/null +++ b/_static/images/pipeline.txt @@ -0,0 +1,73 @@ +# http://sequencediagram.org/ + +title Stainless Pipeline + +actor User +entity Frontend +entity Compiler +control CallBack +database Registry +actor Component + +parallel + + note over Registry: Use ICG:\n Incremental\n Computational\n Graph + + note over Component: Verification and/or\nTermination;\nRun in threads + + note over CallBack: Verification and/or\nTermination + + note over Compiler: dotc, scalac, ... + +parallel off + +activate User + +User -> Frontend: Update Code;\nRun Frontend +activate Frontend + +Frontend -> Compiler: Run Compiler +activate Compiler + +Compiler --> Compiler: Typecheck + +loop for each compilation unit + +Compiler -> CallBack: Compilation Unit\n(xlang.Trees) +activate CallBack + +CallBack ->> Registry: Register new\nFunDef & ClassDef +activate Registry +Registry ->> Registry: Use ICG to identify\nwhat is ready or\nneed to be recomputed. +Registry --> CallBack: Option[self-contained\nprogram] +deactivate Registry + +opt solve + CallBack -> Component: transform trees, generate VCs, ... +end opt + +deactivate CallBack + +end + +deactivate Compiler + +note over Frontend,Component: The "loop" is executed once more to trigger the verification of\nnon-sealed classes now that all the overridden functions are known. + +Frontend -> CallBack: wait for Component's Reports +Component -> CallBack: Reports... +Component -> CallBack: Reports... +Component -> CallBack: Reports... +CallBack -> Frontend: All Reports + +Frontend -> User: Display reports +deactivate Frontend + +parallel + + note over User: under \--watch mode\nthe process restart. + + note over Registry: The Registry's ICG is the center piece that\nenables stainless to verify modified functions\nwhen the code is updated. + +parallel off + diff --git a/_static/invalid/AbstractRefinementMap.html b/_static/invalid/AbstractRefinementMap.html new file mode 100644 index 0000000000..7330c3e48b --- /dev/null +++ b/_static/invalid/AbstractRefinementMap.html @@ -0,0 +1,50 @@ + + + +invalid/AbstractRefinementMap.scala + + +

AbstractRefinementMap.scala [raw]


+
import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+
+object AbstractRefinementMap {
+
+  case class ~>[A,B](private val f: A => B, ens: B => Boolean) {
+    require(forall((b: B) => ens.pre(b)))
+
+    lazy val pre = f.pre
+
+    def apply(x: A): B = {
+      require(f.pre(x))
+      f(x)
+    } ensuring(ens)
+// Counterexample for postcondition violation in `apply`:
+//   when x is:
+//     A#0
+//   when thiss is:
+//     ~>[A, B]((x$304: A) => if (x$304 == A#0) {
+//       B#0
+//     } else {
+//       B#0
+//     }, (x$308: B) => if (x$308 == B#0) {
+//       false
+//     } else if (true) {
+//       false
+//     } else {
+//       false
+//     })
+  }
+
+  def map[A, B](l: List[A], f: A ~> B): List[B] = {
+    require(forall((x:A) => l.contains(x) ==> f.pre(x)))
+    l match {
+      case Cons(x, xs) => Cons[B](f(x), map(xs, f))
+      case Nil() => Nil[B]()
+    }
+  } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) }
+}
+
+
+

back

diff --git a/_static/invalid/AbstractRefinementMap.scala b/_static/invalid/AbstractRefinementMap.scala new file mode 100644 index 0000000000..d11db628b1 --- /dev/null +++ b/_static/invalid/AbstractRefinementMap.scala @@ -0,0 +1,26 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ + +object AbstractRefinementMap { + + case class ~>[A,B](private val f: A => B, ens: B => Boolean) { + require(forall((b: B) => ens.pre(b))) + + lazy val pre = f.pre + + def apply(x: A): B = { + require(f.pre(x)) + f(x) + } ensuring(ens) + } + + def map[A, B](l: List[A], f: A ~> B): List[B] = { + require(forall((x:A) => l.contains(x) ==> f.pre(x))) + l match { + case Cons(x, xs) => Cons[B](f(x), map(xs, f)) + case Nil() => Nil[B]() + } + } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) } +} + diff --git a/_static/invalid/AssociativityProperties.html b/_static/invalid/AssociativityProperties.html new file mode 100644 index 0000000000..dec46b7d76 --- /dev/null +++ b/_static/invalid/AssociativityProperties.html @@ -0,0 +1,81 @@ + + + +invalid/AssociativityProperties.scala + + +

AssociativityProperties.scala [raw]


+
import stainless.lang._
+
+object AssociativityProperties {
+
+  def isAssociative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z)))
+  }
+
+  def isCommutative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A) => f(x, y) == f(y, x))
+  }
+
+  def isRotate[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x))
+  }
+
+  def assocNotCommutative[A](f: (A,A) => A): Boolean = {
+    require(isAssociative(f))
+    isCommutative(f)
+  }.holds
+// Counterexample for postcondition violation in `assocNotCommutative`:
+//   when f is:
+//     (x$412: A, x$413: A) => if (x$412 == A#3 && x$413 == A#3) {
+//       A#3
+//     } else if (x$412 == A#3 && x$413 == A#2) {
+//       A#3
+//     } else if (x$412 == A#2 && x$413 == A#3) {
+//       A#2
+//     } else if (x$412 == A#2 && x$413 == A#2) {
+//       A#2
+//     } else if (x$412 == A#3) {
+//       A#3
+//     } else if (x$413 == A#2) {
+//       A#2
+//     } else if (x$412 == A#2) {
+//       A#2
+//     } else if (x$413 == A#3) {
+//       A#2
+//     } else if (true) {
+//       A#2
+//     } else {
+//       A#2
+//     }
+
+  def commNotAssociative[A](f: (A,A) => A): Boolean = {
+    require(isCommutative(f))
+    isAssociative(f)
+  }.holds
+// Counterexample for postcondition violation in `commNotAssociative`:
+//   when f is:
+//     (x$330: A, x$331: A) => if (x$330 == A#2 && x$331 == A#0) {
+//       A#2
+//     } else if (x$330 == A#0 && x$331 == A#0) {
+//       A#1
+//     } else if (x$330 == A#2 && x$331 == A#2) {
+//       A#0
+//     } else if (x$330 == A#0 && x$331 == A#2) {
+//       A#2
+//     } else if (x$331 == A#0) {
+//       A#2
+//     } else if (x$331 == A#2) {
+//       A#0
+//     } else if (x$330 == A#2) {
+//       A#0
+//     } else if (x$330 == A#0) {
+//       A#2
+//     } else if (true) {
+//       A#0
+//     } else {
+//       A#0
+//     }
+}
+
+

back

diff --git a/_static/invalid/AssociativityProperties.scala b/_static/invalid/AssociativityProperties.scala new file mode 100644 index 0000000000..1dd552c76a --- /dev/null +++ b/_static/invalid/AssociativityProperties.scala @@ -0,0 +1,26 @@ +import stainless.lang._ + +object AssociativityProperties { + + def isAssociative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z))) + } + + def isCommutative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A) => f(x, y) == f(y, x)) + } + + def isRotate[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x)) + } + + def assocNotCommutative[A](f: (A,A) => A): Boolean = { + require(isAssociative(f)) + isCommutative(f) + }.holds + + def commNotAssociative[A](f: (A,A) => A): Boolean = { + require(isCommutative(f)) + isAssociative(f) + }.holds +} diff --git a/_static/invalid/BadConcRope.html b/_static/invalid/BadConcRope.html new file mode 100644 index 0000000000..794ff71fde --- /dev/null +++ b/_static/invalid/BadConcRope.html @@ -0,0 +1,472 @@ +

BadConcRope.scala [raw]


+
package conc
+// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL
+
+import stainless.collection._
+import stainless.lang._
+import ListSpecs._
+import stainless.annotation._
+
+object BadConcRope {
+
+  def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y
+  def abs(x: BigInt): BigInt = if (x < 0) -x else x
+
+  sealed abstract class Conc[T] {
+
+    def isEmpty: Boolean = {
+      this == Empty[T]()
+    }
+
+    def isLeaf: Boolean = {
+      this match {
+        case Empty() => true
+        case Single(_) => true
+        case _ => false
+      }
+    }
+
+    def isNormalized: Boolean = this match {
+      case Append(_, _) => false
+      case _ => true
+    }
+
+    def valid: Boolean = {
+      concInv && balanced && appendInv
+    }
+
+    /**
+     * (a) left and right trees of conc node should be non-empty
+     * (b) they cannot be append nodes
+     */
+    def concInv: Boolean = this match {
+      case CC(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.isNormalized && r.isNormalized &&
+          l.concInv && r.concInv
+      case _ => true
+    }
+
+    def balanced: Boolean = {
+      this match {
+        case CC(l, r) =>
+          l.level - r.level >= -1 && l.level - r.level <= 1 &&
+            l.balanced && r.balanced
+        case _ => true
+      }
+    }
+
+    /**
+     * (a) Right subtree of an append node is not an append node
+     * (b) If the tree is of the form a@Append(b@Append(_,_),_) then
+     * 		a.right.level < b.right.level
+     * (c) left and right are not empty
+     */
+    def appendInv: Boolean = this match {
+      case Append(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.valid && r.valid &&
+          r.isNormalized &&
+          (l match {
+            case Append(_, lr) =>
+              lr.level > r.level
+            case _ =>
+              l.level > r.level
+          })
+      case _ => true
+    }
+
+    val level: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 0
+        case CC(l, r) =>
+          1 + max(l.level, r.level)
+        case Append(l, r) =>
+          1 + max(l.level, r.level)
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    val size: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 1
+        case CC(l, r) =>
+          l.size + r.size
+        case Append(l, r) =>
+          l.size + r.size
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    def toList: List[T] = {
+      this match {
+        case Empty() => Nil[T]()
+        case Single(x) => Cons(x, Nil[T]())
+        case CC(l, r) =>
+          l.toList ++ r.toList // note: left elements precede the right elements in the list
+        case Append(l, r) =>
+          l.toList ++ r.toList
+      }
+    } ensuring (res => res.size == this.size)
+  }
+
+  case class Empty[T]() extends Conc[T]
+  case class Single[T](x: T) extends Conc[T]
+  case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+  case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+
+  def lookup[T](xs: Conc[T], i: BigInt): T = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => x
+      case CC(l, r) =>
+        if (i < l.size) lookup(l, i)
+       else lookup(r, i - l.size)
+      case Append(l, r) =>
+        if (i < l.size) lookup(l, i)
+        else lookup(r, i - l.size)
+    }
+  } ensuring (res =>  instAppendIndexAxiom(xs, i) &&  // an auxiliary axiom instantiation that required for the proof
+    res == xs.toList(i)) // correctness
+
+
+  def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = {
+    require(0 <= i && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case Append(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case _ => true
+    }
+  }.holds
+
+  def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => Single(y)
+      case CC(l, r) =>
+        if (i < l.size) CC(update(l, i, y), r)
+        else CC(l, update(r, i - l.size, y))
+      case Append(l, r) =>
+        Append(update(l, i, y), r)
+// Counterexample for precond. (call update[T](l, i, y)) violation in `update`:
+//   when i is:
+//     2
+//   when xs is:
+//     Append[T](CC[T](Single[T](T#63), Single[T](T#62)), Single[T](T#64))
+    }
+  } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation
+    res.level == xs.level && // heights of the input and output trees are equal
+    res.valid && // tree invariants are preserved
+    res.toList == xs.toList.updated(i, y) && // correctness
+    numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function
+
+  def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case Append(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  /**
+   * A generic concat that applies to general concTrees
+   */
+  def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid)
+    concatNormalized(normalize(xs), normalize(ys))
+  }
+
+  /**
+   * This concat applies only to normalized trees.
+   * This prevents concat from being recursive
+   */
+  def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized)
+    (xs, ys) match {
+      case (xs, Empty()) => xs
+      case (Empty(), ys) => ys
+      case _ =>
+        concatNonEmpty(xs, ys)
+    }
+  } ensuring (res => res.valid && // tree invariants
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    (res.toList == xs.toList ++ ys.toList) && // correctness
+    res.isNormalized //auxiliary properties
+    )
+
+  def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized &&
+      !xs.isEmpty && !ys.isEmpty)
+
+    val diff = ys.level - xs.level
+    if (diff >= -1 && diff <= 1)
+      CC(xs, ys)
+    else if (diff < -1) {
+      // ys is smaller than xs
+      xs match {
+        case CC(l, r) =>
+          if (l.level >= r.level)
+            CC(l, concatNonEmpty(r, ys))
+          else {
+            r match {
+              case CC(rl, rr) =>
+                val nrr = concatNonEmpty(rr, ys)
+                if (nrr.level == xs.level - 3) {
+                  CC(l, CC(rl, nrr))
+                } else {
+                  CC(CC(l, rl), nrr)
+                }
+            }
+          }
+      }
+    } else {
+      ys match {
+        case CC(l, r) =>
+          if (r.level >= l.level) {
+            CC(concatNonEmpty(xs, l), r)
+          } else {
+            l match {
+              case CC(ll, lr) =>
+                val nll = concatNonEmpty(xs, ll)
+                if (nll.level == ys.level - 3) {
+                  CC(CC(nll, lr), r)
+                } else {
+                  CC(nll, CC(lr, r))
+                }
+            }
+          }
+      }
+    }
+  } ensuring (res =>
+    appendAssocInst(xs, ys) && // instantiation of an axiom
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    res.balanced && res.appendInv && res.concInv && //this is should not be needed
+    res.valid && // tree invariant is preserved
+    res.toList == xs.toList ++ ys.toList && // correctness
+    res.isNormalized // auxiliary properties
+    )
+
+
+  def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    (xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation
+          (r match {
+            case CC(rl, rr) =>
+              appendAssoc(rl.toList, rr.toList, ys.toList) &&
+                appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList)
+            case _ => true
+          })
+      case _ => true
+    }) &&
+      (ys match {
+        case CC(l, r) =>
+          appendAssoc(xs.toList, l.toList, r.toList) &&
+            (l match {
+              case CC(ll, lr) =>
+                appendAssoc(xs.toList, ll.toList, lr.toList) &&
+                  appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList)
+              case _ => true
+            })
+        case _ => true
+      })
+  }.holds
+
+
+  def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && i >= 0 && i <= xs.size &&
+      xs.isNormalized) //note the precondition
+    xs match {
+      case Empty() => Single(y)
+      case Single(x) =>
+        if (i == 0)
+          CC(Single(y), xs)
+        else
+          CC(xs, Single(y))
+      case CC(l, r) if i < l.size =>
+        concatNonEmpty(insert(l, i, y), r)
+      case CC(l, r) =>
+       concatNonEmpty(l, insert(r, i - l.size, y))
+    }
+  } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom
+    res.valid && res.isNormalized && // tree invariants
+    res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree
+    res.toList == insertAtIndex(xs.toList, i, y) // correctness
+    )
+
+  /**
+   * Using a different version of insert than of the library
+   * because the library implementation in unnecessarily complicated.
+   */
+  def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = {
+    require(0 <= i && i <= l.size)
+    l match {
+      case Nil() =>
+        Cons[T](y, Nil())
+      case _ if i == 0 =>
+        Cons[T](y, l)
+      case Cons(x, tail) =>
+        Cons[T](x, insertAtIndex(tail, i - 1, y))
+    }
+  }
+
+  // A lemma about `append` and `insertAtIndex`
+  def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = {
+    require(0 <= i && i <= l1.size + l2.size)
+    (l1 match {
+      case Nil() => true
+      case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y)
+    }) &&
+      // lemma
+      (insertAtIndex((l1 ++ l2), i, y) == (
+        if (i < l1.size) insertAtIndex(l1, i, y) ++ l2
+        else l1 ++ insertAtIndex(l2, (i - l1.size), y)))
+  }.holds
+
+  def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i <= xs.size)
+    xs match {
+      case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = {
+    require(xs.valid && xs.isNormalized)
+    xs match {
+      case Empty() =>
+        (Empty[T](), Empty[T]())
+      case s @ Single(x) =>
+        if (n <= 0) {
+          (Empty[T](), s)
+        } else {
+          (s, Empty[T]())
+        }
+      case CC(l, r) =>
+        if (n < l.size) {
+          val (ll, lr) = split(l, n)
+          (ll, concatNormalized(lr, r))
+        } else if (n > l.size) {
+          val (rl, rr) = split(r, n - l.size)
+          (concatNormalized(l, rl), rr)
+        } else {
+          (l, r)
+        }
+    }
+  } ensuring (res  => instSplitAxiom(xs, n) && // instantiation of an axiom
+    res._1.valid && res._2.valid && // tree invariants are preserved
+    res._1.isNormalized && res._2.isNormalized &&
+    xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree
+    res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness
+    )
+
+  def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendTakeDrop(l.toList, r.toList, n)
+      case _ => true
+    }
+  }.holds
+
+  def append[T](xs: Conc[T], x: T): Conc[T] = {
+    require(xs.valid)
+    val ys = Single[T](x)
+    xs match {
+      case xs @ Append(_, _) =>
+        appendPriv(xs, ys)
+      case CC(_, _) =>
+        Append(xs, ys) //creating an append node
+      case Empty() => ys
+      case Single(_) => CC(xs, ys)
+    }
+  } ensuring (res => res.valid && //conctree invariants
+    res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness
+    res.level <= xs.level + 1
+  )
+
+  /**
+   * This is a private method and is not exposed to the
+   * clients of conc trees
+   */
+  def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T]  = {
+    require(xs.valid && ys.valid &&
+      !ys.isEmpty && ys.isNormalized &&
+      xs.right.level >= ys.level)
+
+    if (xs.right.level > ys.level)
+      Append(xs, ys)
+    else {
+      val zs = CC(xs.right, ys)
+      xs.left match {
+        case l @ Append(_, _) => appendPriv(l, zs)
+        case l if l.level <= zs.level => //note: here < is not possible
+          CC(l, zs)
+        case l =>
+          Append(l, zs)
+      }
+    }
+  } ensuring (res => appendAssocInst2(xs, ys) &&
+    res.valid && //conc tree invariants
+    res.toList == xs.toList ++ ys.toList && //correctness invariants
+    res.level <= xs.level + 1 )
+
+  def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case Append(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case _ => true
+    }
+  }.holds
+
+  def numTrees[T](t: Conc[T]): BigInt = {
+    t match {
+      case Append(l, r) => numTrees(l) + 1
+      case _ => BigInt(1)
+    }
+  } ensuring (res => res >= 0)
+
+  def normalize[T](t: Conc[T]): Conc[T] = {
+    require(t.valid)
+    t match {
+      case Append(l @ Append(_, _), r) =>
+        wrap(l, r)
+      case Append(l, r) =>
+        concatNormalized(l, r)
+      case _ => t
+    }
+  } ensuring (res => res.valid &&
+    res.isNormalized &&
+    res.toList == t.toList && //correctness
+    res.size == t.size && res.level <= t.level //normalize preserves level and size
+    )
+
+  def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid && ys.isNormalized &&
+      xs.right.level >= ys.level)
+    val nr  = concatNormalized(xs.right, ys)
+    xs.left match {
+      case l @ Append(_, _) => wrap(l, nr)
+      case l =>
+        concatNormalized(l, nr)
+    }
+  } ensuring (res =>
+    appendAssocInst2(xs, ys) && //some lemma instantiations
+    res.valid &&
+    res.isNormalized &&
+    res.toList == xs.toList ++ ys.toList && //correctness
+    res.size == xs.size + ys.size && //other auxiliary properties
+    res.level <= xs.level
+    )
+}
+
diff --git a/_static/invalid/BadConcRope.scala b/_static/invalid/BadConcRope.scala new file mode 100644 index 0000000000..dfff26ec5b --- /dev/null +++ b/_static/invalid/BadConcRope.scala @@ -0,0 +1,465 @@ +package conc +// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL + +import stainless.collection._ +import stainless.lang._ +import ListSpecs._ +import stainless.annotation._ + +object BadConcRope { + + def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y + def abs(x: BigInt): BigInt = if (x < 0) -x else x + + sealed abstract class Conc[T] { + + def isEmpty: Boolean = { + this == Empty[T]() + } + + def isLeaf: Boolean = { + this match { + case Empty() => true + case Single(_) => true + case _ => false + } + } + + def isNormalized: Boolean = this match { + case Append(_, _) => false + case _ => true + } + + def valid: Boolean = { + concInv && balanced && appendInv + } + + /** + * (a) left and right trees of conc node should be non-empty + * (b) they cannot be append nodes + */ + def concInv: Boolean = this match { + case CC(l, r) => + !l.isEmpty && !r.isEmpty && + l.isNormalized && r.isNormalized && + l.concInv && r.concInv + case _ => true + } + + def balanced: Boolean = { + this match { + case CC(l, r) => + l.level - r.level >= -1 && l.level - r.level <= 1 && + l.balanced && r.balanced + case _ => true + } + } + + /** + * (a) Right subtree of an append node is not an append node + * (b) If the tree is of the form a@Append(b@Append(_,_),_) then + * a.right.level < b.right.level + * (c) left and right are not empty + */ + def appendInv: Boolean = this match { + case Append(l, r) => + !l.isEmpty && !r.isEmpty && + l.valid && r.valid && + r.isNormalized && + (l match { + case Append(_, lr) => + lr.level > r.level + case _ => + l.level > r.level + }) + case _ => true + } + + val level: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 0 + case CC(l, r) => + 1 + max(l.level, r.level) + case Append(l, r) => + 1 + max(l.level, r.level) + }): BigInt + } ensuring (_ >= 0) + + val size: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 1 + case CC(l, r) => + l.size + r.size + case Append(l, r) => + l.size + r.size + }): BigInt + } ensuring (_ >= 0) + + def toList: List[T] = { + this match { + case Empty() => Nil[T]() + case Single(x) => Cons(x, Nil[T]()) + case CC(l, r) => + l.toList ++ r.toList // note: left elements precede the right elements in the list + case Append(l, r) => + l.toList ++ r.toList + } + } ensuring (res => res.size == this.size) + } + + case class Empty[T]() extends Conc[T] + case class Single[T](x: T) extends Conc[T] + case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] + case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T] + + def lookup[T](xs: Conc[T], i: BigInt): T = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => x + case CC(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + case Append(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + } + } ensuring (res => instAppendIndexAxiom(xs, i) && // an auxiliary axiom instantiation that required for the proof + res == xs.toList(i)) // correctness + + + def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = { + require(0 <= i && i < xs.size) + xs match { + case CC(l, r) => + appendIndex(l.toList, r.toList, i) + case Append(l, r) => + appendIndex(l.toList, r.toList, i) + case _ => true + } + }.holds + + def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => Single(y) + case CC(l, r) => + if (i < l.size) CC(update(l, i, y), r) + else CC(l, update(r, i - l.size, y)) + case Append(l, r) => + Append(update(l, i, y), r) + } + } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation + res.level == xs.level && // heights of the input and output trees are equal + res.valid && // tree invariants are preserved + res.toList == xs.toList.updated(i, y) && // correctness + numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function + + def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i < xs.size) + xs match { + case CC(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case Append(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + /** + * A generic concat that applies to general concTrees + */ + def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid) + concatNormalized(normalize(xs), normalize(ys)) + } + + /** + * This concat applies only to normalized trees. + * This prevents concat from being recursive + */ + def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized) + (xs, ys) match { + case (xs, Empty()) => xs + case (Empty(), ys) => ys + case _ => + concatNonEmpty(xs, ys) + } + } ensuring (res => res.valid && // tree invariants + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + (res.toList == xs.toList ++ ys.toList) && // correctness + res.isNormalized //auxiliary properties + ) + + def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized && + !xs.isEmpty && !ys.isEmpty) + + val diff = ys.level - xs.level + if (diff >= -1 && diff <= 1) + CC(xs, ys) + else if (diff < -1) { + // ys is smaller than xs + xs match { + case CC(l, r) => + if (l.level >= r.level) + CC(l, concatNonEmpty(r, ys)) + else { + r match { + case CC(rl, rr) => + val nrr = concatNonEmpty(rr, ys) + if (nrr.level == xs.level - 3) { + CC(l, CC(rl, nrr)) + } else { + CC(CC(l, rl), nrr) + } + } + } + } + } else { + ys match { + case CC(l, r) => + if (r.level >= l.level) { + CC(concatNonEmpty(xs, l), r) + } else { + l match { + case CC(ll, lr) => + val nll = concatNonEmpty(xs, ll) + if (nll.level == ys.level - 3) { + CC(CC(nll, lr), r) + } else { + CC(nll, CC(lr, r)) + } + } + } + } + } + } ensuring (res => + appendAssocInst(xs, ys) && // instantiation of an axiom + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + res.balanced && res.appendInv && res.concInv && //this is should not be needed + res.valid && // tree invariant is preserved + res.toList == xs.toList ++ ys.toList && // correctness + res.isNormalized // auxiliary properties + ) + + + def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = { + (xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation + (r match { + case CC(rl, rr) => + appendAssoc(rl.toList, rr.toList, ys.toList) && + appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList) + case _ => true + }) + case _ => true + }) && + (ys match { + case CC(l, r) => + appendAssoc(xs.toList, l.toList, r.toList) && + (l match { + case CC(ll, lr) => + appendAssoc(xs.toList, ll.toList, lr.toList) && + appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList) + case _ => true + }) + case _ => true + }) + }.holds + + + def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && i >= 0 && i <= xs.size && + xs.isNormalized) //note the precondition + xs match { + case Empty() => Single(y) + case Single(x) => + if (i == 0) + CC(Single(y), xs) + else + CC(xs, Single(y)) + case CC(l, r) if i < l.size => + concatNonEmpty(insert(l, i, y), r) + case CC(l, r) => + concatNonEmpty(l, insert(r, i - l.size, y)) + } + } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom + res.valid && res.isNormalized && // tree invariants + res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree + res.toList == insertAtIndex(xs.toList, i, y) // correctness + ) + + /** + * Using a different version of insert than of the library + * because the library implementation in unnecessarily complicated. + */ + def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = { + require(0 <= i && i <= l.size) + l match { + case Nil() => + Cons[T](y, Nil()) + case _ if i == 0 => + Cons[T](y, l) + case Cons(x, tail) => + Cons[T](x, insertAtIndex(tail, i - 1, y)) + } + } + + // A lemma about `append` and `insertAtIndex` + def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = { + require(0 <= i && i <= l1.size + l2.size) + (l1 match { + case Nil() => true + case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y) + }) && + // lemma + (insertAtIndex((l1 ++ l2), i, y) == ( + if (i < l1.size) insertAtIndex(l1, i, y) ++ l2 + else l1 ++ insertAtIndex(l2, (i - l1.size), y))) + }.holds + + def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i <= xs.size) + xs match { + case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = { + require(xs.valid && xs.isNormalized) + xs match { + case Empty() => + (Empty[T](), Empty[T]()) + case s @ Single(x) => + if (n <= 0) { + (Empty[T](), s) + } else { + (s, Empty[T]()) + } + case CC(l, r) => + if (n < l.size) { + val (ll, lr) = split(l, n) + (ll, concatNormalized(lr, r)) + } else if (n > l.size) { + val (rl, rr) = split(r, n - l.size) + (concatNormalized(l, rl), rr) + } else { + (l, r) + } + } + } ensuring (res => instSplitAxiom(xs, n) && // instantiation of an axiom + res._1.valid && res._2.valid && // tree invariants are preserved + res._1.isNormalized && res._2.isNormalized && + xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree + res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness + ) + + def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = { + xs match { + case CC(l, r) => + appendTakeDrop(l.toList, r.toList, n) + case _ => true + } + }.holds + + def append[T](xs: Conc[T], x: T): Conc[T] = { + require(xs.valid) + val ys = Single[T](x) + xs match { + case xs @ Append(_, _) => + appendPriv(xs, ys) + case CC(_, _) => + Append(xs, ys) //creating an append node + case Empty() => ys + case Single(_) => CC(xs, ys) + } + } ensuring (res => res.valid && //conctree invariants + res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness + res.level <= xs.level + 1 + ) + + /** + * This is a private method and is not exposed to the + * clients of conc trees + */ + def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + !ys.isEmpty && ys.isNormalized && + xs.right.level >= ys.level) + + if (xs.right.level > ys.level) + Append(xs, ys) + else { + val zs = CC(xs.right, ys) + xs.left match { + case l @ Append(_, _) => appendPriv(l, zs) + case l if l.level <= zs.level => //note: here < is not possible + CC(l, zs) + case l => + Append(l, zs) + } + } + } ensuring (res => appendAssocInst2(xs, ys) && + res.valid && //conc tree invariants + res.toList == xs.toList ++ ys.toList && //correctness invariants + res.level <= xs.level + 1 ) + + def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = { + xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case Append(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case _ => true + } + }.holds + + def numTrees[T](t: Conc[T]): BigInt = { + t match { + case Append(l, r) => numTrees(l) + 1 + case _ => BigInt(1) + } + } ensuring (res => res >= 0) + + def normalize[T](t: Conc[T]): Conc[T] = { + require(t.valid) + t match { + case Append(l @ Append(_, _), r) => + wrap(l, r) + case Append(l, r) => + concatNormalized(l, r) + case _ => t + } + } ensuring (res => res.valid && + res.isNormalized && + res.toList == t.toList && //correctness + res.size == t.size && res.level <= t.level //normalize preserves level and size + ) + + def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && ys.isNormalized && + xs.right.level >= ys.level) + val nr = concatNormalized(xs.right, ys) + xs.left match { + case l @ Append(_, _) => wrap(l, nr) + case l => + concatNormalized(l, nr) + } + } ensuring (res => + appendAssocInst2(xs, ys) && //some lemma instantiations + res.valid && + res.isNormalized && + res.toList == xs.toList ++ ys.toList && //correctness + res.size == xs.size + ys.size && //other auxiliary properties + res.level <= xs.level + ) +} diff --git a/_static/invalid/BraunTree.html b/_static/invalid/BraunTree.html new file mode 100644 index 0000000000..67c7f43a4d --- /dev/null +++ b/_static/invalid/BraunTree.html @@ -0,0 +1,55 @@ + + + +invalid/BraunTree.scala + + +

BraunTree.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object BraunTree {
+  abstract class Tree
+  case class Node(value: Int, left: Tree, right: Tree) extends Tree
+  case class Leaf() extends Tree
+
+  def insert(tree: Tree, x: Int): Tree = {
+    require(isBraun(tree))
+    tree match {
+      case Node(value, left, right) =>
+        Node(value, insert(left, x), right)
+      case Leaf() => Node(x, Leaf(), Leaf())
+    }
+  } ensuring { res => isBraun(res) }
+// Counterexample for postcondition violation in `insert`:
+//   when x is:
+//     0
+//   when tree is:
+//     Node(0, Node(0, Leaf(), Leaf()), Leaf())
+
+  def height(tree: Tree): Int = {
+    tree match {
+      case Node(value, left, right) =>
+        val l = height(left)
+        val r = height(right)
+        val max = if (l > r) l else r
+        1 + max
+      case Leaf() => 0
+    }
+  }
+
+  def isBraun(tree: Tree): Boolean = {
+    tree match {
+      case Node(value, left, right) =>
+        isBraun(left) && isBraun(right) && {
+          val l = height(left)
+          val r = height(right)
+          l == r || l == r + 1
+        }
+      case Leaf() => true
+    }
+  }
+}
+
+

back

diff --git a/_static/invalid/BraunTree.scala b/_static/invalid/BraunTree.scala new file mode 100644 index 0000000000..7733dcd0ec --- /dev/null +++ b/_static/invalid/BraunTree.scala @@ -0,0 +1,41 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object BraunTree { + abstract class Tree + case class Node(value: Int, left: Tree, right: Tree) extends Tree + case class Leaf() extends Tree + + def insert(tree: Tree, x: Int): Tree = { + require(isBraun(tree)) + tree match { + case Node(value, left, right) => + Node(value, insert(left, x), right) + case Leaf() => Node(x, Leaf(), Leaf()) + } + } ensuring { res => isBraun(res) } + + def height(tree: Tree): Int = { + tree match { + case Node(value, left, right) => + val l = height(left) + val r = height(right) + val max = if (l > r) l else r + 1 + max + case Leaf() => 0 + } + } + + def isBraun(tree: Tree): Boolean = { + tree match { + case Node(value, left, right) => + isBraun(left) && isBraun(right) && { + val l = height(left) + val r = height(right) + l == r || l == r + 1 + } + case Leaf() => true + } + } +} diff --git a/_static/invalid/Choose.html b/_static/invalid/Choose.html new file mode 100644 index 0000000000..b1c6503787 --- /dev/null +++ b/_static/invalid/Choose.html @@ -0,0 +1,53 @@ + + + +invalid/Choose.scala + + +

Choose.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Choose1 {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def listOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        choose[List] { (res: List) => size(res) == i-1 }
+      }
+    } ensuring ( size(_) == i )
+// Counterexample for postcondition violation in `listOfSize`:
+//   when i is:
+//     1
+
+
+    def listOfSize2(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i > 0) {
+        Cons(0, listOfSize(i-1))
+      } else {
+        Nil()
+      }
+    } ensuring ( size(_) == i )
+}
+
+

back

diff --git a/_static/invalid/Choose.scala b/_static/invalid/Choose.scala new file mode 100644 index 0000000000..7508725001 --- /dev/null +++ b/_static/invalid/Choose.scala @@ -0,0 +1,41 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Choose1 { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def listOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + choose[List] { (res: List) => size(res) == i-1 } + } + } ensuring ( size(_) == i ) + + + def listOfSize2(i: BigInt): List = { + require(i >= 0) + + if (i > 0) { + Cons(0, listOfSize(i-1)) + } else { + Nil() + } + } ensuring ( size(_) == i ) +} diff --git a/_static/invalid/FunctionCaching.html b/_static/invalid/FunctionCaching.html new file mode 100644 index 0000000000..62e39fdf37 --- /dev/null +++ b/_static/invalid/FunctionCaching.html @@ -0,0 +1,47 @@ + + + +invalid/FunctionCaching.scala + + +

FunctionCaching.scala [raw]


+
import stainless.lang._
+import stainless.collection._
+
+object FunctionCaching {
+
+  case class FunCache(var cached: Map[BigInt, BigInt])
+
+  def fun(x: BigInt)(implicit funCache: FunCache): BigInt = {
+    funCache.cached.get(x) match {
+      case None() => 
+        val res = 2*x + 42
+        funCache.cached = funCache.cached.updated(x, res)
+        res
+      case Some(cached) =>
+        cached + 1
+    }
+  }
+
+  def funWronglyCached(x: BigInt, trash: List[BigInt]): Boolean = {
+    implicit val cache = FunCache(Map())
+    val res1 = fun(x)
+    multipleCalls(trash)
+    val res2 = fun(x)
+    res1 == res2
+  } holds
+// Counterexample for postcondition violation in `funWronglyCached`:
+//   when x is:
+//     -21
+//   when trash is:
+//     Nil[BigInt]()
+
+
+  def multipleCalls(args: List[BigInt])(implicit funCache: FunCache): Unit = args match {
+    case Nil() => ()
+    case x::xs => fun(x); multipleCalls(xs)
+  }
+
+}
+
+

back

diff --git a/_static/invalid/FunctionCaching.scala b/_static/invalid/FunctionCaching.scala new file mode 100644 index 0000000000..dea5ff3a87 --- /dev/null +++ b/_static/invalid/FunctionCaching.scala @@ -0,0 +1,33 @@ +import stainless.lang._ +import stainless.collection._ + +object FunctionCaching { + + case class FunCache(var cached: Map[BigInt, BigInt]) + + def fun(x: BigInt)(implicit funCache: FunCache): BigInt = { + funCache.cached.get(x) match { + case None() => + val res = 2*x + 42 + funCache.cached = funCache.cached.updated(x, res) + res + case Some(cached) => + cached + 1 + } + } + + def funWronglyCached(x: BigInt, trash: List[BigInt]): Boolean = { + implicit val cache = FunCache(Map()) + val res1 = fun(x) + multipleCalls(trash) + val res2 = fun(x) + res1 == res2 + } holds + + + def multipleCalls(args: List[BigInt])(implicit funCache: FunCache): Unit = args match { + case Nil() => () + case x::xs => fun(x); multipleCalls(xs) + } + +} diff --git a/_static/invalid/InsertionSort.html b/_static/invalid/InsertionSort.html new file mode 100644 index 0000000000..26c925d558 --- /dev/null +++ b/_static/invalid/InsertionSort.html @@ -0,0 +1,57 @@ + + + +invalid/InsertionSort.scala + + +

InsertionSort.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object InsertionSort {
+  sealed abstract class List
+  case class Cons(head:Int,tail:List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptInt
+  case class Some(value: Int) extends OptInt
+  case class None() extends OptInt
+
+  def size(l : List) : BigInt = (l match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def contents(l: List): Set[Int] = l match {
+    case Nil() => Set.empty
+    case Cons(x,xs) => contents(xs) ++ Set(x)
+  }
+
+  def isSorted(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(x, Nil()) => true
+    case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys))
+  }   
+
+  /* Inserting element 'e' into a sorted list 'l' produces a sorted list with
+   * the expected content and size */
+  def buggySortedIns(e: Int, l: List): List = {
+    // require(isSorted(l))
+    l match {
+      case Nil() => Cons(e,Nil())
+      case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l)
+    } 
+  } ensuring(res => contents(res) == contents(l) ++ Set(e) 
+                    && isSorted(res)
+                    && size(res) == size(l) + 1
+// Counterexample for postcondition violation in `buggySortedIns`:
+//   when e is:
+//     0
+//   when l is:
+//     Cons(-2147483643, Cons(-2147483644, Nil()))
+            )
+}
+
+

back

diff --git a/_static/invalid/InsertionSort.scala b/_static/invalid/InsertionSort.scala new file mode 100644 index 0000000000..98aa2325d1 --- /dev/null +++ b/_static/invalid/InsertionSort.scala @@ -0,0 +1,43 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object InsertionSort { + sealed abstract class List + case class Cons(head:Int,tail:List) extends List + case class Nil() extends List + + sealed abstract class OptInt + case class Some(value: Int) extends OptInt + case class None() extends OptInt + + def size(l : List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def contents(l: List): Set[Int] = l match { + case Nil() => Set.empty + case Cons(x,xs) => contents(xs) ++ Set(x) + } + + def isSorted(l: List): Boolean = l match { + case Nil() => true + case Cons(x, Nil()) => true + case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys)) + } + + /* Inserting element 'e' into a sorted list 'l' produces a sorted list with + * the expected content and size */ + def buggySortedIns(e: Int, l: List): List = { + // require(isSorted(l)) + l match { + case Nil() => Cons(e,Nil()) + case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l) + } + } ensuring(res => contents(res) == contents(l) ++ Set(e) + && isSorted(res) + && size(res) == size(l) + 1 + ) +} diff --git a/_static/invalid/ListOperations.html b/_static/invalid/ListOperations.html new file mode 100644 index 0000000000..b9e8a0cc96 --- /dev/null +++ b/_static/invalid/ListOperations.html @@ -0,0 +1,128 @@ + + + +invalid/ListOperations.scala + + +

ListOperations.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ListOperations {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    sealed abstract class IntPairList
+    case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList
+    case class IPNil() extends IntPairList
+
+    sealed abstract class IntPair
+    case class IP(fst: Int, snd: Int) extends IntPair
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def iplSize(l: IntPairList) : BigInt = (l match {
+      case IPNil() => BigInt(0)
+      case IPCons(_, xs) => 1 + iplSize(xs)
+    }) ensuring(_ >= 0)
+
+    def zip(l1: List, l2: List) : IntPairList = {
+      // try to uncomment this and see how pattern-matching becomes exhaustive
+      // require(size(l1) == size(l2))
+
+      l1 match {
+        case Nil() => IPNil()
+        case Cons(x, xs) => l2 match {
+          case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys))
+        }
+// Counterexample for match exhaustiveness violation in `zip`:
+//   when l2 is:
+//     Nil()
+//   when l1 is:
+//     Cons(0, Nil())
+      }
+    } ensuring(iplSize(_) == size(l1))
+
+    def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0)
+    def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = {
+     require(acc >= 0)
+     l match {
+       case Nil() => acc
+       case Cons(_, xs) => sizeTailRecAcc(xs, acc+1)
+     }
+    } ensuring(res => res == size(l) + acc)
+
+    def sizesAreEquiv(l: List) : Boolean = {
+      size(l) == sizeTailRec(l)
+    }.holds
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def sizeAndContent(l: List) : Boolean = {
+      size(l) == BigInt(0) || content(l) != Set.empty[Int]
+    }.holds
+
+    def drunk(l : List) : List = (l match {
+      case Nil() => Nil()
+      case Cons(x,l1) => Cons(x,Cons(x,drunk(l1)))
+    }) ensuring (size(_) == 2 * size(l))
+
+    def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l))
+    def reverse0(l1: List, l2: List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => reverse0(xs, Cons(x, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    def append(l1 : List, l2 : List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x,xs) => Cons(x, append(xs, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds
+
+    @induct
+    def appendAssoc(xs : List, ys : List, zs : List) : Boolean =
+      (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds
+
+    def revAuxBroken(l1 : List, e : Int, l2 : List) : Boolean = {
+      (append(reverse(l1), Cons(e,l2)) == reverse0(l1, l2))
+    }.holds
+// Counterexample for postcondition violation in `revAuxBroken`:
+//   when e is:
+//     0
+//   when l1 is:
+//     Nil()
+//   when l2 is:
+//     Nil()
+
+    @induct
+    def sizeAppend(l1 : List, l2 : List) : Boolean =
+      (size(append(l1, l2)) == size(l1) + size(l2)).holds
+
+    @induct
+    def concat(l1: List, l2: List) : List =
+      concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def concat0(l1: List, l2: List, l3: List) : List = (l1 match {
+      case Nil() => l2 match {
+        case Nil() => reverse(l3)
+        case Cons(y, ys) => {
+          concat0(Nil(), ys, Cons(y, l3))
+        }
+      }
+      case Cons(x, xs) => concat0(xs, l2, Cons(x, l3))
+    }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3))
+}
+
+

back

diff --git a/_static/invalid/ListOperations.scala b/_static/invalid/ListOperations.scala new file mode 100644 index 0000000000..7ba835b52d --- /dev/null +++ b/_static/invalid/ListOperations.scala @@ -0,0 +1,107 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ListOperations { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class IntPairList + case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList + case class IPNil() extends IntPairList + + sealed abstract class IntPair + case class IP(fst: Int, snd: Int) extends IntPair + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def iplSize(l: IntPairList) : BigInt = (l match { + case IPNil() => BigInt(0) + case IPCons(_, xs) => 1 + iplSize(xs) + }) ensuring(_ >= 0) + + def zip(l1: List, l2: List) : IntPairList = { + // try to uncomment this and see how pattern-matching becomes exhaustive + // require(size(l1) == size(l2)) + + l1 match { + case Nil() => IPNil() + case Cons(x, xs) => l2 match { + case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys)) + } + } + } ensuring(iplSize(_) == size(l1)) + + def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0) + def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = { + require(acc >= 0) + l match { + case Nil() => acc + case Cons(_, xs) => sizeTailRecAcc(xs, acc+1) + } + } ensuring(res => res == size(l) + acc) + + def sizesAreEquiv(l: List) : Boolean = { + size(l) == sizeTailRec(l) + }.holds + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def sizeAndContent(l: List) : Boolean = { + size(l) == BigInt(0) || content(l) != Set.empty[Int] + }.holds + + def drunk(l : List) : List = (l match { + case Nil() => Nil() + case Cons(x,l1) => Cons(x,Cons(x,drunk(l1))) + }) ensuring (size(_) == 2 * size(l)) + + def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l)) + def reverse0(l1: List, l2: List) : List = (l1 match { + case Nil() => l2 + case Cons(x, xs) => reverse0(xs, Cons(x, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + def append(l1 : List, l2 : List) : List = (l1 match { + case Nil() => l2 + case Cons(x,xs) => Cons(x, append(xs, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds + + @induct + def appendAssoc(xs : List, ys : List, zs : List) : Boolean = + (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds + + def revAuxBroken(l1 : List, e : Int, l2 : List) : Boolean = { + (append(reverse(l1), Cons(e,l2)) == reverse0(l1, l2)) + }.holds + + @induct + def sizeAppend(l1 : List, l2 : List) : Boolean = + (size(append(l1, l2)) == size(l1) + size(l2)).holds + + @induct + def concat(l1: List, l2: List) : List = + concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def concat0(l1: List, l2: List, l3: List) : List = (l1 match { + case Nil() => l2 match { + case Nil() => reverse(l3) + case Cons(y, ys) => { + concat0(Nil(), ys, Cons(y, l3)) + } + } + case Cons(x, xs) => concat0(xs, l2, Cons(x, l3)) + }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3)) +} diff --git a/_static/invalid/Lists.html b/_static/invalid/Lists.html new file mode 100644 index 0000000000..c27cd96486 --- /dev/null +++ b/_static/invalid/Lists.html @@ -0,0 +1,46 @@ + + + +invalid/Lists.scala + + +

Lists.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object Lists {
+  abstract class List[T]
+  case class Cons[T](head: T, tail: List[T]) extends List[T]
+  case class Nil[T]() extends List[T]
+
+  def forall[T](list: List[T], f: T => Boolean): Boolean = list match {
+    case Cons(head, tail) => f(head) && forall(tail, f)
+    case Nil() => true
+  }
+
+  def positive(list: List[Int]): Boolean = list match {
+    case Cons(head, tail) => if (head < 0) false else positive(tail)
+    case Nil() => true
+  }
+
+  def gt(i: Int): Int => Boolean = x => x > i
+
+  def positive_lemma(list: List[Int]): Boolean = {
+    positive(list) == forall(list, gt(0))
+  }
+
+  def failling_1(list: List[Int]): Boolean = {
+    list match {
+      case Nil() => positive_lemma(list)
+      case Cons(head, tail) => positive_lemma(list) && failling_1(tail)
+    }
+  }.holds
+// Counterexample for postcondition violation in `failling_1`:
+//   when list is:
+//     Cons[Int](0, Nil[Int]())
+}
+
+// vim: set ts=4 sw=4 et:
+
+

back

diff --git a/_static/invalid/Lists.scala b/_static/invalid/Lists.scala new file mode 100644 index 0000000000..7b3a056760 --- /dev/null +++ b/_static/invalid/Lists.scala @@ -0,0 +1,34 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object Lists { + abstract class List[T] + case class Cons[T](head: T, tail: List[T]) extends List[T] + case class Nil[T]() extends List[T] + + def forall[T](list: List[T], f: T => Boolean): Boolean = list match { + case Cons(head, tail) => f(head) && forall(tail, f) + case Nil() => true + } + + def positive(list: List[Int]): Boolean = list match { + case Cons(head, tail) => if (head < 0) false else positive(tail) + case Nil() => true + } + + def gt(i: Int): Int => Boolean = x => x > i + + def positive_lemma(list: List[Int]): Boolean = { + positive(list) == forall(list, gt(0)) + } + + def failling_1(list: List[Int]): Boolean = { + list match { + case Nil() => positive_lemma(list) + case Cons(head, tail) => positive_lemma(list) && failling_1(tail) + } + }.holds +} + +// vim: set ts=4 sw=4 et: diff --git a/_static/invalid/Mean.html b/_static/invalid/Mean.html new file mode 100644 index 0000000000..ff317d449c --- /dev/null +++ b/_static/invalid/Mean.html @@ -0,0 +1,27 @@ + + + +invalid/Mean.scala + + +

Mean.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Mean {
+
+  def meanOverflow(x: Int, y: Int): Int = {
+    require(x <= y && x >= 0 && y >= 0)
+    (x + y)/2
+  } ensuring(m => m >= x && m <= y)
+// Counterexample for postcondition violation in `meanOverflow`:
+//   when y is:
+//     1865154560
+//   when x is:
+//     1277440000
+
+}
+
+

back

diff --git a/_static/invalid/Mean.scala b/_static/invalid/Mean.scala new file mode 100644 index 0000000000..c79ad49794 --- /dev/null +++ b/_static/invalid/Mean.scala @@ -0,0 +1,13 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Mean { + + def meanOverflow(x: Int, y: Int): Int = { + require(x <= y && x >= 0 && y >= 0) + (x + y)/2 + } ensuring(m => m >= x && m <= y) + +} diff --git a/_static/invalid/PropositionalLogic.html b/_static/invalid/PropositionalLogic.html new file mode 100644 index 0000000000..1ca8f024c8 --- /dev/null +++ b/_static/invalid/PropositionalLogic.html @@ -0,0 +1,62 @@ + + + +invalid/PropositionalLogic.scala + + +

PropositionalLogic.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object PropositionalLogic { 
+
+  sealed abstract class Formula
+  case class And(lhs: Formula, rhs: Formula) extends Formula
+  case class Or(lhs: Formula, rhs: Formula) extends Formula
+  case class Implies(lhs: Formula, rhs: Formula) extends Formula
+  case class Not(f: Formula) extends Formula
+  case class Literal(id: BigInt) extends Formula
+
+  def simplify(f: Formula): Formula = (f match {
+    case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs))
+    case _ => f
+  }) ensuring(isSimplified(_))
+// Counterexample for postcondition violation in `simplify`:
+//   when f is:
+//     And(Literal(8), Implies(Literal(7), Literal(6)))
+
+  def isSimplified(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Implies(_,_) => false
+    case Not(f) => isSimplified(f)
+    case Literal(_) => true
+  }
+
+  def isNNF(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Not(Literal(_)) => true
+    case Not(_) => false
+    case Literal(_) => true
+  }
+
+
+  // @induct
+  // def wrongCommutative(f: Formula) : Boolean = {
+  //   nnf(simplify(f)) == simplify(nnf(f))
+  // }.holds
+
+ def simplifyBreaksNNF(f: Formula) : Boolean = {
+    require(isNNF(f))
+    isNNF(simplify(f))
+  }.holds
+// Counterexample for postcondition violation in `simplifyBreaksNNF`:
+//   when f is:
+//     Implies(And(Literal(255), Literal(256)), Literal(267))
+}
+
+

back

diff --git a/_static/invalid/PropositionalLogic.scala b/_static/invalid/PropositionalLogic.scala new file mode 100644 index 0000000000..654a28d303 --- /dev/null +++ b/_static/invalid/PropositionalLogic.scala @@ -0,0 +1,47 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object PropositionalLogic { + + sealed abstract class Formula + case class And(lhs: Formula, rhs: Formula) extends Formula + case class Or(lhs: Formula, rhs: Formula) extends Formula + case class Implies(lhs: Formula, rhs: Formula) extends Formula + case class Not(f: Formula) extends Formula + case class Literal(id: BigInt) extends Formula + + def simplify(f: Formula): Formula = (f match { + case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs)) + case _ => f + }) ensuring(isSimplified(_)) + + def isSimplified(f: Formula): Boolean = f match { + case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Implies(_,_) => false + case Not(f) => isSimplified(f) + case Literal(_) => true + } + + def isNNF(f: Formula): Boolean = f match { + case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Not(Literal(_)) => true + case Not(_) => false + case Literal(_) => true + } + + + // @induct + // def wrongCommutative(f: Formula) : Boolean = { + // nnf(simplify(f)) == simplify(nnf(f)) + // }.holds + + def simplifyBreaksNNF(f: Formula) : Boolean = { + require(isNNF(f)) + isNNF(simplify(f)) + }.holds +} diff --git a/_static/invalid/RedBlackTree2.html b/_static/invalid/RedBlackTree2.html new file mode 100644 index 0000000000..aa2f672af0 --- /dev/null +++ b/_static/invalid/RedBlackTree2.html @@ -0,0 +1,106 @@ + + + +invalid/RedBlackTree2.scala + + +

RedBlackTree2.scala [raw]


+
/* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object RedBlackTree2 { 
+  sealed abstract class Color
+  case class Red() extends Color
+  case class Black() extends Color
+ 
+  sealed abstract class Tree
+  case class Empty() extends Tree
+  case class Node(color: Color, left: Tree, value: Int, right: Tree) extends Tree
+
+  sealed abstract class OptionInt
+  case class Some(v : Int) extends OptionInt
+  case class None() extends OptionInt
+
+  def content(t: Tree) : Set[Int] = t match {
+    case Empty() => Set.empty
+    case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def size(t: Tree) : BigInt = (t match {
+    case Empty() => BigInt(0)
+    case Node(_, l, v, r) => size(l) + 1 + size(r)
+  }) ensuring(_ >= 0)
+
+  def isBlack(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(),_,_,_) => true
+    case _ => false
+  }
+
+  def redNodesHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+    case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def redDescHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def blackBalanced(t : Tree) : Boolean = t match {
+    case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r)
+    case Empty() => true
+  }
+
+  def blackHeight(t : Tree) : Int = t match {
+    case Empty() => 1
+    case Node(Black(), l, _, _) => blackHeight(l) + 1
+    case Node(Red(), l, _, _) => blackHeight(l)
+  }
+
+  def ins(x: Int, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    t match {
+      case Empty() => Node(Red(),Empty(),x,Empty())
+      case Node(c,a,y,b) =>
+        if      (x < y)  balance(c, ins(x, a), y, b)
+        else if (x == y) Node(c,a,y,b)
+        else             balance(c,a,y,ins(x, b))
+    }
+  } ensuring (res => content(res) == content(t) ++ Set(x) 
+                   && size(t) <= size(res) && size(res) <= size(t) + 1
+                   && redDescHaveBlackChildren(res)
+                   && blackBalanced(res))
+
+  def balance(c: Color, a: Tree, x: Int, b: Tree): Tree = {
+    Node(c,a,x,b) match {
+      case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(c,a,xV,b) => Node(c,a,xV,b)
+    }
+  } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res))
+
+  def buggyAdd(x: Int, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t))
+    ins(x, t)
+// Counterexample for precond. (call ins(x, t)) violation in `buggyAdd`:
+//   when t is:
+//     Node(Black(), Node(Black(), Empty(), 0, Empty()), 0, Empty())
+  } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res))
+// Counterexample for postcondition violation in `buggyAdd`:
+//   when x is:
+//     0
+//   when t is:
+//     Node(Red(), Empty(), 1048576, Empty())
+}
+
+

back

diff --git a/_static/invalid/RedBlackTree2.scala b/_static/invalid/RedBlackTree2.scala new file mode 100644 index 0000000000..6fc4b6cf74 --- /dev/null +++ b/_static/invalid/RedBlackTree2.scala @@ -0,0 +1,89 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object RedBlackTree2 { + sealed abstract class Color + case class Red() extends Color + case class Black() extends Color + + sealed abstract class Tree + case class Empty() extends Tree + case class Node(color: Color, left: Tree, value: Int, right: Tree) extends Tree + + sealed abstract class OptionInt + case class Some(v : Int) extends OptionInt + case class None() extends OptionInt + + def content(t: Tree) : Set[Int] = t match { + case Empty() => Set.empty + case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def size(t: Tree) : BigInt = (t match { + case Empty() => BigInt(0) + case Node(_, l, v, r) => size(l) + 1 + size(r) + }) ensuring(_ >= 0) + + def isBlack(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(),_,_,_) => true + case _ => false + } + + def redNodesHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def redDescHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def blackBalanced(t : Tree) : Boolean = t match { + case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r) + case Empty() => true + } + + def blackHeight(t : Tree) : Int = t match { + case Empty() => 1 + case Node(Black(), l, _, _) => blackHeight(l) + 1 + case Node(Red(), l, _, _) => blackHeight(l) + } + + def ins(x: Int, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + t match { + case Empty() => Node(Red(),Empty(),x,Empty()) + case Node(c,a,y,b) => + if (x < y) balance(c, ins(x, a), y, b) + else if (x == y) Node(c,a,y,b) + else balance(c,a,y,ins(x, b)) + } + } ensuring (res => content(res) == content(t) ++ Set(x) + && size(t) <= size(res) && size(res) <= size(t) + 1 + && redDescHaveBlackChildren(res) + && blackBalanced(res)) + + def balance(c: Color, a: Tree, x: Int, b: Tree): Tree = { + Node(c,a,x,b) match { + case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(c,a,xV,b) => Node(c,a,xV,b) + } + } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res)) + + def buggyAdd(x: Int, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t)) + ins(x, t) + } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res)) +} diff --git a/_static/invalid/SpecWithExtern.html b/_static/invalid/SpecWithExtern.html new file mode 100644 index 0000000000..064d0fb80b --- /dev/null +++ b/_static/invalid/SpecWithExtern.html @@ -0,0 +1,33 @@ + + + +invalid/SpecWithExtern.scala + + +

SpecWithExtern.scala [raw]


+
import stainless.annotation._
+
+object SpecWithExtern {
+
+
+  //random between returns any value between l and h.
+  //For execution via scalac, we pick one valid implementation, but
+  //we would like the program to be verified versus any possible
+  //implementation, which should happen thanks to @extern
+  @extern
+  def randomBetween(l: Int, h: Int): Int = {
+    require(l <= h)
+    l
+  } ensuring(res => (res >= l && res <= h))
+
+  //postcondition is wrong, but if stainless considers 
+  //actual body of randomBetween it would be correct
+  def wrongProp(): Int = {
+    randomBetween(0, 10)
+  } ensuring(res => res >= 0 && res < 10)
+// Counterexample for postcondition violation in `wrongProp`:
+// empty counter example
+
+}
+
+

back

diff --git a/_static/invalid/SpecWithExtern.scala b/_static/invalid/SpecWithExtern.scala new file mode 100644 index 0000000000..4480b715f1 --- /dev/null +++ b/_static/invalid/SpecWithExtern.scala @@ -0,0 +1,22 @@ +import stainless.annotation._ + +object SpecWithExtern { + + + //random between returns any value between l and h. + //For execution via scalac, we pick one valid implementation, but + //we would like the program to be verified versus any possible + //implementation, which should happen thanks to @extern + @extern + def randomBetween(l: Int, h: Int): Int = { + require(l <= h) + l + } ensuring(res => (res >= l && res <= h)) + + //postcondition is wrong, but if stainless considers + //actual body of randomBetween it would be correct + def wrongProp(): Int = { + randomBetween(0, 10) + } ensuring(res => res >= 0 && res < 10) + +} diff --git a/_static/jquery.js b/_static/jquery.js new file mode 100644 index 0000000000..624bca829e --- /dev/null +++ b/_static/jquery.js @@ -0,0 +1,10879 @@ +/*! + * jQuery JavaScript Library v3.6.0 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright OpenJS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + // Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5 + // Plus for old WebKit, typeof returns "function" for HTML collections + // (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756) + return typeof obj === "function" && typeof obj.nodeType !== "number" && + typeof obj.item !== "function"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.6.0", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), + function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); + } ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.6 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2021-02-16 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem && elem.namespaceURI, + docElem = elem && ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +} +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the primary Deferred + primary = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + primary.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( primary.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return primary.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject ); + } + + return primary.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + + // Support: Chrome 86+ + // In Chrome, if an element having a focusout handler is blurred by + // clicking outside of it, it invokes the handler synchronously. If + // that handler calls `.remove()` on the element, the data is cleared, + // leaving `result` undefined. We need to guard against this. + return result && result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + which: true +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + // Suppress native focus or blur as it's already being fired + // in leverageNative. + _default: function() { + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + // + // Support: Firefox 70+ + // Only Firefox includes border widths + // in computed dimensions. (gh-4529) + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate"; + tr.style.cssText = "border:1px solid"; + + // Support: Chrome 86+ + // Height set through cssText does not get applied. + // Computed height then comes back as 0. + tr.style.height = "1px"; + trChild.style.height = "9px"; + + // Support: Android 8 Chrome 86+ + // In our bodyBackground.html iframe, + // display for all div elements is set to "inline", + // which causes a problem only in Android 8 Chrome 86. + // Ensuring the div is display: block + // gets around this issue. + trChild.style.display = "block"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) + + parseInt( trStyle.borderTopWidth, 10 ) + + parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml, parserErrorElem; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) {} + + parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ]; + if ( !xml || parserErrorElem ) { + jQuery.error( "Invalid XML: " + ( + parserErrorElem ? + jQuery.map( parserErrorElem.childNodes, function( el ) { + return el.textContent; + } ).join( "\n" ) : + data + ) ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ).filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ).map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + +originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script but not if jsonp + if ( !isSuccess && + jQuery.inArray( "script", s.dataTypes ) > -1 && + jQuery.inArray( "json", s.dataTypes ) < 0 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " + + + + + + + + + + + + +
+
+
+
+
+
+
+
+
+
+
+
+
+

Packages

+ +
+
+
+ +
+
p
+ +

root package + + + +

+ +
+ +

+ + + package + + + root + +

+ + +
+ + + + +
+
+ + + + + + + + + + + +
+ +
+ + +
+ +
+
+

Ungrouped

+ +
+
+ +
+ +
+ + + +
+
+
+ + diff --git a/_static/stainless-library/index.js b/_static/stainless-library/index.js new file mode 100644 index 0000000000..c53b2200d8 --- /dev/null +++ b/_static/stainless-library/index.js @@ -0,0 +1 @@ +Index.PACKAGES = {"stainless.io" : [{"name" : "stainless.io.FileInputStream", "shortDescription" : "", "object" : "stainless\/io\/FileInputStream$.html", "members_object" : [{"label" : "open", "tail" : "(filename: String)(state: State): FileInputStream", "member" : "stainless.io.FileInputStream.open", "link" : "stainless\/io\/FileInputStream$.html#open(filename:String)(implicitstate:stainless.io.State):stainless.io.FileInputStream", "kind" : "def"}, {"label" : "synchronized", "tail" : "(arg0: ⇒ T0): T0", "member" : "scala.AnyRef.synchronized", "link" : "stainless\/io\/FileInputStream$.html#synchronized[T0](x$1:=>T0):T0", "kind" : "final def"}, {"label" : "##", "tail" : "(): Int", "member" : "scala.AnyRef.##", "link" : "stainless\/io\/FileInputStream$.html###():Int", "kind" : 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window. + */ +$(document).ready(function() +{ + // hide diagrams in browsers not supporting SVG + if(Modernizr && !Modernizr.inlinesvg) + return; + + if($("#content-diagram").length) + $("#inheritance-diagram").css("padding-bottom", "20px"); + + $(".diagram-container").css("display", "block"); + + $(".diagram").each(function() { + // store initial dimensions + $(this).data("width", $("svg", $(this)).width()); + $(this).data("height", $("svg", $(this)).height()); + // store unscaled clone of SVG element + $(this).data("svg", $(this).get(0).childNodes[0].cloneNode(true)); + }); + + // make diagram visible, hide container + $(".diagram").css("display", "none"); + $(".diagram svg").css({ + "position": "static", + "visibility": "visible", + "z-index": "auto" + }); + + // enable linking to diagrams + if($(location).attr("hash") == "#inheritance-diagram") { + diagrams.toggle($("#inheritance-diagram-container"), true); + } else if($(location).attr("hash") == "#content-diagram") { + diagrams.toggle($("#content-diagram-container"), true); + } + + $(".diagram-link").click(function() { + diagrams.toggle($(this).parent()); + }); + + // register resize function + $(window).resize(diagrams.resize); + + // don't bubble event to parent div + // when clicking on a node of a resized + // diagram + $("svg a").click(function(e) { + e.stopPropagation(); + }); + + diagrams.initHighlighting(); + + $("button#diagram-fs").click(function() { + $(".diagram-container").toggleClass("full-screen"); + $(".diagram-container > div.diagram").css({ + height: $("svg").height() + "pt" + }); + + $panzoom.panzoom("reset", { animate: false, contain: false }); + }); +}); + +/** + * Initializes highlighting for nodes and edges. + */ +diagrams.initHighlighting = function() +{ + // helper function since $.hover doesn't work in IE + + function hover(elements, fn) + { + elements.mouseover(fn); + elements.mouseout(fn); + } + + // inheritance edges + + hover($("svg .edge.inheritance"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + var parts = $(this).attr("id").split("_"); + toggleClass($("#" + parts[0] + "_" + parts[1])); + toggleClass($("#" + parts[0] + "_" + parts[2])); + toggleClass($(this)); + }); + + // nodes + + hover($("svg .node"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + var parts = $(this).attr("id").split("_"); + var index = parts[1]; + $("svg#" + parts[0] + " .edge.inheritance").each(function(){ + var parts2 = $(this).attr("id").split("_"); + if(parts2[1] == index) + { + toggleClass($("#" + parts2[0] + "_" + parts2[2])); + toggleClass($(this)); + } else if(parts2[2] == index) + { + toggleClass($("#" + parts2[0] + "_" + parts2[1])); + toggleClass($(this)); + } + }); + }); + + // incoming implicits + + hover($("svg .node.implicit-incoming"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .edge.implicit-incoming")); + toggleClass($("svg .node.this")); + }); + + hover($("svg .edge.implicit-incoming"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .node.this")); + $("svg .node.implicit-incoming").each(function(){ + toggleClass($(this)); + }); + }); + + // implicit outgoing nodes + + hover($("svg .node.implicit-outgoing"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .edge.implicit-outgoing")); + toggleClass($("svg .node.this")); + }); + + hover($("svg .edge.implicit-outgoing"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .node.this")); + $("svg .node.implicit-outgoing").each(function(){ + toggleClass($(this)); + }); + }); +}; + +/** + * Resizes the diagrams according to the available width. + */ +diagrams.resize = function() { + // available width + var availableWidth = $(".diagram-container").width(); + + $(".diagram-container").each(function() { + // unregister click event on whole div + $(".diagram", this).unbind("click"); + var diagramWidth = $(".diagram", this).data("width"); + var diagramHeight = $(".diagram", this).data("height"); + + if (diagramWidth > availableWidth) { + // resize diagram + var height = diagramHeight / diagramWidth * availableWidth; + $(".diagram svg", this).width(availableWidth); + $(".diagram svg", this).height(height); + } else { + // restore full size of diagram + $(".diagram svg", this).width(diagramWidth); + $(".diagram svg", this).height(diagramHeight); + // don't show custom cursor any more + $(".diagram", this).removeClass("magnifying"); + } + }); +}; + +/** + * Shows or hides a diagram depending on its current state. + */ +diagrams.toggle = function(container, dontAnimate) +{ + // change class of link + $(".diagram-link", container).toggleClass("open"); + // get element to show / hide + var div = $(".diagram", container); + if (div.is(':visible')) { + $(".diagram-help", container).hide(); + div.unbind("click"); + div.slideUp(100); + + $("#diagram-controls", container).hide(); + $("#inheritance-diagram-container").unbind('mousewheel.focal'); + } else { + diagrams.resize(); + if(dontAnimate) + div.show(); + else + div.slideDown(100); + $(".diagram-help", container).show(); + + $("#diagram-controls", container).show(); + + $(".diagram-container").on('mousewheel.focal', function(e) { + e.preventDefault(); + var delta = e.delta || e.originalEvent.wheelDelta; + var zoomOut = delta ? delta < 0 : e.originalEvent.deltaY > 0; + $panzoom.panzoom('zoom', zoomOut, { + increment: 0.1, + animate: true, + focal: e + }); + }); + } +}; + +/** + * Helper method that adds a class to a SVG element. + */ +diagrams.addClass = function(svgElem, newClass) { + newClass = newClass || "over"; + var classes = svgElem.attr("class"); + if ($.inArray(newClass, classes.split(/\s+/)) == -1) { + classes += (classes ? ' ' : '') + newClass; + svgElem.attr("class", classes); + } +}; + +/** + * Helper method that removes a class from a SVG element. + */ +diagrams.removeClass = function(svgElem, oldClass) { + oldClass = oldClass || "over"; + var classes = svgElem.attr("class"); + classes = $.grep(classes.split(/\s+/), function(n, i) { return n != oldClass; }).join(' '); + svgElem.attr("class", classes); +}; diff --git a/_static/stainless-library/lib/index.css b/_static/stainless-library/lib/index.css new file mode 100644 index 0000000000..488bf3b8b5 --- /dev/null +++ b/_static/stainless-library/lib/index.css @@ -0,0 +1,928 @@ +/* Fonts */ +@font-face { + font-family: 'Lato'; + font-style: normal; + font-weight: 100; + src: url('lato-v11-latin-regular.eot'); + src: local('Lato'), local('Lato'), + url('lato-v11-latin-100.eot?#iefix') format('embedded-opentype'), + url('lato-v11-latin-100.woff') format('woff'), + url('lato-v11-latin-100.ttf') format('truetype'); +} + +@font-face { + font-family: 'Lato'; + font-style: normal; + font-weight: 400; + src: url('lato-v11-latin-regular.eot'); + src: local('Lato'), local('Lato'), + url('lato-v11-latin-regular.eot?#iefix') format('embedded-opentype'), + url('lato-v11-latin-regular.woff') format('woff'), + url('lato-v11-latin-regular.ttf') format('truetype'); +} + +@font-face { + font-family: 'Open Sans'; + font-style: normal; + font-weight: 400; + src: url('open-sans-v13-latin-regular.eot'); + src: local('Open Sans'), local('OpenSans'), + url('open-sans-v13-latin-regular.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-regular.woff') format('woff'), + url('open-sans-v13-latin-regular.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: italic; + font-weight: 400; + src: url('open-sans-v13-latin-400i.eot'); + src: local('Open Sans Italic'), local('OpenSans-Italic'), + url('open-sans-v13-latin-400i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-400i.woff') format('woff'), + url('open-sans-v13-latin-400i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: oblique; + font-weight: 400; + src: url('open-sans-v13-latin-400i.eot'); + src: local('Open Sans Italic'), local('OpenSans-Italic'), + url('open-sans-v13-latin-400i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-400i.woff') format('woff'), + url('open-sans-v13-latin-400i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: normal; + font-weight: 700; + src: url('open-sans-v13-latin-700.eot'); + src: local('Open Sans Bold'), local('OpenSans-Bold'), + url('open-sans-v13-latin-700.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700.woff') format('woff'), + url('open-sans-v13-latin-700.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: italic; + font-weight: 700; + src: url('open-sans-v13-latin-700i.eot'); + src: local('Open Sans Bold Italic'), local('OpenSans-BoldItalic'), + url('open-sans-v13-latin-700i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700i.woff') format('woff'), + url('open-sans-v13-latin-700i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: oblique; + font-weight: 700; + src: url('open-sans-v13-latin-700i.eot'); + src: local('Open Sans Bold Italic'), local('OpenSans-BoldItalic'), + url('open-sans-v13-latin-700i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700i.woff') format('woff'), + url('open-sans-v13-latin-700i.ttf') format('truetype'); +} + +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 400; + src: url('source-code-pro-v6-latin-regular.eot'); + src: local('Source Code Pro'), local('SourceCodePro-Regular'), + url('source-code-pro-v6-latin-regular.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-regular.woff') format('woff'), + url('source-code-pro-v6-latin-regular.ttf') format('truetype'); +} +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 700; + src: url('source-code-pro-v6-latin-700.eot'); + src: local('Source Code Pro Bold'), local('SourceCodePro-Bold'), + url('source-code-pro-v6-latin-700.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-700.woff') format('woff'), + url('source-code-pro-v6-latin-700.ttf') format('truetype'); +} + +* { + color: inherit; + text-decoration: none; + font-family: "Lato", Arial, sans-serif; + border-width: 0px; + margin: 0px; +} + +u { + text-decoration: underline; +} + +a { + cursor: pointer; + text-decoration: none; +} + +a:hover { + text-decoration: underline; +} + +span.entity > a { + padding: 0.1em 0.5em; + margin-left: 0.2em; +} + +span.entity > a.selected { + background-color: #C2D2DC; + border-radius: 0.2em; +} + +html { + background-color: #f0f3f6; + box-sizing: border-box; +} +*, *:before, *:after { + box-sizing: inherit; +} + +textarea, input { outline: none; } + +#library { + display: none; +} + +#browser { + width: 17.5em; + top: 0px; + left: 0; + bottom: 0px; + display: block; + position: fixed; + background-color: #f0f3f6; +} + +#browser.full-screen { + left: -17.5em; +} + +#search { + background-color: #103a51; /* typesafe blue */ + min-height: 5.5em; + position: fixed; + top: 0; + left: 0; + right: 0; + height: 3em; + min-height: initial; + z-index: 103; + box-shadow: 0 0 4px rgba(0, 0, 0, 0.18), 0 4px 8px rgba(0, 0, 0, 0.28); +} + +#search > h1 { + font-size: 2em; + position: absolute; + left: 0.25em; + top: 0.5em; +} + +#search > h2 { + position: absolute; + left: 3.8em; + top: 3em; +} + +#search > img.scala-logo { + width: 3em; + height: auto; + position: absolute; + left: 5.8em; + top: 0.43em; +} + +#search > span.toggle-sidebar { + position: absolute; + top: 0.8em; + left: 0.2em; + color: #fff; + z-index: 99; + width: 1.5em; + height: 1.5em; +} + +#search > span#doc-title { + color: #fff; + position: absolute; + top: 0.8em; + left: 0; + width: 18em; + text-align: center; + cursor: pointer; + z-index: 2; +} + +#search > span#doc-title > span#doc-version { + color: #c2c2c2; + font-weight: 100; + font-size: 0.72em; + display: inline-block; + width: 12ex; + overflow: hidden; + white-space: nowrap; + text-overflow: ellipsis; +} + +#search > span#doc-title > span#doc-version:hover { + overflow: visible; +} + +#search > span.toggle-sidebar:hover { + cursor: pointer; +} + +/* Pseudo element replacing UTF8-symbol "Trigram From Heaven" */ +#search > span.toggle-sidebar:before { + position: absolute; + top: -0.45em; + left: 0.45em; + content: ""; + display: block; + width: 0.7em; + -webkit-box-shadow: 0 0.8em 0 1px #fff, 0 1.1em 0 1px #fff, 0 1.4em 0 1px #fff; + box-shadow: 0 0.8em 0 1px #fff, 0 1.1em 0 1px #fff, 0 1.4em 0 1px #fff; +} + +#search > span.toggle-sidebar:hover:before { + -webkit-box-shadow: 0 0.8em 0 1px #c2c2c2, 0 1.1em 0 1px #c2c2c2, 0 1.4em 0 1px #c2c2c2; + box-shadow: 0 0.8em 0 1px #c2c2c2, 0 1.1em 0 1px #c2c2c2, 0 1.4em 0 1px #c2c2c2; +} + +#textfilter > .pre { + display: block; + position: absolute; + top: 0; + left: 0; + height: 23px; + width: 21px; +} + +#textfilter { + position: absolute; + top: 0.5em; + bottom: 0.8em; + left: 0; + right: 0; + display: block; + height: 2em; +} + +#textfilter > .input { + position: relative; + display: block; + padding: 0.2em; + max-width: 48.5em; + margin: 0 auto; +} + +#textfilter > .input > i#search-icon { + color: rgba(255,255,255, 0.4); + position: absolute; + left: 0.34em; + top: 0.3em; + font-size: 1.3rem; +} + +#textfilter > span.toggle { + cursor: pointer; + padding-left: 15px; + position: absolute; + left: -0.55em; + top: 3em; + z-index: 99; + color: #fff; + font-size: 0.8em; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#textfilter > span.toggle:hover { + color: #c2c2c2; +} + +#textfilter > span.toggle:hover { + cursor: pointer; +} + +#textfilter > .hide:hover { + cursor: pointer; + color: #a2a2a2; +} + +#textfilter > .input > input { + font-family: "Open Sans"; + font-size: 0.85em; + height: 2em; + padding: 0 0 0 2.1em; + color: #fff; + width: 100%; + border-radius: 0.2em; + background: rgba(255, 255, 255, 0.2); +} + + +#textfilter > .input > input::-webkit-input-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input::-moz-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input:-ms-input-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input:-moz-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#focusfilter > .focusremove:hover { + text-decoration: none; +} + +#textfilter > .input > .clear { + display: none; + position: absolute; + font-size: 0.9em; + top: 0.7em; + right: 0.1em; + height: 23px; + width: 21px; + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > .clear:hover { + cursor: pointer; + color: #fff; +} + +#focusfilter { + font-size: 0.9em; + position: relative; + text-align: center; + display: none; + padding: 0.6em; + background-color: #f16665; + color: #fff; + margin: 3.9em 0.55em 0 0.35em; + border-radius: 0.2em; + z-index: 1; +} + +div#search-progress { + position: absolute; + top: 0; + left: 0; + width: 100%; + height: 0.25em; +} + +div#search-progress > div#progress-fill { + width: 0%; + background-color: #f16665; + transition: 0.1s; +} + +#focusfilter .focuscoll { + font-weight: bold; +} + +#focusfilter a.focusremove { + margin-left: 0.2em; + font-size: 0.9em; +} + +#kindfilter-container { + position: fixed; + display: block; + z-index: 99; + bottom: 0.5em; + left: 0; + width: 17.25em; +} + +#kindfilter { + float: right; + text-align: center; + padding: 0.3em 1em; + border-radius: 0.8em; + background: #f16665; + border-bottom: 2px solid #d64546; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; + color: #fff; + font-size: 0.8em; +} + +#kindfilter:hover { + cursor: pointer; + background-color: rgb(226, 87, 88); +} + +#letters { + position: relative; + text-align: center; + border: 0; + margin-top: 0em; + color: #fff; +} + +#letters > a, #letters > span { + color: #fff; + font-size: 0.67em; + padding-right: 2px; +} + +#letters > a:hover { + text-decoration: none; + color: #c2c2c2; +} + +#letters > span { + color: #bbb; +} + +div#content-scroll-container { + position: absolute; + top: 0; + right: 0; + bottom: 0; + left: 0; + z-index: 100; + overflow-x: hidden; + overflow-y: auto; +} + +div#content-container { + max-width: 1140px; + margin: 0 auto; +} + +div#content-container > div#content { + -webkit-overflow-scrolling: touch; + display: block; + overflow-y: hidden; + max-width: 1140px; + margin: 4em auto 0; +} + +div#content-container > div#subpackage-spacer { + float: right; + height: 100%; + margin: 1.1rem 0.5rem 0 0.5em; + font-size: 0.8em; + min-width: 8rem; + max-width: 16rem; +} + +div#packages > h1 { + color: #103a51; +} + +div#packages > ul { + list-style-type: none; +} + +div#packages > ul > li { + position: relative; + margin: 0.5rem 0; + width: 100%; + border-radius: 0.2em; + min-height: 1.5em; + padding-left: 2em; +} + +div#packages > ul > li.current-entities { + margin: 0.3rem 0; +} + +div#packages > ul > li.current:hover { + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + cursor: pointer; +} + +div#packages > ul > li.current-entities > *:nth-child(1), +div#packages > ul > li.current-entities > *:nth-child(2) { + float: left; + display: inline; + height: 1rem; + width: 1rem; + margin: 1px 0 0 0; + cursor: pointer; +} + +div#packages > ul > li > a.class { + background: url("class.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.trait { + background: url("trait.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.object { + background: url("object.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.abstract.type { + background: url("abstract_type.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a { + text-decoration: none !important; + margin-left: 1px; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.9em; +} + +/* Indentation levels for packages */ +div#packages > ul > li.indented0 { padding-left: 0em; } +div#packages > ul > li.indented1 { padding-left: 1em; } +div#packages > ul > li.indented2 { padding-left: 2em; } +div#packages > ul > li.indented3 { padding-left: 3em; } +div#packages > ul > li.indented4 { padding-left: 4em; } +div#packages > ul > li.indented5 { padding-left: 5em; } +div#packages > ul > li.indented6 { padding-left: 6em; } +div#packages > ul > li.indented7 { padding-left: 7em; } +div#packages > ul > li.indented8 { padding-left: 8em; } +div#packages > ul > li.indented9 { padding-left: 9em; } +div#packages > ul > li.indented10 { padding-left: 10em; } +div#packages > ul > li.current.indented0 { padding-left: -0.5em } +div#packages > ul > li.current.indented1 { padding-left: 0.5em } +div#packages > ul > li.current.indented2 { padding-left: 1.5em } +div#packages > ul > li.current.indented3 { padding-left: 2.5em } +div#packages > ul > li.current.indented4 { padding-left: 3.5em } +div#packages > ul > li.current.indented5 { padding-left: 4.5em } +div#packages > ul > li.current.indented6 { padding-left: 5.5em } +div#packages > ul > li.current.indented7 { padding-left: 6.5em } +div#packages > ul > li.current.indented8 { padding-left: 7.5em } +div#packages > ul > li.current.indented9 { padding-left: 8.5em } +div#packages > ul > li.current.indented10 { padding-left: 9.5em } + +div#packages > ul > li.current > span.symbol { + border-left: 0.25em solid #72D0EB; + padding-left: 0.25em; +} + +div#packages > ul > li > span.symbol > a { + text-decoration: none; +} + +div#packages > ul > li > span.symbol > span.name { + font-weight: normal; +} + +div#packages > ul > li .fullcomment, +div#packages > ul > li .modifier_kind, +div#packages > ul > li .permalink, +div#packages > ul > li .shortcomment { + display: none; +} + +div#search-results { + color: #103a51; + position: absolute; + left: 0; + top: 3em; + right: 0; + bottom: 0; + background-color: rgb(240, 243, 246); + z-index: 101; + overflow-x: hidden; + display: none; + padding: 1em; + -webkit-overflow-scrolling: touch; +} + +div#search > span.close-results { + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + position: fixed; + top: 0.8em; + left: 1em; + color: #fff; + display: none; + z-index: 1; +} + +div#search > span.close-results:hover { + cursor: pointer; +} + +div#results-content { + max-width: 1140px; + margin: 0 auto; +} + +div#results-content > span.search-text { + margin-left: 1em; + font-size: 1.2em; + float: left; + width: 100%; +} + +div#results-content > span.search-text > span.query-str { + font-weight: 900; +} + +div#results-content > div > h1.result-type { + font-size: 1.5em; + margin: 1em 0 0.3em; + font-family: "Open Sans"; + font-weight: 300; + border-bottom: 1px solid #103a51; +} + +div#results-content > div#entity-results { + float: left; + width: 50%; + padding: 1em; + display: inline; +} + +div#results-content > div#member-results { + float: left; + width: 50%; + padding: 1em; + display: inline; +} + +div#results-content > div#member-results > a.package, +div#results-content > div#entity-results > a.package { + font-size: 1em; + margin: 0 0 1em 0; + color: #f16665; + cursor: pointer; +} + +div#results-content > div#member-results > ul.entities, +div#results-content > div#entity-results > ul.entities { + list-style-type: none; + padding-left: 0; +} + +div#results-content > div#member-results > ul.entities > li, +div#results-content > div#entity-results > ul.entities > li { + margin: 0.5em 0; +} + +div#results-content > div#member-results > ul.entities > li > .icon, +div#results-content > div#entity-results > ul.entities > li > .icon { + float: left; + display: inline; + height: 1em; + width: 1em; + margin: 0.23em 0 0; + cursor: pointer; +} + +div#results-content > div#member-results > ul.entities > li > .icon.class, +div#results-content > div#entity-results > ul.entities > li > .icon.class { + background: url("class.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > .icon.trait, +div#results-content > div#entity-results > ul.entities > li > .icon.trait { + background: url("trait.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > .icon.object, +div#results-content > div#entity-results > ul.entities > li > .icon.object { + background: url("object.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > span.entity, +div#results-content > div#entity-results > ul.entities > li > span.entity { + font-size: 1.1em; + font-weight: 900; +} + +div#results-content > div#member-results > ul.entities > li > ul.members, +div#results-content > div#entity-results > ul.entities > li > ul.members { + margin-top: 0.5em; + list-style-type: none; + font-size: 0.85em; + margin-left: 0.2em; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li, +div#results-content > div#entity-results > ul.entities > li > ul.members > li { + margin: 0.5em 0; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.kind, +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.tail, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > span.kind, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > span.tail { + margin-right: 0.6em; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.kind { + font-weight: 600; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > a.label, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > a.label { + color: #2C3D9B; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +/** Scrollpane settings needed for jquery.scrollpane.min.js */ +.jspContainer { + overflow: hidden; + position: relative; +} + +.jspPane { + position: absolute; +} + +.jspVerticalBar { + position: absolute; + top: 0; + right: 0; + width: 0.6em; + height: 100%; + background: transparent; +} + +.jspHorizontalBar { + position: absolute; + bottom: 0; + left: 0; + width: 100%; + height: 16px; + background: red; +} + +.jspCap { + display: none; +} + +.jspHorizontalBar .jspCap { + float: left; +} + +.jspTrack { + background: #f0f3f6; + position: relative; +} + +.jspDrag { + display: none; + background: rgba(0, 0, 0, 0.35); + position: relative; + top: 0; + left: 0; + cursor: pointer; +} + +#tpl:hover .jspDrag { + display: block; +} + +.jspHorizontalBar .jspTrack, +.jspHorizontalBar .jspDrag { + float: left; + height: 100%; +} + +.jspArrow { + background: #50506d; + text-indent: -20000px; + display: block; + cursor: pointer; + padding: 0; + margin: 0; +} + +.jspArrow.jspDisabled { + cursor: default; + background: #80808d; +} + +.jspVerticalBar .jspArrow { + height: 16px; +} + +.jspHorizontalBar .jspArrow { + width: 16px; + float: left; + height: 100%; +} + +.jspVerticalBar .jspArrow:focus { + outline: none; +} + +.jspCorner { + background: #eeeef4; + float: left; + height: 100%; +} + +/* CSS Hack for IE6 3 pixel bug */ +* html .jspCorner { + margin: 0 -3px 0 0; +} + +/* Media query rules for smaller viewport */ +@media only screen /* Large screen with a small window */ +and (max-width: 1300px) +{ + #textfilter { + left: 17.8em; + right: 0.35em; + } + + #textfilter .input { + max-width: none; + margin: 0; + } +} + +@media only screen /* Large screen with a smaller window */ +and (max-width: 800px) +{ + div#results-content > div#entity-results { + width: 100%; + padding: 0em; + } + + div#results-content > div#member-results { + width: 100%; + padding: 0em; + } +} + +/* Media query rules specifically for mobile devices */ +@media +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + div#content-container > div#subpackage-spacer { + display: none; + } + + div#content-container > div#content { + margin: 3.3em auto 0; + } + + #search > span#doc-title { + width: 100%; + text-align: left; + padding-left: 0.7em; + top: 0.95em; + z-index: 1; + } + + #search > div#textfilter { + z-index: 2; + } + + #search > span#doc-title > span#doc-version { + display: none; + } + + #textfilter { + left: 12.2em; + } +} diff --git a/_static/stainless-library/lib/index.js b/_static/stainless-library/lib/index.js new file mode 100644 index 0000000000..12f6ed6889 --- /dev/null +++ b/_static/stainless-library/lib/index.js @@ -0,0 +1,616 @@ +// © 2009–2010 EPFL/LAMP +// code by Gilles Dubochet with contributions by Johannes Rudolph, "spiros", Marcin Kubala and Felix Mulder + +var scheduler = undefined; + +var title = $(document).attr('title'); + +var lastFragment = ""; + +var Index = {}; +(function (ns) { + ns.keyLength = 0; + ns.keys = function (obj) { + var result = []; + var key; + for (key in obj) { + result.push(key); + ns.keyLength++; + } + return result; + } +})(Index); + +/** Find query string from URL */ +var QueryString = function(key) { + if (QueryString.map === undefined) { // only calc once + QueryString.map = {}; + var keyVals = window.location.search.split("?").pop().split("&"); + keyVals.forEach(function(elem) { + var pair = elem.split("="); + if (pair.length == 2) QueryString.map[pair[0]] = pair[1]; + }); + } + + return QueryString.map[key]; +}; + +$(document).ready(function() { + // Clicking #doc-title returns the user to the root package + $("#doc-title").on("click", function() { document.location = toRoot + "index.html" }); + + scheduler = new Scheduler(); + scheduler.addLabel("init", 1); + scheduler.addLabel("focus", 2); + scheduler.addLabel("filter", 4); + scheduler.addLabel("search", 5); + + configureTextFilter(); + + $("#index-input").on("input", function(e) { + if($(this).val().length > 0) + $("#textfilter > .input > .clear").show(); + else + $("#textfilter > .input > .clear").hide(); + }); + + if (QueryString("search") !== undefined) { + $("#index-input").val(QueryString("search")); + searchAll(); + } +}); + +/* Handles all key presses while scrolling around with keyboard shortcuts in search results */ +function handleKeyNavigation() { + /** Iterates both back and forth among selected elements */ + var EntityIterator = function (litems, ritems) { + var it = this; + this.index = -1; + + this.items = litems; + this.litems = litems; + this.ritems = ritems; + + if (litems.length == 0) + this.items = ritems; + + /** Returns the next entry - if trying to select past last element, it + * returns the last element + */ + it.next = function() { + it.index = Math.min(it.items.length - 1, it.index + 1); + return $(it.items[it.index]); + }; + + /** Returns the previous entry - will return `undefined` instead if + * selecting up from first element + */ + it.prev = function() { + it.index = Math.max(-1, it.index - 1); + return it.index == -1 ? undefined : $(it.items[it.index]); + }; + + it.right = function() { + if (it.ritems.length != 0) { + it.items = it.ritems; + it.index = Math.min(it.index, it.items.length - 1); + } + return $(it.items[it.index]); + }; + + it.left = function() { + if (it.litems.length != 0) { + it.items = it.litems; + it.index = Math.min(it.index, it.items.length - 1); + } + return $(it.items[it.index]); + }; + }; + + function safeOffset($elem) { + return $elem.length ? $elem.offset() : { top:0, left:0 }; // offset relative to viewport + } + + /** Scroll helper, ensures that the selected elem is inside the viewport */ + var Scroller = function ($container) { + scroller = this; + scroller.container = $container; + + scroller.scrollDown = function($elem) { + var offset = safeOffset($elem); + if (offset !== undefined) { + var yPos = offset.top; + if ($container.height() < yPos || (yPos - $("#search").height()) < 0) { + $container.animate({ + scrollTop: $container.scrollTop() + yPos - $("#search").height() - 10 + }, 200); + } + } + }; + + scroller.scrollUp = function ($elem) { + var offset = safeOffset($elem); + if (offset !== undefined) { + var yPos = offset.top; + if (yPos < $("#search").height()) { + $container.animate({ + scrollTop: $container.scrollTop() + yPos - $("#search").height() - 10 + }, 200); + } + } + }; + + scroller.scrollTop = function() { + $container.animate({ + scrollTop: 0 + }, 200); + } + }; + + scheduler.add("init", function() { + $("#textfilter input").trigger("blur"); + var items = new EntityIterator( + $("div#results-content > div#entity-results > ul.entities span.entity > a").toArray(), + $("div#results-content > div#member-results > ul.entities span.entity > a").toArray() + ); + + var scroller = new Scroller($("#search-results")); + + var $old = items.next(); + $old.addClass("selected"); + scroller.scrollDown($old); + + $(window).on("keydown", function(e) { + switch ( e.keyCode ) { + case 9: // tab + $old.removeClass("selected"); + break; + + case 13: // enter + var href = $old.attr("href"); + location.replace(href); + $old.trigger("click"); + $("#textfilter input").val(""); + break; + + case 27: // escape + $("#textfilter input").val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + break; + + case 37: // left + var oldTop = safeOffset($old).top; + $old.removeClass("selected"); + $old = items.left(); + $old.addClass("selected"); + + (oldTop - safeOffset($old).top < 0 ? scroller.scrollDown : scroller.scrollUp)($old); + break; + + case 38: // up + $old.removeClass('selected'); + $old = items.prev(); + + if ($old === undefined) { // scroll past top + $(window).off("keydown"); + $("#textfilter input").trigger("focus"); + scroller.scrollTop(); + return false; + } else { + $old.addClass("selected"); + scroller.scrollUp($old); + } + break; + + case 39: // right + var oldTop = safeOffset($old).top; + $old.removeClass("selected"); + $old = items.right(); + $old.addClass("selected"); + + (oldTop - safeOffset($old).top < 0 ? scroller.scrollDown : scroller.scrollUp)($old); + break; + + case 40: // down + $old.removeClass("selected"); + $old = items.next(); + $old.addClass("selected"); + scroller.scrollDown($old); + break; + } + }); + }); +} + +/* Configures the text filter */ +function configureTextFilter() { + scheduler.add("init", function() { + var input = $("#textfilter input"); + input.on('keyup', function(event) { + switch ( event.keyCode ) { + case 27: // escape + input.val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + break; + + case 38: // up arrow + return false; + + case 40: // down arrow + $(window).off("keydown"); + handleKeyNavigation(); + return false; + } + + searchAll(); + }); + }); + scheduler.add("init", function() { + $("#textfilter > .input > .clear").on("click", function() { + $("#textfilter input").val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + + $(this).hide(); + }); + }); + + scheduler.add("init", function() { + $("div#search > span.close-results").on("click", function() { + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + $("#textfilter input").val(""); + }); + }); +} + +function compilePattern(query) { + var escaped = query.replace(/([\.\*\+\?\|\(\)\[\]\\])/g, '\\$1'); + + if (query.toLowerCase() != query) { + // Regexp that matches CamelCase subbits: "BiSe" is + // "[a-z]*Bi[a-z]*Se" and matches "BitSet", "ABitSet", ... + return new RegExp(escaped.replace(/([A-Z])/g,"[a-z]*$1")); + } + else { // if query is all lower case make a normal case insensitive search + return new RegExp(escaped, "i"); + } +} + +/** Searches packages for entites matching the search query using a regex + * + * @param {[Object]} pack: package being searched + * @param {RegExp} regExp: a regular expression for finding matching entities + */ +function searchPackage(pack, regExp) { + scheduler.add("search", function() { + var entities = Index.PACKAGES[pack]; + var matched = []; + var notMatching = []; + + scheduler.add("search", function() { + searchMembers(entities, regExp, pack); + }); + + entities.forEach(function (elem) { + regExp.test(elem.name) ? matched.push(elem) : notMatching.push(elem); + }); + + var results = { + "matched": matched, + "package": pack + }; + + scheduler.add("search", function() { + handleSearchedPackage(results, regExp); + setProgress(); + }); + }); +} + +function searchMembers(entities, regExp, pack) { + var memDiv = document.getElementById("member-results"); + var packLink = document.createElement("a"); + packLink.className = "package"; + packLink.appendChild(document.createTextNode(pack)); + packLink.style.display = "none"; + packLink.title = pack; + packLink.href = toRoot + urlFriendlyEntity(pack).replace(new RegExp("\\.", "g"), "/") + "/index.html"; + memDiv.appendChild(packLink); + + var entityUl = document.createElement("ul"); + entityUl.className = "entities"; + memDiv.appendChild(entityUl); + + entities.forEach(function(entity) { + var entityLi = document.createElement("li"); + var name = entity.name.split('.').pop() + + var iconElem = document.createElement("a"); + iconElem.className = "icon " + entity.kind; + iconElem.title = name + " " + entity.kind; + iconElem.href = toRoot + entity[entity.kind]; + entityLi.appendChild(iconElem); + + if (entity.kind != "object" && entity.object) { + var companion = document.createElement("a"); + companion.className = "icon object"; + companion.title = name + " companion object"; + companion.href = toRoot + entity.object; + entityLi.insertBefore(companion, iconElem); + } else { + var spacer = document.createElement("div"); + spacer.className = "icon spacer"; + entityLi.insertBefore(spacer, iconElem); + } + + var nameElem = document.createElement("span"); + nameElem.className = "entity"; + + var entityUrl = document.createElement("a"); + entityUrl.title = entity.shortDescription ? entity.shortDescription : name; + entityUrl.href = toRoot + entity[entity.kind]; + entityUrl.appendChild(document.createTextNode(name)); + + nameElem.appendChild(entityUrl); + entityLi.appendChild(nameElem); + + var membersUl = document.createElement("ul"); + membersUl.className = "members"; + entityLi.appendChild(membersUl); + + + searchEntity(entity, membersUl, regExp) + .then(function(res) { + if (res.length > 0) { + packLink.style.display = "block"; + entityUl.appendChild(entityLi); + } + }); + }); +} + +/** This function inserts `li` into the `ul` ordered by the li's id + * + * @param {Node} ul: the list in which to insert `li` + * @param {Node} li: item to insert + */ +function insertSorted(ul, li) { + var lis = ul.childNodes; + var beforeLi = null; + + for (var i = 0; i < lis.length; i++) { + if (lis[i].id > li.id) + beforeLi = lis[i]; + } + + // if beforeLi == null, it will be inserted last + ul.insertBefore(li, beforeLi); +} + +/** Defines the callback when a package has been searched and searches its + * members + * + * It will search all entities which matched the regExp. + * + * @param {Object} res: this is the searched package. It will contain the map + * from the `searchPackage`function. + * @param {RegExp} regExp + */ +function handleSearchedPackage(res, regExp) { + $("div#search-results").show(); + $("#search > span.close-results").show(); + $("#search > span#doc-title").hide(); + + var searchRes = document.getElementById("results-content"); + var entityDiv = document.getElementById("entity-results"); + + var packLink = document.createElement("a"); + packLink.className = "package"; + packLink.title = res.package; + packLink.href = toRoot + urlFriendlyEntity(res.package).replace(new RegExp("\\.", "g"), "/") + "/index.html"; + packLink.appendChild(document.createTextNode(res.package)); + + if (res.matched.length == 0) + packLink.style.display = "none"; + + entityDiv.appendChild(packLink); + + var ul = document.createElement("ul") + ul.className = "entities"; + + // Generate html list items from results + res.matched + .map(function(entity) { return listItem(entity, regExp); }) + .forEach(function(li) { ul.appendChild(li); }); + + entityDiv.appendChild(ul); +} + +/** Searches an entity asynchronously for regExp matches in an entity's members + * + * @param {Object} entity: the entity to be searched + * @param {Node} ul: the list in which to insert the list item created + * @param {RegExp} regExp + */ +function searchEntity(entity, ul, regExp) { + return new Promise(function(resolve, reject) { + var allMembers = + (entity.members_trait || []) + .concat(entity.members_class || []) + .concat(entity.members_object || []) + + var matchingMembers = $.grep(allMembers, function(member, i) { + return regExp.test(member.label); + }); + + resolve(matchingMembers); + }) + .then(function(res) { + res.forEach(function(elem) { + var kind = document.createElement("span"); + kind.className = "kind"; + kind.appendChild(document.createTextNode(elem.kind)); + + var label = document.createElement("a"); + label.title = elem.label; + label.href = toRoot + elem.link; + label.className = "label"; + label.appendChild(document.createTextNode(elem.label)); + + var tail = document.createElement("span"); + tail.className = "tail"; + tail.appendChild(document.createTextNode(elem.tail)); + + var li = document.createElement("li"); + li.appendChild(kind); + li.appendChild(label); + li.appendChild(tail); + + ul.appendChild(li); + }); + return res; + }); +} + +/** Creates a list item representing an entity + * + * @param {Object} entity, the searched entity to be displayed + * @param {RegExp} regExp + * @return {Node} list item containing entity + */ +function listItem(entity, regExp) { + var name = entity.name.split('.').pop() + var nameElem = document.createElement("span"); + nameElem.className = "entity"; + + var entityUrl = document.createElement("a"); + entityUrl.title = entity.shortDescription ? entity.shortDescription : name; + entityUrl.href = toRoot + entity[entity.kind]; + + entityUrl.appendChild(document.createTextNode(name)); + nameElem.appendChild(entityUrl); + + var iconElem = document.createElement("a"); + iconElem.className = "icon " + entity.kind; + iconElem.title = name + " " + entity.kind; + iconElem.href = toRoot + entity[entity.kind]; + + var li = document.createElement("li"); + li.id = entity.name.replace(new RegExp("\\.", "g"),"-"); + li.appendChild(iconElem); + li.appendChild(nameElem); + + if (entity.kind != "object" && entity.object) { + var companion = document.createElement("a"); + companion.title = name + " companion object"; + companion.href = toRoot + entity.object; + companion.className = "icon object"; + li.insertBefore(companion, iconElem); + } else { + var spacer = document.createElement("div"); + spacer.className = "icon spacer"; + li.insertBefore(spacer, iconElem); + } + + var ul = document.createElement("ul"); + ul.className = "members"; + + li.appendChild(ul); + + return li; +} + +/** Searches all packages and entities for the current search string in + * the input field "#textfilter" + * + * Then shows the results in div#search-results + */ +function searchAll() { + scheduler.clear("search"); // clear previous search + maxJobs = 1; // clear previous max + var searchStr = ($("#textfilter input").val() || '').trim(); + + if (searchStr === '') { + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + return; + } + + // Replace ?search=X with current search string if not hosted locally on Chrome + try { + window.history.replaceState({}, "", "?search=" + searchStr); + } catch(e) {} + + $("div#results-content > span.search-text").remove(); + + var memberResults = document.getElementById("member-results"); + memberResults.innerHTML = ""; + var memberH1 = document.createElement("h1"); + memberH1.className = "result-type"; + memberH1.innerHTML = "Member results"; + memberResults.appendChild(memberH1); + + var entityResults = document.getElementById("entity-results"); + entityResults.innerHTML = ""; + var entityH1 = document.createElement("h1"); + entityH1.className = "result-type"; + entityH1.innerHTML = "Entity results"; + entityResults.appendChild(entityH1); + + $("div#results-content").prepend( + $("") + .addClass("search-text") + .append(document.createTextNode(" Showing results for ")) + .append($("").addClass("query-str").text(searchStr)) + ); + + var regExp = compilePattern(searchStr); + + // Search for all entities matching query + Index + .keys(Index.PACKAGES) + .sort() + .forEach(function(elem) { searchPackage(elem, regExp); }) +} + +/** Check if user agent is associated with a known mobile browser */ +function isMobile() { + return /Android|webOS|Mobi|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini/i.test(navigator.userAgent); +} + +function urlFriendlyEntity(entity) { + var corr = { + '\\+': '$plus', + ':': '$colon' + }; + + for (k in corr) + entity = entity.replace(new RegExp(k, 'g'), corr[k]); + + return entity; +} + +var maxJobs = 1; +function setProgress() { + var running = scheduler.numberOfJobs("search"); + 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Code Pro Bold'), local('SourceCodePro-Bold'), + url('source-code-pro-v6-latin-700.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-700.woff') format('woff'), + url('source-code-pro-v6-latin-700.ttf') format('truetype'); +} + +body { + font-size: 10pt; + font-family: Arial, sans-serif; +} + +a { + color:#315479; +} + +.letters { + width:100%; + text-align:center; + margin:0.6em; + padding:0.1em; + border-bottom:1px solid gray; +} + +div.entry { + padding: 0.5em; + background-color: #e1e7ed; + border-radius: 0.2em; + color: #103a51; + margin: 0.5em 0; +} + +.name { + font-family: "Source Code Pro"; + font-size: 1.1em; +} + +.occurrences { + margin-left: 1em; + margin-top: 5px; +} diff --git a/_static/stainless-library/lib/scheduler.js b/_static/stainless-library/lib/scheduler.js new file mode 100644 index 0000000000..eb396bb5d3 --- /dev/null +++ b/_static/stainless-library/lib/scheduler.js @@ -0,0 +1,108 @@ +// © 2010 EPFL/LAMP +// code by Gilles Dubochet, Felix Mulder + +function Scheduler() { + var scheduler = this; + var resolution = 0; + this.timeout = undefined; + this.queues = new Array(0); // an array of work packages indexed by index in the labels table. + this.labels = new Array(0); // an indexed array of labels indexed by priority. This should be short. + + this.label = function(name, priority) { + this.name = name; + this.priority = priority; + } + + this.work = function(fn, self, args) { + this.fn = fn; + this.self = self; + this.args = args; + } + + this.addLabel = function(name, priority) { + var idx = 0; + while (idx < scheduler.queues.length && scheduler.labels[idx].priority <= priority) { idx = idx + 1; } + scheduler.labels.splice(idx, 0, new scheduler.label(name, priority)); + scheduler.queues.splice(idx, 0, new Array(0)); + } + + this.clearLabel = function(name) { + var idx = scheduler.indexOf(name); + if (idx != -1) { + scheduler.labels.splice(idx, 1); + scheduler.queues.splice(idx, 1); + } + } + + this.nextWork = function() { + var fn = undefined; + var idx = 0; + while (idx < scheduler.queues.length && scheduler.queues[idx].length == 0) { idx = idx + 1; } + + if (idx < scheduler.queues.length && scheduler.queues[idx].length > 0) + var fn = scheduler.queues[idx].shift(); + + return fn; + } + + this.add = function(labelName, fn, self, args) { + var doWork = function() { + scheduler.timeout = setTimeout(function() { + var work = scheduler.nextWork(); + if (work != undefined) { + if (work.args == undefined) { work.args = new Array(0); } + work.fn.apply(work.self, work.args); + doWork(); + } + else { + scheduler.timeout = undefined; + } + }, resolution); + } + + var idx = scheduler.indexOf(labelName) + if (idx != -1) { + scheduler.queues[idx].push(new scheduler.work(fn, self, args)); + if (scheduler.timeout == undefined) doWork(); + } else { + throw("queue for add is non-existent"); + } + } + + this.clear = function(labelName) { + scheduler.queues[scheduler.indexOf(labelName)] = new Array(); + } + + this.indexOf = function(label) { + var idx = 0; + while (idx < scheduler.labels.length && scheduler.labels[idx].name != label) + idx++; + + return idx < scheduler.queues.length && scheduler.labels[idx].name == label ? idx : -1; + } + + this.queueEmpty = function(label) { + var idx = scheduler.indexOf(label); + if (idx != -1) + return scheduler.queues[idx].length == 0; + else + throw("queue for label '" + label + "' is non-existent"); + } + + this.scheduleLast = function(label, fn) { + if (scheduler.queueEmpty(label)) { + fn(); + } else { + scheduler.add(label, function() { + scheduler.scheduleLast(label, fn); + }); + } + } + + this.numberOfJobs = function(label) { + var index = scheduler.indexOf(label); + if (index == -1) throw("queue for label '" + label + "' non-existent"); + + return scheduler.queues[index].length; + } +}; diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-700.eot b/_static/stainless-library/lib/source-code-pro-v6-latin-700.eot new file mode 100644 index 0000000000..094e578e59 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-700.eot differ diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-700.ttf b/_static/stainless-library/lib/source-code-pro-v6-latin-700.ttf new file mode 100644 index 0000000000..04159884d6 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-700.ttf differ diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-700.woff b/_static/stainless-library/lib/source-code-pro-v6-latin-700.woff new file mode 100644 index 0000000000..6ac8a3b295 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-700.woff differ diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-regular.eot b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.eot new file mode 100644 index 0000000000..60bd73b583 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.eot differ diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf new file mode 100644 index 0000000000..268a2e4322 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf differ diff --git a/_static/stainless-library/lib/source-code-pro-v6-latin-regular.woff b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.woff new file mode 100644 index 0000000000..7daeecc8a6 Binary files /dev/null and b/_static/stainless-library/lib/source-code-pro-v6-latin-regular.woff differ diff --git a/_static/stainless-library/lib/template.css b/_static/stainless-library/lib/template.css new file mode 100644 index 0000000000..ae285a7023 --- /dev/null +++ b/_static/stainless-library/lib/template.css @@ -0,0 +1,1224 @@ +/* Reset */ + +html, body, div, span, object, iframe, +h1, h2, h3, h4, h5, h6, p, blockquote, pre, +a, abbr, acronym, address, code, pre, +del, dfn, em, img, q, dl, dt, dd, ol, ul, li, +fieldset, form, label, legend, input, +table, caption, tbody, tfoot, thead, tr, th, td { + margin: 0; + padding: 0; + border: 0; + font-weight: inherit; + font-style: inherit; + font-size: 100%; + font-family: inherit; + vertical-align: baseline; +} + +table { border-collapse: separate; border-spacing: 0; } +caption, th, td { text-align: left; font-weight: normal; } +table, td, th { vertical-align: middle; } + +textarea, input { outline: none; } + +blockquote:before, blockquote:after, q:before, q:after { content: ""; } +blockquote, q { quotes: none; } + +a img { border: none; } + +input { border-width: 0px; } + +/* Page */ +body { + overflow-x: hidden; + font-family: Arial, sans-serif; + background-color: #f0f3f6; +} + +#footer { + text-align: center; + color: #858484; + bottom: 0; + min-height: 20px; + margin: 0 1em 0.5em; +} + +#content-container a[href] { + text-decoration: underline; + color: #315479; +} + +#content-container a[href]:hover { + text-decoration: none; +} + +#types ol li > p { + margin-top: 5px; +} + +#types ol li:last-child { + margin-bottom: 5px; +} + +#definition { + position: relative; + display: block; + padding: 5px 0; + padding: 0; + margin: 0.5em; + min-height: 4.72em; +} + +#definition > a > img { + float: left; + padding-right: 6px; + padding-left: 5px; +} + +#definition p + h1 { + margin-top: 3px; +} + +#definition > h1 { + float: left; + color: #103a51; + display: inline-block; + overflow: hidden; + margin-top: 10px; + font-size: 2.0em; +} + +#definition h1 > a { + color: #103a51 !important; + text-decoration: none !important; +} + +#template ol > li > span.permalink > a > i { + transform: rotate(-45deg); +} + +#definition #owner { + color: #103a51; + padding-top: 1.3em; + font-size: 0.8em; + overflow: hidden; +} + +#definition > h3 { + margin-top: 0.85em; + padding: 0; +} + +#definition #owner > a { + color: #103a51; +} + +#definition #owner > a:hover { + text-decoration: none; +} + +#signature { + background-color: #c2d2dc; + min-height: 18px; + font-size: 0.9em; + padding: 8px; + color: #103a51; + border-radius: 0.2em; + margin: 0 0.5rem; +} + +#signature > span.modifier_kind { + display: inline; + float: left; + text-align: left; + width: auto; + position: static; + padding-left: 0; +} + +span.symbol > a { + display: inline-block; +} + +#signature > span.symbol { + text-align: left; + display: inline; + padding-left: 0.7em; +} + +/* Linear super types and known subclasses */ +.hiddenContent { + display: none; +} + +.toggleContainer .toggle { + position: relative; + color: #103a51; + margin-left: 0.3em; + cursor: pointer; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +.toggleContainer .toggle > i { + position: absolute; + left: -1.5em; + top: 0em; + font-size: 1.3em; + transition: 0.1s; +} + +.toggleContainer .toggle.open > i { + transform: rotate(90deg); +} + +.toggleContainer .hiddenContent { + margin-top: 1.5em; +} + +#memberfilter > i.arrow { + position: absolute; + top: 0.45em; + left: -0.9em; + color: #fff; + font-size: 1.3em; + opacity: 0; + transition: 0.1s; + cursor: pointer; +} + +#memberfilter > i.arrow.rotate { + transform: rotate(90deg); +} + +#memberfilter:hover > i.arrow { + opacity: 1; +} + +.big-circle { + box-sizing: content-box; + height: 5.7em; + width: 5.7em; + float: left; + color: transparent; +} + +.big-circle:hover { + background-size: 5.7em; +} + +.big-circle.class { + background: url("class.svg") no-repeat center; +} + +.big-circle.class-companion-object { + background: url("class_comp.svg") no-repeat center; +} + +.big-circle.object-companion-class { + background: url("object_comp.svg") no-repeat center; +} + +.big-circle.trait-companion-object { + background: url("trait_comp.svg") no-repeat center; +} + +.big-circle.object-companion-trait { + background: url("object_comp_trait.svg") no-repeat center; +} + +.big-circle.object { + background: url("object.svg") no-repeat center; +} + +.big-circle.trait { + background: url("trait.svg") no-repeat center; +} + +.big-circle.package { + background: url("package.svg") no-repeat center; +} + +body.abstract.type div.big-circle { + background: url("abstract_type.svg") no-repeat center; +} + +body.alias.type div.big-circle { + background: url("abstract_type.svg") no-repeat center; +} + +#template { + margin: 0.9em 0.75em 0.75em; + padding-bottom: 0.5em; +} + +#template h3 { + color: #103a51; + height: 2em; + padding: 1em 1em 2em; + font-size: 1.2em; +} + +#order { + margin-top: 1.5em; +} + +h3 { + color: #103a51; + padding: 5px 10px; + font-size: 1em; + font-weight: bold; +} + +dl.attributes > dt { + display: block; + float: left; + font-style: italic; + font-weight: bold; +} + +dl.attributes > dt.implicit { + font-weight: bold; + color: darkgreen; +} + +dl.attributes > dd { + display: block; + padding-left: 10em; + margin-bottom: 5px; + min-height: 15px; +} + +.values ol li:last-child { + margin-bottom: 5px; +} + +#constructors > h3 { + height: 2em; + padding: 1em 1em 2em; + color: #2C475C; +} + +#inheritedMembers > div.parent > h3 { + height: 17px; + font-style: italic; +} + +#inheritedMembers > div.parent > h3 * { + color: white; +} + +#inheritedMembers > div.conversion > h3 { + height: 2em; + padding: 1em; + font-style: italic; + color: #2C475C; +} + +#groupedMembers > div.group > h3 { + color: #2C475C; + height: 2em; + padding: 1em 1em 2em; +} + +/* Member cells */ +div.members > ol { + list-style: none; +} + +div.members > ol > li { + display: table; + width: 100%; + position: relative; + background-color: #fff; + border-radius: 0.2em; + color: #103a51; + padding: 5px 0 5px; + margin-bottom: 0.4em; + min-height: 3.7em; + border-left: 0.25em solid white; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.1); + box-shadow: 0 0 10px rgba(0,0,0,0.1); + transition: 0.1s; +} + +div.members > ol >li.selected, +div.members > ol > li:hover { + background-color: #dae7f0; + border-left-color: #dae7f0; +} + +div.members > ol >li[fullComment=yes].selected, +div.members > ol > li[fullComment=yes]:hover { + cursor: pointer; + border-left: 0.25em solid #72D0EB; +} + +div.members > ol > li:last-child { + padding: 5px 0 5px; +} + +/* Member signatures */ + +#tooltip { + background: #EFD5B5; + border: 1px solid gray; + color: black; + display: none; + padding: 5px; + position: absolute; +} + +.signature { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.8rem; + line-height: 18px; + clear: both; + display: block; +} + +.modifier_kind { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.8rem; + padding-right: 0.5em; + text-align: right; + display: table-cell; + white-space: nowrap; + width: 16em; +} + +.symbol { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +a > .symbol > .name { + text-decoration: underline; +} + +a:hover > .symbol > .name { + text-decoration: none; +} + +.signature > a { + text-decoration: none; +} + +.signature > .symbol { + display: inline; +} + +.signature .name { + display: inline-block; + font-weight: bold; +} + +span.symbol > span.name { + font-weight: bold; +} + +#types > ol > li > span.symbol > span.result { + display: none; +} + +#types > ol > li > span.symbol > span.result.alias, +#types > ol > li:hover > span.symbol > span.result, +#types > ol > li.open > span.symbol > span.result { + display: inline; +} + +.symbol > .implicit { + display: inline-block; + font-weight: bold; + text-decoration: underline; + color: darkgreen; +} + +.symbol .shadowed { + color: darkseagreen; +} + +.symbol .params > .implicit { + font-style: italic; +} + +.symbol .deprecated { + text-decoration: line-through; +} + +.symbol .params .default { + font-style: italic; +} + +#template .closed { + cursor: pointer; +} + +#template .opened { + cursor: pointer; +} + +i.unfold-arrow { + font-size: 1em; + position: absolute; + top: 0.55em; + left: 0.7em; + transition: 0.1s; +} + +#template .modifier_kind.opened > i.unfold-arrow { + transform: rotate(90deg); +} + +#template .values .name { + font-weight: 600; + color: #315479; +} + +#template .types .name { + font-weight: 600; + color: darkgreen; +} + +.full-signature-usecase h4 span { + font-size: 0.8rem; +} + +.full-signature-usecase > #signature { + padding-top: 0px; + position: relative; + top: 0; +} + +/* Hide unfold arrow where appropriate */ +#template li[fullComment=no] .modifier_kind > i.unfold-arrow, +div#definition > h4#signature > span.modifier_kind > i.unfold-arrow, +.full-signature-usecase > .signature > .closed > i.unfold-arrow, +.full-signature-usecase > .signature > .opened > i.unfold-arrow { + display: none; +} + +#template .full-signature-usecase > .signature > .closed { + background: none; +} + +#template .full-signature-usecase > .signature > .opened { + background: none; +} + +.full-signature-block { + padding: 5px 0 0; + border-top: 1px solid #EBEBEB; + margin-top: 5px; + margin-bottom: 5px; +} + +#definition .morelinks { + text-align: right; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +#definition .morelinks a { + color: #103a51; +} + +#template .members li .permalink { + position: absolute; + left: 0.25em; + top: 0.95em; +} + +#definition .permalink { + display: none; + color: black; +} + +#definition .permalink a { + color: #103a51; + transform: rotate(-45deg); +} + +#definition > h1 > span > a > i { + font-size: 1.4rem; +} + +#template ol > li > span.permalink > a > i { + color: #fff; +} + +#template .members li .permalink, +#definition .permalink a { + display: none; +} + +#template .members li:hover .permalink, +#definition:hover .permalink a { + display: block; +} + +#template .members li .permalink a, +#definition .permalink a { + text-decoration: none; + font-weight: bold; +} + +/* Comments text formatting */ + +.cmt { + color: #103a51; +} + +.cmt p { + margin: 0.7em 0; +} + +.cmt p:first-child { + margin-top: 0; +} + +.cmt p:last-child { + margin-bottom: 0; +} + +.cmt h3, +.cmt h4, +.cmt h5, +.cmt h6 { + margin-bottom: 0.7em; + margin-top: 1.4em; + display: block; + text-align: left; + font-weight: bold; +} + +.cmt pre { + padding: 0.5em; + border: 0px solid #ddd; + background-color: #fff; + margin: 5px 0; + display: block; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + border-radius: 0.2em; + overflow-x: auto; +} + +.cmt pre span.ano { + color: blue; +} + +.cmt pre span.cmt { + color: green; +} + +.cmt pre span.kw { + font-weight: bold; +} + +.cmt pre span.lit { + color: #c71585; +} + +.cmt pre span.num { + color: #1e90ff; /* dodgerblue */ +} + +.cmt pre span.std { + color: #008080; /* teal */ +} + +.cmt ul { + display: block; + list-style: circle; + padding-left: 20px; +} + +.cmt ol { + display: block; + padding-left:20px; +} + +.cmt ol.decimal { + list-style: decimal; +} + +.cmt ol.lowerAlpha { + list-style: lower-alpha; +} + +.cmt ol.upperAlpha { + list-style: upper-alpha; +} + +.cmt ol.lowerRoman { + list-style: lower-roman; +} + +.cmt ol.upperRoman { + list-style: upper-roman; +} + +.cmt li { + display: list-item; +} + +.cmt code { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +.cmt a { + font-style: bold; +} + +.cmt em, .cmt i { + font-style: italic; +} + +.cmt strong, .cmt b { + font-weight: bold; +} + +/* Comments structured layout */ + +.group > div.comment { + display: block; + padding: 0 1.2em 1em; + font-family: "Open Sans"; +} + +p.comment { + display: block; + margin-left: 14.7em; + margin-top: 5px; +} + +.shortcomment { + display: block; + margin: 5px 10px; +} + +.shortcomment > span.badge { + display: block; + position: absolute; + right: 0; + top: 0.7em; +} + +div.fullcommenttop { + padding: 1em 0.8em; +} + +div.fullcomment { + margin: 5px 10px; +} + +#template div.fullcommenttop, +#template div.fullcomment { + display:none; + margin: 0.5em 1em 0 0; +} + +#template .shortcomment { + margin: 5px 0 0 0; + padding: 0; + font-family: "Open Sans"; +} + +div.fullcomment .block { + padding: 5px 0 0; + border-top: 2px solid #fff; + margin-top: 5px; + overflow: hidden; + font-family: "Open Sans"; +} + +div.fullcommenttop .block { + position: relative; + padding: 1em; + margin: 0.5em 0; + border-radius: 0.2em; + background-color: #fff; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.1); + box-shadow: 0 0 10px rgba(0,0,0,0.1); +} + +div.fullcommenttop .toggleContainer { + border-left: 0 solid #72D0EB; + transition: 0.1s; + cursor: pointer; +} + +div.fullcommenttop .toggleContainer:hover { + border-left: 0.25em solid #72D0EB; +} + +div#comment, +div#mbrsel, +div#template, +div#footer { + font-size: 0.8em; +} + +#comment { + font-family: "Open Sans"; +} + +#comment > dl { + background: transparent; + -webkit-box-shadow: none; + box-shadow: none; +} + +#comment > dl > div > ol { + list-style-type: none; +} + +div.fullcomment div.block ol li p, +div.fullcomment div.block ol li { + display:inline +} + +div.fullcomment .block > h5 { + font-style: italic; + font-weight: normal; + display: inline-block; +} + +div.fullcomment .comment { + font-family: "Open Sans"; + margin: 5px 0 10px; +} + +div.fullcommenttop .comment:last-child, +div.fullcomment .comment:last-child { + margin-bottom: 0; +} + +div.fullcommenttop dl.paramcmts { + margin-bottom: 0.8em; + padding-bottom: 0.8em; +} + +div.fullcommenttop dl.paramcmts > dt, +div.fullcomment dl.paramcmts > dt { + display: block; + float: left; + font-weight: bold; + min-width: 70px; +} + +div.fullcommenttop dl.paramcmts > dd, +div.fullcomment dl.paramcmts > dd { + display: block; + padding-left: 10px; + margin-bottom: 5px; + margin-left: 70px; + min-height: 15px; +} + +/* Author Content Table formatting */ + +.doctbl { + border-collapse: collapse; + margin: 1.0em 0em; +} + +.doctbl-left { + text-align: left; +} + +.doctbl-center { + text-align: center; +} + +.doctbl-right { + text-align: right; +} + +table.doctbl th { + border: 1px dotted #364550; + background-color: #c2d2dc; + padding: 5px; + color: #103a51; + font-weight: bold; +} + +table.doctbl td { + border: 1px dotted #364550; + padding: 5px; +} + +/* Members filter tool */ + +#memberfilter { + position: relative; + display: block; + height: 2.7em; + margin-bottom: 5px; + margin-left: 1.5em; +} + +#memberfilter > .input { + display: block; + position: absolute; + top: 0; + left: -1.65em; + right: -0.2em; + transition: 0.2s; +} + +#memberfilter > .input > input { + color: #fff; + width: 100%; + border-radius: 0.2em; + padding: 0.5em; + background: rgba(255, 255, 255, 0.2); + font-family: "Open Sans"; +} + +#memberfilter > .input > input::-webkit-input-placeholder { + color: #fff; + opacity: 0.6; +} +#memberfilter > .input > input:-ms-input-placeholder { + color: #fff; + opacity: 0.6; +} +#memberfilter > .input > input::placeholder { + color: #fff; + opacity: 0.6; +} + +#memberfilter > .clear { + display: none; + position: absolute; + top: 0.55em; + color: rgba(255, 255, 255, 0.4); + right: 0; + font-size: 1.2em; +} + +#memberfilter > .clear:hover { + color: #fff; + cursor: pointer; +} + +#mbrsel { + display: block; + padding: 1em 1em 0.5em; + margin: 0.8em; + border-radius: 0.2em; + background-color: #364550; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.2); + box-shadow: 0 0 10px rgba(0,0,0,0.2); + position: relative; +} + +#mbrsel > div.toggle { + opacity: 0; + position: absolute; + left: 1.85em; + top: 1.75em; + width: 1em; + height: 1em; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; + transition: 0.2s; +} + +#mbrsel:hover > div.toggle { + opacity: 1; +} + +#mbrsel:hover #memberfilter > .input { + left: 0.7em; +} + +#mbrsel > div.toggle > i { + cursor: pointer; + position: absolute; + left: 0; + top: 0; + color: #fff; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#mbrsel > div.toggle.open > i { + transform: rotate(90deg); +} + +#mbrsel > div#filterby { + display: none; +} + +#mbrsel > div#filterby > div { + margin-bottom: 5px; +} + +#mbrsel > div#filterby > div:last-child { + margin-bottom: 0; +} + +#mbrsel > div#filterby > div > span.filtertype { + color: #fff; + padding: 4px; + margin-right: 1em; + float: left; + display: inline-block; + font-weight: bold; + width: 4.5em; +} + +#mbrsel > div#filterby > div > ol { + display: inline-block; +} + +#mbrsel > div#filterby > div > a { + position:relative; + top: -8px; + font-size: 11px; +} + +#mbrsel > div#filterby > div > ol#linearization { + display: table; + margin-left: 70px; +} + +#mbrsel > div#filterby > div > ol#linearization > li.in { + text-decoration: none; + float: left; + margin-right: 5px; + background-position: right 0px; +} + +#mbrsel > div#filterby > div > ol#linearization > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol#implicits { + display: table; + margin-left: 70px; +} + +#mbrsel > div#filterby > div > ol#implicits > li { + text-decoration: none; + float: left; + margin: 0.4em 0.4em 0.4em 0; +} + +#mbrsel > div#filterby > div > ol#implicits > li.in { + text-decoration: none; + float: left; +} + +#mbrsel > div#filterby > div > ol#implicits > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol > li { + line-height: 1.5em; + display: inline-block; + cursor: pointer; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#mbrsel > div#filterby > div > ol > li.in { + text-decoration: none; + float: left; + margin-right: 5px; + + font-size: 0.8em; + -webkit-border-radius: 0.2em; + border-radius: 0.2em; + padding: 5px 15px; + cursor: pointer; + background: #f16665; + border-bottom: 2px solid #d64546; + color: #fff; + font-weight: 700; +} + +#mbrsel > div#filterby > div > ol > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol > li.out { + text-decoration: none; + float: left; + padding-right: 10px; + margin-right: 5px; + font-size: 0.8em; + -webkit-border-radius: 0.2em; + border-radius: 0.2em; + padding: 5px 15px; + cursor: pointer; + background: #c2d2dc; + border-bottom: 2px solid rgba(0, 0, 0, 0.1); + color: #103a51; + font-weight: 700; +} + +#mbrsel > div#filterby > div > ol > li.out > span{ + float: left; +} + +.badge { + display: inline-block; + padding: 0.3em 1em; + font-size: 0.8em; + font-weight: bold; + color: #ffffff; + white-space: nowrap; + vertical-align: middle; + background-color: #999999; + -webkit-border-radius: 9px; + -moz-border-radius: 9px; + border-radius: 1em; + font-family: "Open Sans"; +} + +.badge-red { + background-color: #b94a48; + margin-right: 0.8em !important; +} + +/* Media query rules for smaller viewport */ +@media only screen /* Large screen with a small window */ +and (max-width: 650px) +, +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + body, + body > h4#signature { + min-width: 300px; + } + + #template .modifier_kind { + width: 1px; + padding-left: 2.5em; + } + + span.modifier_kind > span.modifier { + display: none; + } + + #definition { + height: 6em; + } + + #definition > h1 { + font-size: 1em; + margin-right: 0.3em; + } + + #definition > h3 { + float: left; + margin: 0.3em 0; + } + + #definition > #owner { + padding-top: 2.6em; + } + + #definition .morelinks { + text-align: left; + font-size: 0.8em; + } + + .big-circle { + margin-top: 0.6em; + } +} + +/* Media query rules specifically for mobile devices */ +@media +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + #signature { + font-size: 0.7em; + } + + #definition > h1 { + font-size: 1.3em; + } + + #definition .morelinks { + display: none; + } + + #definition #owner { + padding-top: 0.7em; + } + + #signature > span.modifier_kind { + width: auto; + } + + div.fullcomment dl.attributes > dt { + margin: 0.5em 0; + clear: both; + } + + div.fullcomment dl.attributes > dd { + padding-left: 0; + clear: both; + } + + .big-circle { + width: 3em; + height: 3em; + background-size: 3em !important; + margin: 0.5em; + } + + div#template { + margin-bottom: 0.5em; + } + + div#footer { + font-size: 0.5em; + } + + .shortcomment > span.badge { + display: none; + } +} diff --git a/_static/stainless-library/lib/template.js b/_static/stainless-library/lib/template.js new file mode 100644 index 0000000000..89112cb02e --- /dev/null +++ b/_static/stainless-library/lib/template.js @@ -0,0 +1,548 @@ +// © 2009–2010 EPFL/LAMP +// code by Gilles Dubochet with contributions by Pedro Furlanetto, Marcin Kubala and Felix Mulder + +var $panzoom = undefined; +$(document).ready(function() { + // Add zoom functionality to type inheritance diagram + $panzoom = $(".diagram-container > .diagram").panzoom({ + increment: 0.1, + minScale: 1, + maxScale: 7, + transition: true, + duration: 200, + contain: 'invert', + easing: "ease-in-out", + $zoomIn: $('#diagram-zoom-in'), + $zoomOut: $('#diagram-zoom-out'), + }); + + var oldWidth = $("div#subpackage-spacer").width() + 1 + "px"; + $("div#packages > ul > li.current").on("click", function() { + $("div#subpackage-spacer").css({ "width": oldWidth }); + $("li.current-entities").toggle(); + }); + + var controls = { + visibility: { + publicOnly: $("#visbl").find("> ol > li.public"), + all: $("#visbl").find("> ol > li.all") + } + }; + + // Escapes special characters and returns a valid jQuery selector + function escapeJquery(str){ + return str.replace(/([;&,\.\+\*\~':"\!\^#$%@\[\]\(\)=<>\|])/g, '\\$1'); + } + + function toggleVisibilityFilter(ctrlToEnable, ctrToDisable) { + if (ctrlToEnable.hasClass("out")) { + ctrlToEnable.removeClass("out").addClass("in"); + ctrToDisable.removeClass("in").addClass("out"); + filter(); + } + } + + controls.visibility.publicOnly.on("click", function() { + toggleVisibilityFilter(controls.visibility.publicOnly, controls.visibility.all); + }); + + controls.visibility.all.on("click", function() { + toggleVisibilityFilter(controls.visibility.all, controls.visibility.publicOnly); + }); + + function exposeMember(jqElem) { + var jqElemParent = jqElem.parent(), + parentName = jqElemParent.attr("name"), + ancestorName = /^([^#]*)(#.*)?$/gi.exec(parentName)[1]; + + // switch visibility filter if necessary + if (jqElemParent.attr("visbl") == "prt") { + toggleVisibilityFilter(controls.visibility.all, controls.visibility.publicOnly); + } + + // toggle appropriate ancestor filter buttons + if (ancestorName) { + $("#filterby li.out[name='" + ancestorName + "']").removeClass("out").addClass("in"); + } + + filter(); + jqElemParent.addClass("selected"); + commentToggleFct(jqElemParent); + $("#content-scroll-container").animate({scrollTop: $("#content-scroll-container").scrollTop() + jqElemParent.offset().top - $("#search").height() - 23 }, 1000); + } + + var isHiddenClass = function (name) { + return name == 'scala.Any' || + name == 'scala.AnyRef'; + }; + + var isHidden = function (elem) { + return $(elem).attr("data-hidden") == 'true'; + }; + + $("#linearization li:gt(0)").filter(function(){ + return isHiddenClass($(this).attr("name")); + }).removeClass("in").addClass("out"); + + $("#implicits li").filter(function(){ + return isHidden(this); + }).removeClass("in").addClass("out"); + + $("#memberfilter > i.arrow").on("click", function() { + $(this).toggleClass("rotate"); + $("#filterby").toggle(); + }); + + // Pre-filter members + filter(); + + // Member filter box + var input = $("#memberfilter input"); + input.on("keyup", function(event) { + + switch ( event.keyCode ) { + + case 27: // escape key + input.val(""); + filter(true); + break; + + case 38: // up + input.val(""); + filter(false); + window.scrollTo(0, $("body").offset().top); + input.trigger("focus"); + break; + + case 33: //page up + input.val(""); + filter(false); + break; + + case 34: //page down + input.val(""); + filter(false); + break; + + default: + window.scrollTo(0, $("#mbrsel").offset().top - 130); + filter(true); + break; + + } + }); + input.on("focus", function(event) { + input.trigger("select"); + }); + $("#memberfilter > .clear").on("click", function() { + $("#memberfilter input").val(""); + $(this).hide(); + filter(); + }); + $(document).on("keydown", function(event) { + if (event.keyCode == 9) { // tab + $("#index-input", window.parent.document).trigger("focus"); + input.val( ""); + return false; + } + }); + + $("#linearization li").on("click", function(){ + if ($(this).hasClass("in")) { + $(this).removeClass("in"); + $(this).addClass("out"); + } else if ($(this).hasClass("out")) { + $(this).removeClass("out"); + $(this).addClass("in"); + } + filter(); + }); + + $("#implicits li").on("click", function(){ + if ($(this).hasClass("in")) { + $(this).removeClass("in"); + $(this).addClass("out"); + } else if ($(this).hasClass("out")) { + $(this).removeClass("out"); + $(this).addClass("in"); + } + filter(); + }); + + $("#mbrsel > div > div.ancestors > ol > li.hideall").on("click", function() { + $("#linearization li.in").removeClass("in").addClass("out"); + $("#linearization li:first").removeClass("out").addClass("in"); + $("#implicits li.in").removeClass("in").addClass("out"); + + if ($(this).hasClass("out") && $("#mbrsel > div > div.ancestors > ol > li.showall").hasClass("in")) { + $(this).removeClass("out").addClass("in"); + $("#mbrsel > div > div.ancestors > ol > li.showall").removeClass("in").addClass("out"); + } + + filter(); + }) + $("#mbrsel > div > div.ancestors > ol > li.showall").on("click", function() { + var filteredLinearization = + $("#linearization li.out").filter(function() { + return ! isHiddenClass($(this).attr("name")); + }); + filteredLinearization.removeClass("out").addClass("in"); + + var filteredImplicits = + $("#implicits li.out").filter(function() { + return ! isHidden(this); + }); + filteredImplicits.removeClass("out").addClass("in"); + + if ($(this).hasClass("out") && $("#mbrsel > div > div.ancestors > ol > li.hideall").hasClass("in")) { + $(this).removeClass("out").addClass("in"); + $("#mbrsel > div > div.ancestors > ol > li.hideall").removeClass("in").addClass("out"); + } + + filter(); + }); + $("#order > ol > li.alpha").on("click", function() { + if ($(this).hasClass("out")) + orderAlpha(); + }) + $("#order > ol > li.inherit").on("click", function() { + if ($(this).hasClass("out")) + orderInherit(); + }); + $("#order > ol > li.group").on("click", function() { + if ($(this).hasClass("out")) + orderGroup(); + }); + $("#groupedMembers").hide(); + + initInherit(); + + // Create tooltips + $(".extype").add(".defval").each(function(_,e) { + var $this = $(e); + $this.attr("title", $this.attr("name")); + }); + + /* Add toggle arrows */ + $("#template li[fullComment=yes] .modifier_kind").addClass("closed"); + + function commentToggleFct(element){ + $("#template li.selected").removeClass("selected"); + if (element.is("[fullcomment=no]")) { + return; + } + element.toggleClass("open"); + var signature = element.find(".modifier_kind") + var shortComment = element.find(".shortcomment"); + var fullComment = element.find(".fullcomment"); + var vis = $(":visible", fullComment); + signature.toggleClass("closed").toggleClass("opened"); + if (vis.length > 0) { + if (!isMobile()) { + shortComment.slideDown(100); + fullComment.slideUp(100); + } else { + fullComment.hide(); + shortComment.show(); + } + } + else { + if (!isMobile()) { + shortComment.slideUp(100); + fullComment.slideDown(100); + } else { + shortComment.hide(); + fullComment.show(); + } + } + }; + + $("#template li[fullComment=yes]").on("click", function() { + var sel = window.getSelection().toString(); + if (!sel) commentToggleFct($(this)); + }); + + /* Linear super types and known subclasses */ + function toggleShowContentFct(e){ + e.toggleClass("open"); + var content = $(".hiddenContent", e); + if(content.is(':visible')) { + if (!isMobile()) content.slideUp(100); + else content.hide(); + } else { + if (!isMobile()) content.slideDown(100); + else content.show(); + } + }; + + $(".toggleContainer:not(.diagram-container):not(.full-signature-block)").on("click", function() { + toggleShowContentFct($(this)); + }); + + $(".toggleContainer.full-signature-block").on("click", function() { + toggleShowContentFct($(this)); + return false; + }); + + if ($("#order > ol > li.group").length == 1) { orderGroup(); }; + + function findElementByHash(locationHash) { + var temp = locationHash.replace('#', ''); + var memberSelector = '#' + escapeJquery(temp); + return $(memberSelector); + } + + // highlight and jump to selected member if an anchor is provided + if (window.location.hash) { + var jqElem = findElementByHash(window.location.hash); + if (jqElem.length > 0) + exposeMember(jqElem); + } + + $("#template span.permalink").on("click", function(e) { + e.preventDefault(); + var href = $("a", this).attr("href"); + if (href.indexOf("#") != -1) { + var hash = href.split("#").pop() + try { + window.history.pushState({}, "", "#" + hash) + } catch (e) { + // fallback for file:// URLs, has worse scrolling behavior + location.hash = hash; + } + exposeMember(findElementByHash(hash)) + } + return false; + }); + + $("#mbrsel-input").on("input", function() { + if ($(this).val().length > 0) + $("#memberfilter > .clear").show(); + else + $("#memberfilter > .clear").hide(); + }); +}); + +function orderAlpha() { + $("#order > ol > li.alpha").removeClass("out").addClass("in"); + $("#order > ol > li.inherit").removeClass("in").addClass("out"); + $("#order > ol > li.group").removeClass("in").addClass("out"); + $("#template > div.parent").hide(); + $("#template > div.conversion").hide(); + $("#mbrsel > div.ancestors").show(); + filter(); +}; + +function orderInherit() { + $("#order > ol > li.inherit").removeClass("out").addClass("in"); + $("#order > ol > li.alpha").removeClass("in").addClass("out"); + $("#order > ol > li.group").removeClass("in").addClass("out"); + $("#template > div.parent").show(); + $("#template > div.conversion").show(); + $("#mbrsel > div.ancestors").hide(); + filter(); +}; + +function orderGroup() { + $("#order > ol > li.group").removeClass("out").addClass("in"); + $("#order > ol > li.alpha").removeClass("in").addClass("out"); + $("#order > ol > li.inherit").removeClass("in").addClass("out"); + $("#template > div.parent").hide(); + $("#template > div.conversion").hide(); + $("#mbrsel > div.ancestors").show(); + filter(); +}; + +/** Prepares the DOM for inheritance-based display. To do so it will: + * - hide all statically-generated parents headings; + * - copy all members from the value and type members lists (flat members) to corresponding lists nested below the + * parent headings (inheritance-grouped members); + * - initialises a control variable used by the filter method to control whether filtering happens on flat members + * or on inheritance-grouped members. */ +function initInherit() { + // inheritParents is a map from fully-qualified names to the DOM node of parent headings. + var inheritParents = new Object(); + var groupParents = new Object(); + $("#inheritedMembers > div.parent").each(function(){ + inheritParents[$(this).attr("name")] = $(this); + }); + $("#inheritedMembers > div.conversion").each(function(){ + inheritParents[$(this).attr("name")] = $(this); + }); + $("#groupedMembers > div.group").each(function(){ + groupParents[$(this).attr("name")] = $(this); + }); + + $("#types > ol > li").each(function(){ + var mbr = $(this); + this.mbrText = mbr.find("> .fullcomment .cmt").text(); + var qualName = mbr.attr("name"); + var owner = qualName.slice(0, qualName.indexOf("#")); + var name = qualName.slice(qualName.indexOf("#") + 1); + var inheritParent = inheritParents[owner]; + if (inheritParent != undefined) { + var types = $("> .types > ol", inheritParent); + if (types.length == 0) { + inheritParent.append("

Type Members

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      "); + types = $("> .types > ol", groupParent); + } + var clone = mbr.clone(); + clone[0].mbrText = this.mbrText; + types.append(clone); + } + }); + + $(".values > ol > li").each(function(){ + var mbr = $(this); + this.mbrText = mbr.find("> .fullcomment .cmt").text(); + var qualName = mbr.attr("name"); + var owner = qualName.slice(0, qualName.indexOf("#")); + var name = qualName.slice(qualName.indexOf("#") + 1); + var inheritParent = inheritParents[owner]; + if (inheritParent != undefined) { + var values = $("> .values > ol", inheritParent); + if (values.length == 0) { + inheritParent.append("

      Value Members

        "); + values = $("> .values > ol", inheritParent); + } + var clone = mbr.clone(); + clone[0].mbrText = this.mbrText; + values.append(clone); + } + var group = mbr.attr("group") + var groupParent = groupParents[group]; + if (groupParent != undefined) { + var values = $("> .values > ol", groupParent); + if (values.length == 0) { + groupParent.append("
          "); + values = $("> .values > ol", groupParent); + } + var clone = mbr.clone(); + clone[0].mbrText = this.mbrText; + values.append(clone); + } + }); + $("#inheritedMembers > div.parent").each(function() { + if ($("> div.members", this).length == 0) { $(this).remove(); }; + }); + $("#inheritedMembers > div.conversion").each(function() { + if ($("> div.members", this).length == 0) { $(this).remove(); }; + }); + $("#groupedMembers > div.group").each(function() { + if ($("> div.members", this).length == 0) { $(this).remove(); }; + }); +}; + +/* filter used to take boolean scrollToMember */ +function filter() { + var query = $.trim($("#memberfilter input").val()).toLowerCase(); + query = query.replace(/[-[\]{}()*+?.,\\^$|#]/g, "\\$&").replace(/\s+/g, "|"); + var queryRegExp = new RegExp(query, "i"); + var privateMembersHidden = $("#visbl > ol > li.public").hasClass("in"); + var orderingAlphabetic = $("#order > ol > li.alpha").hasClass("in"); + var orderingInheritance = $("#order > ol > li.inherit").hasClass("in"); + var orderingGroups = $("#order > ol > li.group").hasClass("in"); + var hiddenSuperclassElementsLinearization = orderingInheritance ? $("#linearization > li:gt(0)") : $("#linearization > li.out"); + var hiddenSuperclassesLinearization = hiddenSuperclassElementsLinearization.map(function() { + return $(this).attr("name"); + }).get(); + var hiddenSuperclassElementsImplicits = orderingInheritance ? $("#implicits > li") : $("#implicits > li.out"); + var hiddenSuperclassesImplicits = hiddenSuperclassElementsImplicits.map(function() { + return $(this).attr("name"); + }).get(); + + var hideInheritedMembers; + + if (orderingAlphabetic) { + $("#allMembers").show(); + $("#inheritedMembers").hide(); + $("#groupedMembers").hide(); + hideInheritedMembers = true; + $("#allMembers > .members").each(filterFunc); + } else if (orderingGroups) { + $("#groupedMembers").show(); + $("#inheritedMembers").hide(); + $("#allMembers").hide(); + hideInheritedMembers = true; + $("#groupedMembers > .group > .members").each(filterFunc); + $("#groupedMembers > div.group").each(function() { + $(this).show(); + if ($("> div.members", this).not(":hidden").length == 0) { + $(this).hide(); + } else { + $(this).show(); + } + }); + } else if (orderingInheritance) { + $("#inheritedMembers").show(); + $("#groupedMembers").hide(); + $("#allMembers").hide(); + hideInheritedMembers = false; + $("#inheritedMembers > .parent > .members").each(filterFunc); + $("#inheritedMembers > .conversion > .members").each(filterFunc); + } + + + function filterFunc() { + var membersVisible = false; + var members = $(this); + members.find("> ol > li").each(function() { + var mbr = $(this); + if (privateMembersHidden && mbr.attr("visbl") == "prt") { + mbr.hide(); + return; + } + var name = mbr.attr("name"); + // Owner filtering must not happen in "inherited from" member lists + if (hideInheritedMembers) { + var ownerIndex = name.indexOf("#"); + if (ownerIndex < 0) { + ownerIndex = name.lastIndexOf("."); + } + var owner = name.slice(0, ownerIndex); + for (var i = 0; i < hiddenSuperclassesLinearization.length; i++) { + if (hiddenSuperclassesLinearization[i] == owner) { + mbr.hide(); + return; + } + }; + for (var i = 0; i < hiddenSuperclassesImplicits.length; i++) { + if (hiddenSuperclassesImplicits[i] == owner) { + mbr.hide(); + return; + } + }; + } + if (query && !(queryRegExp.test(name) || queryRegExp.test(this.mbrText))) { + mbr.hide(); + return; + } + mbr.show(); + membersVisible = true; + }); + + if (membersVisible) + members.show(); + else + members.hide(); + }; + + return false; +}; + +/** Check if user agent is associated with a known mobile browser */ +function isMobile() { + return /Android|webOS|Mobi|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini/i.test(navigator.userAgent); +} diff --git a/_static/stainless-library/lib/trait.svg b/_static/stainless-library/lib/trait.svg new file mode 100644 index 0000000000..207a89f37f --- /dev/null +++ b/_static/stainless-library/lib/trait.svg @@ -0,0 +1,54 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + t + + + + + + + diff --git a/_static/stainless-library/lib/trait_comp.svg b/_static/stainless-library/lib/trait_comp.svg new file mode 100644 index 0000000000..8c83dec1f1 --- /dev/null +++ b/_static/stainless-library/lib/trait_comp.svg @@ -0,0 +1,57 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + t + + + + + + + + diff --git a/_static/stainless-library/lib/trait_diagram.png b/_static/stainless-library/lib/trait_diagram.png new file mode 100644 index 0000000000..88983254ce Binary files /dev/null and b/_static/stainless-library/lib/trait_diagram.png differ diff --git a/_static/stainless-library/lib/type_diagram.png b/_static/stainless-library/lib/type_diagram.png new file mode 100644 index 0000000000..d8152529fd Binary files /dev/null and b/_static/stainless-library/lib/type_diagram.png differ diff --git a/_static/stainless-library/stainless/annotation/erasable.html b/_static/stainless-library/stainless/annotation/erasable.html new file mode 100644 index 0000000000..bf2e91a7c8 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/erasable.html @@ -0,0 +1,666 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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            AnyRef → Any
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          + + + package + + + annotation + +

          + + +
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          + Ordering +
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          Type Members

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            Only extract the contracts and replace the annotated function's body with a choose.

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            Don't unfold the function's body during verification.

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            Instruct Stainless to partially evaluate calls to the annotated function.

            Instruct Stainless to partially evaluate calls to the annotated function.

            Annotations
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            Specify that the annotated function is pure, which will be checked.

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            Attributes
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            Definition Classes
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            Definition Classes
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            Definition Classes
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            Definition Classes
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            Definition Classes
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            Definition Classes
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          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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            Definition Classes
            AnyRef → Any
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          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
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          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
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          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
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          Value Members

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            Definition Classes
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            Definition Classes
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            Definition Classes
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            Definition Classes
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          +

          stainless.annotation.isabelle

          +

          lemma + + + +

          +

          +
          + +

          + + + class + + + lemma extends Annotation with StaticAnnotation + +

          + + +
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          +
          1. + + + + + + + + + new + + + lemma(about: String) + + + +
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          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
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            Attributes
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          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
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            protected[java.lang]
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
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            + @native() + +
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          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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            Definition Classes
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          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
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          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
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          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
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            Definition Classes
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            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
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          + +
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          +

          Inherited from StaticAnnotation

          +
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          Inherited from Annotation

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          Inherited from AnyRef

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          Inherited from Any

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          Ungrouped

          + +
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          + + diff --git a/_static/stainless-library/stainless/annotation/isabelle$$noBody.html b/_static/stainless-library/stainless/annotation/isabelle$$noBody.html new file mode 100644 index 0000000000..e7d2b81030 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/isabelle$$noBody.html @@ -0,0 +1,648 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          Packages

          + +
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          c
          +

          stainless.annotation.isabelle

          +

          noBody + + + +

          +

          +
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          + + + class + + + noBody extends Annotation with StaticAnnotation + +

          + + +
          Annotations
          + @ignore() + +
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            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
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            Definition Classes
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            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
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            Definition Classes
            AnyRef → Any
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            Attributes
            protected[java.lang]
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
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            + @native() + +
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          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
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            + @native() + +
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          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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            Definition Classes
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            Definition Classes
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          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
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          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
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          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
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            20. +
          +
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          + +
          +
          +

          Inherited from StaticAnnotation

          +
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          Inherited from Annotation

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          Inherited from AnyRef

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          Inherited from Any

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          Ungrouped

          + +
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          + + diff --git a/_static/stainless-library/stainless/annotation/isabelle$$proof.html b/_static/stainless-library/stainless/annotation/isabelle$$proof.html new file mode 100644 index 0000000000..d5acfb2789 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/isabelle$$proof.html @@ -0,0 +1,648 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          Packages

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          c
          +

          stainless.annotation.isabelle

          +

          proof + + + +

          +

          +
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          + + + class + + + proof extends Annotation with StaticAnnotation + +

          + + +
          Annotations
          + @ignore() + +
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          StaticAnnotation, Annotation, AnyRef, Any
          +
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          Value Members

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            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
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          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
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            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
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            + @native() + +
            +
          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
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            Definition Classes
            AnyRef
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            Definition Classes
            AnyRef
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            + @native() + +
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          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
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            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
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          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
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          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
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          + +
          +
          +

          Inherited from StaticAnnotation

          +
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          Inherited from Annotation

          +
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          Inherited from AnyRef

          +
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          Inherited from Any

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          + +
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          Ungrouped

          + +
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          + +
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          Packages

          + +
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          +
          c
          +

          stainless.annotation.isabelle

          +

          script + + + +

          +

          +
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          + + + class + + + script extends Annotation with StaticAnnotation + +

          + + +
          Annotations
          + @ignore() + +
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          StaticAnnotation, Annotation, AnyRef, Any
          +
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          1. + + + + + + + + + new + + + script(name: String, source: String) + + + +
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          Value Members

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            Definition Classes
            AnyRef → Any
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          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
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          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
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          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
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          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
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            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
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          + + + + +
          + +
          +
          +

          Inherited from StaticAnnotation

          +
          +

          Inherited from Annotation

          +
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          Inherited from AnyRef

          +
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          Inherited from Any

          +
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          Ungrouped

          + +
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          + +
          + +
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          +
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          Packages

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          1. + + + + + + + + + new + + + typ(name: String) + + + +
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          Value Members

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          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
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          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
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          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
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          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
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            Definition Classes
            AnyRef
            +
          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
          + + + + +
          + +
          +
          +

          Inherited from StaticAnnotation

          +
          +

          Inherited from Annotation

          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
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          + +
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          +
          + + diff --git a/_static/stainless-library/stainless/annotation/isabelle$.html b/_static/stainless-library/stainless/annotation/isabelle$.html new file mode 100644 index 0000000000..a0fecaa964 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/isabelle$.html @@ -0,0 +1,797 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
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          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          o
          +

          stainless.annotation

          +

          isabelle + + + +

          +

          +
          + +

          + + + object + + + isabelle + +

          + + +
          + + Linear Supertypes + +
          AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
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            4. +
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            +
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          Type Members

          +
          1. + + + + + + + + + class + + + constructor extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
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          2. + + + + + + + + + class + + + fullBody extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
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          3. + + + + + + + + + class + + + function extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          4. + + + + + + + + + class + + + lemma extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          5. + + + + + + + + + class + + + noBody extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          6. + + + + + + + + + class + + + proof extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          7. + + + + + + + + + class + + + script extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          8. + + + + + + + + + class + + + typ extends Annotation with StaticAnnotation + + +
            Annotations
            + @ignore() + +
            +
          +
          + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
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          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
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          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
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            Definition Classes
            AnyRef → Any
            +
          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
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          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
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          12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
          + + + + +
          + +
          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/annotation/keep.html b/_static/stainless-library/stainless/annotation/keep.html new file mode 100644 index 0000000000..b94b26b68c --- /dev/null +++ b/_static/stainless-library/stainless/annotation/keep.html @@ -0,0 +1,669 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
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          +
          +
          +
          +
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          +
          +

          Packages

          + +
          +
          +
          + +
          +
          c
          +

          stainless.annotation

          +

          keep + + + +

          +

          +
          + +

          + + + class + + + keep extends Annotation + +

          + + +

          Can be used to mark a library function/class/object so that it is not +filtered out by the keep objects. Use the command-line option --keep=g to +keep all objects marked by @keep(g) +

          Annotations
          + @ignore() + +
          + + Linear Supertypes + +
          Annotation, AnyRef, Any
          +
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          +
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          +
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          + Ordering +
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          +
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          Instance Constructors

          +
          1. + + + + + + + + + new + + + keep(g: String) + + + +
          +
          + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Annotation

          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/annotation/law.html b/_static/stainless-library/stainless/annotation/law.html new file mode 100644 index 0000000000..3063771364 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/law.html @@ -0,0 +1,668 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          c
          +

          stainless.annotation

          +

          law + + + +

          +

          +
          + +

          + + + class + + + law extends Annotation + +

          + + +

          Mark this function as expressing a law that must be satisfied +by instances or subclasses of the enclosing class. +

          Annotations
          + @ignore() + +
          + + Linear Supertypes + +
          Annotation, AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
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            2. +
          2. By Inheritance
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          +           +
            +
          1. law
          2. Annotation
          3. AnyRef
          4. Any
            5. +
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            +
          1. Hide All
            2. +
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          +
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          Instance Constructors

          +
          1. + + + + + + + + + new + + + law() + + + +
          +
          + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Annotation

          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/annotation/library.html b/_static/stainless-library/stainless/annotation/library.html new file mode 100644 index 0000000000..4c70843990 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/library.html @@ -0,0 +1,667 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
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          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          c
          +

          stainless.annotation

          +

          library + + + +

          +

          +
          + +

          + + + class + + + library extends Annotation + +

          + + +

          The annotated function or class' methods are not verified +by default (use --functions=... to override this).

          Annotations
          + @ignore() + +
          + + Linear Supertypes + +
          Annotation, AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
          +
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          +           +
            +
          1. library
          2. Annotation
          3. AnyRef
          4. Any
            5. +
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            +
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            2. +
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          +
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          Instance Constructors

          +
          1. + + + + + + + + + new + + + library() + + + +
          +
          + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          8. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          10. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          13. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            20. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Annotation

          +
          +

          Inherited from AnyRef

          +
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          Inherited from Any

          +
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          + +
          +
          +

          Ungrouped

          + +
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          +
          +
          + + diff --git a/_static/stainless-library/stainless/annotation/mutable.html b/_static/stainless-library/stainless/annotation/mutable.html new file mode 100644 index 0000000000..b2b9cf3ca4 --- /dev/null +++ b/_static/stainless-library/stainless/annotation/mutable.html @@ -0,0 +1,669 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
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          Packages

          + +
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          c
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          Don't unfold the function's body during verification.

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          stainless.annotation

          +

          partialEval + + + +

          +

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          + + + class + + + partialEval extends Annotation + +

          + + +

          Instruct Stainless to partially evaluate calls to the annotated function.

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          Specify that the annotated function is pure, which will be checked.

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          +

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          Disable overflow checks for sized integer arithmetic operations within the annotated function.

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            Definition Classes
            AnyRef → Any
            +
          7. + + + + + + + + + def + + + appendInv: Boolean + + +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            Definition Classes
            Conc
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          8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
            Definition Classes
            Conc
            +
          9. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          10. + + + + + + + + + def + + + balanced: Boolean + + +
            Definition Classes
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            +
          11. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          12. + + + + + + + + + def + + + concInv: Boolean + + +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            Definition Classes
            Conc
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          13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
            Definition Classes
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          14. + + + + + + + + + def + + + content: Set[T] + + +
            Definition Classes
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            Definition Classes
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            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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          18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Definition Classes
            Conc
            +
          19. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + +
            Definition Classes
            Conc
            +
          20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Definition Classes
            Conc
            +
          21. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Definition Classes
            Conc
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          22. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
            Conc
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          23. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          24. + + + + + + + + + def + + + head: T + + +
            Definition Classes
            Conc
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          25. + + + + + + + + + def + + + headOption: Option[T] + + +
            Definition Classes
            Conc
            +
          26. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Definition Classes
            Conc
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          27. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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            Definition Classes
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          29. + + + + + + + + + def + + + isNormalized: Boolean + + +
            Definition Classes
            Conc
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          30. + + + + + + + + + val + + + left: Conc[T] + + + +
          31. + + + + + + + + + val + + + level: BigInt + + +
            Definition Classes
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            +
          32. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
            Definition Classes
            Conc
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          33. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
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          34. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
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          35. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          36. + + + + + + + + + val + + + right: Conc[T] + + + +
          37. + + + + + + + + + val + + + size: BigInt + + +
            Definition Classes
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            +
          38. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          39. + + + + + + + + + def + + + toList: List[T] + + +
            Definition Classes
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          40. + + + + + + + + + def + + + toSet: Set[T] + + +
            Definition Classes
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          41. + + + + + + + + + def + + + valid: Boolean + + +
            Definition Classes
            Conc
            +
          42. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          43. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
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          44. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
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            45. +
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          Inherited from Serializable

          +
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          Inherited from Serializable

          +
          +

          Inherited from Product

          +
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          Inherited from Equals

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          Inherited from Conc[T]

          +
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          Inherited from AnyRef

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          Inherited from Any

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          Ungrouped

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          stainless.collection.ConcRope

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            Definition Classes
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            Attributes
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          6. + + + + + + + + + def + + + empty[T]: Conc[T] + + + +
          7. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
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          8. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
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          10. + + + + + + + + + def + + + flatten[T](xs: Conc[Conc[T]]): Conc[T] + + + +
          11. + + + + + + + + + def + + + fromList[T](xs: List[T]): Conc[T] + + + +
          12. + + + + + + + + + def + + + fromListReversed[T](xs: List[T]): Conc[T] + + + +
          13. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
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          14. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
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          15. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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            Definition Classes
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            Definition Classes
            AnyRef
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          18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
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            Annotations
            + @native() + +
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          19. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          20. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
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            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
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          22. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
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          23. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
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          Inherited from AnyRef

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          Ungrouped

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            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + + def + + + ++(that: Conc[T]): Conc[T] + + + +
          4. + + + + + + + + + def + + + :+(x: T): Conc[T] + + + +
          5. + + + + + + + + + def + + + ::(x: T): Conc[T] + + + +
          6. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          7. + + + + + + + + + def + + + appendInv: Boolean + + +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            +
          8. + + + + + + + + + def + + + apply(i: BigInt): T + + + +
          9. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
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          10. + + + + + + + + + def + + + balanced: Boolean + + + +
          11. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          12. + + + + + + + + + def + + + concInv: Boolean + + +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            +
          13. + + + + + + + + + def + + + contains(v: T): Boolean + + + +
          14. + + + + + + + + + def + + + content: Set[T] + + + +
          15. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          17. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + + +
          18. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          19. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + + +
          20. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + + +
          21. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + + +
          22. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + + +
          23. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + + +
          24. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
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            Annotations
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          25. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
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            + @native() + +
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          26. + + + + + + + + + def + + + head: T + + + +
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          28. + + + + + + + + + def + + + isEmpty: Boolean + + + +
          29. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          30. + + + + + + + + + def + + + isLeaf: Boolean + + + +
          31. + + + + + + + + + def + + + isNormalized: Boolean + + + +
          32. + + + + + + + + + val + + + level: BigInt + + + +
          33. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + + +
          34. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          35. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
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          36. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
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          37. + + + + + + + + + val + + + size: BigInt + + + +
          38. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          39. + + + + + + + + + def + + + toList: List[T] + + + +
          40. + + + + + + + + + def + + + toSet: Set[T] + + + +
          41. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          42. + + + + + + + + + def + + + valid: Boolean + + + +
          43. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
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          44. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
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          45. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
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          4. + + + + + + + + + def + + + :+(x: T): Conc[T] + + +
            Definition Classes
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            Definition Classes
            Conc
            +
          6. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          7. + + + + + + + + + def + + + appendInv: Boolean + + +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            Definition Classes
            Conc
            +
          8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
            Definition Classes
            Conc
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          9. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
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            Definition Classes
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            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          12. + + + + + + + + + def + + + concInv: Boolean + + +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            Definition Classes
            Conc
            +
          13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
            Definition Classes
            Conc
            +
          14. + + + + + + + + + def + + + content: Set[T] + + +
            Definition Classes
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          15. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
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          16. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
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          17. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Definition Classes
            Conc
            +
          19. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + +
            Definition Classes
            Conc
            +
          20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Definition Classes
            Conc
            +
          21. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Definition Classes
            Conc
            +
          22. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
            Conc
            +
          23. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          24. + + + + + + + + + def + + + head: T + + +
            Definition Classes
            Conc
            +
          25. + + + + + + + + + def + + + headOption: Option[T] + + +
            Definition Classes
            Conc
            +
          26. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Definition Classes
            Conc
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          27. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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          28. + + + + + + + + + def + + + isLeaf: Boolean + + +
            Definition Classes
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          29. + + + + + + + + + def + + + isNormalized: Boolean + + +
            Definition Classes
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          30. + + + + + + + + + val + + + level: BigInt + + +
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          31. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
            Definition Classes
            Conc
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          32. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
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          33. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
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            + @native() + +
            +
          34. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          35. + + + + + + + + + val + + + size: BigInt + + +
            Definition Classes
            Conc
            +
          36. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
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          37. + + + + + + + + + def + + + toList: List[T] + + +
            Definition Classes
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          38. + + + + + + + + + def + + + toSet: Set[T] + + +
            Definition Classes
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          39. + + + + + + + + + def + + + valid: Boolean + + +
            Definition Classes
            Conc
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          40. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          41. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          42. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            43. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Product

          +
          +

          Inherited from Equals

          +
          +

          Inherited from Conc[T]

          +
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          Inherited from AnyRef

          +
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          Inherited from Any

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          + +
          + +
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          +

          Ungrouped

          + +
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          +
          + + diff --git a/_static/stainless-library/stainless/collection/ConcRope$$Single.html b/_static/stainless-library/stainless/collection/ConcRope$$Single.html new file mode 100644 index 0000000000..d81a9b7a63 --- /dev/null +++ b/_static/stainless-library/stainless/collection/ConcRope$$Single.html @@ -0,0 +1,1038 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          stainless.collection.ConcRope

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          Single + + + +

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          + + + case class + + + Single[T](x: T) extends Conc[T] with Product with Serializable + +

          + + +
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            Definition Classes
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            Definition Classes
            AnyRef → Any
            +
          7. + + + + + + + + + def + + + appendInv: Boolean + + +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

            Definition Classes
            Conc
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          8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
            Definition Classes
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            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
            +
          12. + + + + + + + + + def + + + concInv: Boolean + + +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

            Definition Classes
            Conc
            +
          13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
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            Attributes
            protected[java.lang]
            Definition Classes
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          18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Definition Classes
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          19. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + +
            Definition Classes
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          20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Definition Classes
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          21. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Definition Classes
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          22. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
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          23. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
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            + @native() + +
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          24. + + + + + + + + + def + + + head: T + + +
            Definition Classes
            Conc
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          25. + + + + + + + + + def + + + headOption: Option[T] + + +
            Definition Classes
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          26. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Definition Classes
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          27. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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          28. + + + + + + + + + def + + + isLeaf: Boolean + + +
            Definition Classes
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            +
          29. + + + + + + + + + def + + + isNormalized: Boolean + + +
            Definition Classes
            Conc
            +
          30. + + + + + + + + + val + + + level: BigInt + + +
            Definition Classes
            Conc
            +
          31. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
            Definition Classes
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            +
          32. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          33. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
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            + @native() + +
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          34. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
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          35. + + + + + + + + + val + + + size: BigInt + + +
            Definition Classes
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          36. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          37. + + + + + + + + + def + + + toList: List[T] + + +
            Definition Classes
            Conc
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          38. + + + + + + + + + def + + + toSet: Set[T] + + +
            Definition Classes
            Conc
            +
          39. + + + + + + + + + def + + + valid: Boolean + + +
            Definition Classes
            Conc
            +
          40. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          41. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          42. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          43. + + + + + + + + + val + + + x: T + + + +
            44. +
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          + + + + +
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          Inherited from Serializable

          +
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          Inherited from Serializable

          +
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          Inherited from Product

          +
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          Inherited from Equals

          +
          +

          Inherited from Conc[T]

          +
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          Inherited from AnyRef

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          Inherited from Any

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          +

          Ungrouped

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          +
          + + diff --git a/_static/stainless-library/stainless/collection/ConcRope$.html b/_static/stainless-library/stainless/collection/ConcRope$.html new file mode 100644 index 0000000000..f993aec0f7 --- /dev/null +++ b/_static/stainless-library/stainless/collection/ConcRope$.html @@ -0,0 +1,1092 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          ConcRope + + + +

          +

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          + + + object + + + ConcRope + +

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            Annotations
            + @library() + +
            +
          2. + + + + + + + + + case class + + + CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] with Product with Serializable + + +
            Annotations
            + @library() + +
            +
          3. + + + + + + + + sealed abstract + class + + + Conc[T] extends AnyRef + + +
            Annotations
            + @library() + +
            +
          4. + + + + + + + + + case class + + + Empty[T]() extends Conc[T] with Product with Serializable + + +
            Annotations
            + @library() + +
            +
          5. + + + + + + + + + case class + + + Single[T](x: T) extends Conc[T] with Product with Serializable + + +
            Annotations
            + @library() + +
            +
          +
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          Value Members

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            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
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          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + + def + + + abs(x: BigInt): BigInt + + + +
          5. + + + + + + + + + def + + + append[T](xs: Conc[T], x: T): Conc[T] + + + +
          6. + + + + + + + + + def + + + appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean + + + +
          7. + + + + + + + + + def + + + appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean + + + +
          8. + + + + + + + + + def + + + appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
          9. + + + + + + + + + def + + + appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] + + +

            This is a private method and is not exposed to the +clients of conc trees +

            +
          10. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          11. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
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            + @throws( + + ... + ) + + @native() + +
            +
          12. + + + + + + + + + def + + + concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + +

            A generic concat that applies to general concTrees +

            +
          13. + + + + + + + + + def + + + concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + + +
          14. + + + + + + + + + def + + + concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + +

            This concat applies only to normalized trees.

            This concat applies only to normalized trees. +This prevents concat from being recursive +

            +
          15. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          16. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
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            Attributes
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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            Definition Classes
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            + @native() + +
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          20. + + + + + + + + + def + + + insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] + + + +
          21. + + + + + + + + + def + + + insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean + + + +
          22. + + + + + + + + + def + + + insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] + + +

            Using a different version of insert than of the library +because the library implementation in unnecessarily complicated.

            +
          23. + + + + + + + + + def + + + instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean + + + +
          24. + + + + + + + + + def + + + instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean + + + +
          25. + + + + + + + + + def + + + instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean + + + +
          26. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
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          28. + + + + + + + + + def + + + max(x: BigInt, y: BigInt): BigInt + + + +
          29. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          30. + + + + + + + + + def + + + normalize[T](t: Conc[T]): Conc[T] + + + +
          31. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
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          32. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
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          33. + + + + + + + + + def + + + numTrees[T](t: Conc[T]): BigInt + + + +
          34. + + + + + + + + + def + + + split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) + + + +
          35. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
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          36. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
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          37. + + + + + + + + + def + + + update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] + + + +
          38. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + +
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            Definition Classes
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            Definition Classes
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            + @throws( + + ... + ) + + @native() + +
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          41. + + + + + + + + + def + + + wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] + + + +
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          +
          + +

          + + + case class + + + Cons[T](h: T, t: List[T]) extends List[T] with Product with Serializable + +

          + + +
          Annotations
          + @library() + + @constructor( + name = + "List.list.Cons" + ) + +
          + + Linear Supertypes + +
          Serializable, Serializable, Product, Equals, List[T], AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
          +
          +
          + Inherited
          +           +
            +
          1. Cons
          2. Serializable
          3. Serializable
          4. Product
          5. Equals
          6. List
          7. AnyRef
          8. Any
            9. +
          +
          + +
            +
          1. Hide All
            2. +
          2. Show All
            3. +
          +
          +
          + Visibility +
          1. Public
          2. All
          +
          +
          +
          + +
          +
          +
          +

          Instance Constructors

          +
          1. + + + + + + + + + new + + + Cons(h: T, t: List[T]) + + + +
          +
          + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + +
            Definition Classes
            List
            +
          4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.append" + ) + +
            +
          5. + + + + + + + + + def + + + -(e: T): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs x. removeAll x xs" + ) + +
            +
          6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + +
            Definition Classes
            List
            +
          7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs x. xs @ [x]" + ) + +
            +
          8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs x. x # xs" + ) + +
            +
          9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
            Definition Classes
            List
            Annotations
            + @fullBody() + +
            +
          11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + +
            Definition Classes
            List
            +
          13. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.member" + ) + +
            +
          15. + + + + + + + + + def + + + content: Set[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.list.set" + ) + +
            +
          16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + +
            Definition Classes
            List
            +
          17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + +
            Definition Classes
            List
            +
          18. + + + + + + + + + def + + + dropWhile(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          20. + + + + + + + + + def + + + evenSplit: (List[T], List[T]) + + +
            Definition Classes
            List
            +
          21. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
            +
          22. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          23. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          24. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          25. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs P. List.find P xs" + ) + +
            +
          26. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.bind" + ) + +
            +
          27. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
            +
          28. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%as b f. List.foldr f as b" + ) + +
            +
          29. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs P. List.list_all P xs" + ) + +
            +
          30. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          31. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + +
            Definition Classes
            List
            +
          32. + + + + + + + + + val + + + h: T + + + +
          33. + + + + + + + + + def + + + head: T + + +
            Definition Classes
            List
            +
          34. + + + + + + + + + def + + + headOption: Option[T] + + +
            Definition Classes
            List
            +
          35. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + +
            Definition Classes
            List
            +
          36. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + +
            Definition Classes
            List
            +
          37. + + + + + + + + + def + + + init: List[T] + + +
            Definition Classes
            List
            +
          38. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + +
            Definition Classes
            List
            +
          39. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + +
            Definition Classes
            List
            +
          40. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.null" + ) + +
            +
          41. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          42. + + + + + + + + + def + + + last: T + + +
            Definition Classes
            List
            +
          43. + + + + + + + + + def + + + lastOption: Option[T] + + +
            Definition Classes
            List
            +
          44. + + + + + + + + + def + + + length: BigInt + + +
            Definition Classes
            List
            +
          45. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs f. List.list.map f xs" + ) + +
            +
          46. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          47. + + + + + + + + + def + + + nonEmpty: Boolean + + +
            Definition Classes
            List
            +
          48. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          49. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          50. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + +
            Definition Classes
            List
            +
          51. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + +
            Definition Classes
            List
            +
          52. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + +
            Definition Classes
            List
            +
          53. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + +
            Definition Classes
            List
            +
          54. + + + + + + + + + def + + + reverse: List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.rev" + ) + +
            +
          55. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + +
            Definition Classes
            List
            +
          56. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + +
            Definition Classes
            List
            +
          57. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + +
            Definition Classes
            List
            +
          58. + + + + + + + + + def + + + size: BigInt + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "Int.int o List.length" + ) + +
            +
          59. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + +
            Definition Classes
            List
            +
          60. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + +
            Definition Classes
            List
            +
          61. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + +
            Definition Classes
            List
            +
          62. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + +
            Definition Classes
            List
            +
          63. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          64. + + + + + + + + + val + + + t: List[T] + + + +
          65. + + + + + + + + + def + + + tail: List[T] + + +
            Definition Classes
            List
            +
          66. + + + + + + + + + def + + + tailOption: Option[List[T]] + + +
            Definition Classes
            List
            +
          67. + + + + + + + + + def + + + take(i: BigInt): List[T] + + +
            Definition Classes
            List
            +
          68. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          69. + + + + + + + + + def + + + toSet: Set[T] + + +
            Definition Classes
            List
            +
          70. + + + + + + + + + def + + + unique: List[T] + + +
            Definition Classes
            List
            +
          71. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + +
            Definition Classes
            List
            +
          72. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          73. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          74. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          75. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          76. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.zip" + ) + +
            +
            77. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Product

          +
          +

          Inherited from Equals

          +
          +

          Inherited from List[T]

          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/collection/List$.html b/_static/stainless-library/stainless/collection/List$.html new file mode 100644 index 0000000000..7c895b96c0 --- /dev/null +++ b/_static/stainless-library/stainless/collection/List$.html @@ -0,0 +1,711 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          o
           +

          stainless.collection

          +

          List + + + +

          +

          + Companion class List +

          +
          + +

          + + + object + + + List + +

          + + +
          + + Linear Supertypes + +
          AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
          +
          +
          + Inherited
          +           +
            +
          1. List
          2. AnyRef
          3. Any
            4. +
          +
          + +
            +
          1. Hide All
            2. +
          2. Show All
            3. +
          +
          +
          + Visibility +
          1. Public
          2. All
          +
          +
          +
          + +
          +
          + + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + + def + + + apply[T](elems: T*): List[T] + + +
            Annotations
            + @ignore() + +
            +
          5. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          6. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          7. + + + + + + + + + def + + + empty[T]: List[T] + + +
            Annotations
            + @library() + +
            +
          8. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          9. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          10. + + + + + + + + + def + + + fill[T](n: BigInt)(x: T): List[T] + + +
            Annotations
            + @library() + +
            +
          11. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          12. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          13. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          14. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          15. + + + + + + + + + def + + + mkString[A](l: List[A], mid: String, f: (A) ⇒ String): String + + +
            Annotations
            + @library() + +
            +
          16. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          17. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          19. + + + + + + + + + def + + + range(start: BigInt, until: BigInt): List[BigInt] + + +
            Annotations
            + @library() + +
            +
          20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          21. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          22. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            25. +
          +
          + + + + +
          + +
          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/collection/List.html b/_static/stainless-library/stainless/collection/List.html new file mode 100644 index 0000000000..71b11bb0f3 --- /dev/null +++ b/_static/stainless-library/stainless/collection/List.html @@ -0,0 +1,1662 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          c
           +

          stainless.collection

          +

          List + + + +

          +

          + Companion object List +

          +
          + +

          + + sealed abstract + class + + + List[T] extends AnyRef + +

          + + +
          Annotations
          + @library() + + @typ( + name = + "List.list" + ) + +
          + + Linear Supertypes + +
          AnyRef, Any
          +
          + + Known Subclasses + +
          Cons, Nil
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
          +
          +
          + Inherited
          +           +
            +
          1. List
          2. AnyRef
          3. Any
            4. +
          +
          + +
            +
          1. Hide All
            2. +
          2. Show All
            3. +
          +
          +
          + Visibility +
          1. Public
          2. All
          +
          +
          +
          + +
          +
          + + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + + +
          4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
            Annotations
            + @function( + term = + "List.append" + ) + +
            +
          5. + + + + + + + + + def + + + -(e: T): List[T] + + +
            Annotations
            + @function( + term = + "%xs x. removeAll x xs" + ) + +
            +
          6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + + +
          7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
            Annotations
            + @function( + term = + "%xs x. xs @ [x]" + ) + +
            +
          8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
            Annotations
            + @function( + term = + "%xs x. x # xs" + ) + +
            +
          9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
            Annotations
            + @fullBody() + +
            +
          11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + + +
          13. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
            Annotations
            + @function( + term = + "List.member" + ) + +
            +
          15. + + + + + + + + + def + + + content: Set[T] + + +
            Annotations
            + @function( + term = + "List.list.set" + ) + +
            +
          16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + + +
          17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + + +
          18. + + + + + + + + + def + + + dropWhile(p: (T) ⇒ Boolean): List[T] + + + +
          19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
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            +
          20. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
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          21. + + + + + + + + + def + + + evenSplit: (List[T], List[T]) + + + +
          22. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
            Annotations
            + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
            +
          23. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + + +
          24. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + + +
          25. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
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            Definition Classes
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          26. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Annotations
            + @function( + term = + "%xs P. List.find P xs" + ) + +
            +
          27. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
            Annotations
            + @function( + term = + "List.bind" + ) + +
            +
          28. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Annotations
            + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
            +
          29. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Annotations
            + @function( + term = + "%as b f. List.foldr f as b" + ) + +
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          30. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Annotations
            + @function( + term = + "%xs P. List.list_all P xs" + ) + +
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          31. + + + + + + + + final + def + + + getClass(): Class[_] + + +
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          32. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + + +
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          34. + + + + + + + + + def + + + head: T + + + +
          35. + + + + + + + + + def + + + headOption: Option[T] + + + +
          36. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + + +
          37. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + + +
          38. + + + + + + + + + def + + + init: List[T] + + + +
          39. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + + +
          40. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + + +
          41. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Annotations
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          43. + + + + + + + + + def + + + last: T + + + +
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          46. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
            Annotations
            + @function( + term = + "%xs f. List.list.map f xs" + ) + +
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          47. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
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          48. + + + + + + + + + def + + + nonEmpty: Boolean + + + +
          49. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
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          50. + + + + + + + + final + def + + + notifyAll(): Unit + + +
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          51. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + + +
          52. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + + +
          53. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + + +
          54. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + + +
          55. + + + + + + + + + def + + + reverse: List[T] + + +
            Annotations
            + @function( + term = + "List.rev" + ) + +
            +
          56. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + + +
          57. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + + +
          58. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + + +
          59. + + + + + + + + + def + + + size: BigInt + + +
            Annotations
            + @function( + term = + "Int.int o List.length" + ) + +
            +
          60. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + + +
          61. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + + +
          62. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + + +
          63. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + + +
          64. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          65. + + + + + + + + + def + + + tail: List[T] + + + +
          66. + + + + + + + + + def + + + tailOption: Option[List[T]] + + + +
          67. + + + + + + + + + def + + + take(i: BigInt): List[T] + + + +
          68. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + + +
          69. + + + + + + + + + def + + + toSet: Set[T] + + + +
          70. + + + + + + + + + def + + + toString(): String + + +
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          71. + + + + + + + + + def + + + unique: List[T] + + + +
          72. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + + +
          73. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
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            + @throws( + + ... + ) + +
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          74. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
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          75. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
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            + @throws( + + ... + ) + + @native() + +
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          76. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + + +
          77. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
            Annotations
            + @function( + term = + "List.zip" + ) + +
            +
            78. +
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          Inherited from AnyRef

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          Inherited from Any

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          + + diff --git a/_static/stainless-library/stainless/collection/ListOps$.html b/_static/stainless-library/stainless/collection/ListOps$.html new file mode 100644 index 0000000000..3a5f27c0d0 --- /dev/null +++ b/_static/stainless-library/stainless/collection/ListOps$.html @@ -0,0 +1,703 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          9. + + + + + + + + + def + + + flatten[T](ls: List[List[T]]): List[T] + + +
            Annotations
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          12. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
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          13. + + + + + + + + + def + + + isSorted(ls: List[BigInt]): Boolean + + + +
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            Definition Classes
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          15. + + + + + + + + final + def + + + notify(): Unit + + +
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          16. + + + + + + + + final + def + + + notifyAll(): Unit + + +
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          17. + + + + + + + + + def + + + sorted(ls: List[BigInt]): List[BigInt] + + + +
          18. + + + + + + + + + def + + + sum(l: List[BigInt]): BigInt + + + +
          19. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          20. + + + + + + + + + def + + + toMap[K, V](l: List[(K, V)]): Map[K, V] + + + +
          21. + + + + + + + + + def + + + toString(): String + + +
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          22. + + + + + + + + final + def + + + wait(): Unit + + +
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            + @throws( + + ... + ) + +
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          23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
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          24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
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            25. +
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          Inherited from AnyRef

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          + + diff --git a/_static/stainless-library/stainless/collection/ListSpecs$.html b/_static/stainless-library/stainless/collection/ListSpecs$.html new file mode 100644 index 0000000000..fb3eb8607a --- /dev/null +++ b/_static/stainless-library/stainless/collection/ListSpecs$.html @@ -0,0 +1,1007 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          ListSpecs + + + +

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          + + + object + + + ListSpecs + +

          + + +
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            Definition Classes
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          4. + + + + + + + + + def + + + appendAssoc[T](l1: List[T], l2: List[T], l3: List[T]): Boolean + + + +
          5. + + + + + + + + + def + + + appendContent[A](l1: List[A], l2: List[A]): Boolean + + + +
          6. + + + + + + + + + def + + + appendIndex[T](l1: List[T], l2: List[T], i: BigInt): Boolean + + + +
          7. + + + + + + + + + def + + + appendInsert[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
          8. + + + + + + + + + def + + + appendTakeDrop[T](l1: List[T], l2: List[T], n: BigInt): Boolean + + + +
          9. + + + + + + + + + def + + + appendUpdate[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
          10. + + + + + + + + + def + + + applyForAll[T](l: List[T], i: BigInt, p: (T) ⇒ Boolean): Boolean + + +

            A way to apply the forall axiom

            +
          11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          12. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
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            + @throws( + + ... + ) + + @native() + +
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          13. + + + + + + + + + def + + + consIndex[T](h: T, t: List[T], i: BigInt): Boolean + + +
            Annotations
            + @lemma( + about = + "stainless.collection.List.apply" + ) + +
            +
          14. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
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          17. + + + + + + + + + def + + + flattenPreservesContent[T](ls: List[List[T]]): Boolean + + + +
          18. + + + + + + + + + def + + + folds[A, B](xs: List[A], z: B, f: (B, A) ⇒ B): Boolean + + + +
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          21. + + + + + + + + + def + + + headReverseLast[T](l: List[T]): Boolean + + + +
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            Definition Classes
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          23. + + + + + + + + + def + + + leftUnitAppend[T](l1: List[T]): Boolean + + + +
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            Definition Classes
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          25. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
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          26. + + + + + + + + final + def + + + notifyAll(): Unit + + +
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          27. + + + + + + + + + def + + + reverseAppend[T](l1: List[T], l2: List[T]): Boolean + + + +
          28. + + + + + + + + + def + + + reverseIndex[T](l: List[T], i: BigInt): Boolean + + + +
          29. + + + + + + + + + def + + + reverseReverse[T](l: List[T]): Boolean + + + +
          30. + + + + + + + + + def + + + rightUnitAppend[T](l1: List[T]): Boolean + + + +
          31. + + + + + + + + + def + + + scanVsFoldLeft[A, B](l: List[A], z: B, f: (B, A) ⇒ B): Boolean + + + +
          32. + + + + + + + + + def + + + scanVsFoldRight[A, B](l: List[A], z: B, f: (A, B) ⇒ B): Boolean + + + +
          33. + + + + + + + + + def + + + snocAfterAppend[T](l1: List[T], l2: List[T], t: T): Boolean + + + +
          34. + + + + + + + + + def + + + snocFoldRight[A, B](xs: List[A], y: A, z: B, f: (A, B) ⇒ B): Boolean + + + +
          35. + + + + + + + + + def + + + snocIndex[T](l: List[T], t: T, i: BigInt): Boolean + + + +
          36. + + + + + + + + + def + + + snocIsAppend[T](l: List[T], t: T): Boolean + + + +
          37. + + + + + + + + + def + + + snocLast[T](l: List[T], x: T): Boolean + + + +
          38. + + + + + + + + + def + + + snocReverse[T](l: List[T], t: T): Boolean + + + +
          39. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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          40. + + + + + + + + + def + + + toString(): String + + +
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          + + diff --git a/_static/stainless-library/stainless/collection/Nil.html b/_static/stainless-library/stainless/collection/Nil.html new file mode 100644 index 0000000000..d48a3213ea --- /dev/null +++ b/_static/stainless-library/stainless/collection/Nil.html @@ -0,0 +1,1633 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          +
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          + + + case class + + + Nil[T]() extends List[T] with Product with Serializable + +

          + + +
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          + @library() + + @constructor( + name = + "List.list.Nil" + ) + +
          + + Linear Supertypes + +
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          Value Members

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            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + +
            Definition Classes
            List
            +
          4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
            Definition Classes
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            Annotations
            + @function( + term = + "List.append" + ) + +
            +
          5. + + + + + + + + + def + + + -(e: T): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs x. removeAll x xs" + ) + +
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          6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + +
            Definition Classes
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            +
          7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
            Definition Classes
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            + @function( + term = + "%xs x. xs @ [x]" + ) + +
            +
          8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs x. x # xs" + ) + +
            +
          9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
            Definition Classes
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          11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
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          12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + +
            Definition Classes
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          13. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + ... + ) + + @native() + +
            +
          14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
            Definition Classes
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            Annotations
            + @function( + term = + "List.member" + ) + +
            +
          15. + + + + + + + + + def + + + content: Set[T] + + +
            Definition Classes
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            + @function( + term = + "List.list.set" + ) + +
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          16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + +
            Definition Classes
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          17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + +
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          19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
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          21. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
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            Annotations
            + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
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          22. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
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          23. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
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          24. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
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            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          25. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs P. List.find P xs" + ) + +
            +
          26. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.bind" + ) + +
            +
          27. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
            +
          28. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%as b f. List.foldr f as b" + ) + +
            +
          29. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs P. List.list_all P xs" + ) + +
            +
          30. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
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            + @native() + +
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          31. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + +
            Definition Classes
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          32. + + + + + + + + + def + + + head: T + + +
            Definition Classes
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          33. + + + + + + + + + def + + + headOption: Option[T] + + +
            Definition Classes
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          34. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + +
            Definition Classes
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          35. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + +
            Definition Classes
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          36. + + + + + + + + + def + + + init: List[T] + + +
            Definition Classes
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          37. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + +
            Definition Classes
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          38. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + +
            Definition Classes
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            +
          39. + + + + + + + + + def + + + isEmpty: Boolean + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.null" + ) + +
            +
          40. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
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          41. + + + + + + + + + def + + + last: T + + +
            Definition Classes
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          42. + + + + + + + + + def + + + lastOption: Option[T] + + +
            Definition Classes
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          43. + + + + + + + + + def + + + length: BigInt + + +
            Definition Classes
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            +
          44. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "%xs f. List.list.map f xs" + ) + +
            +
          45. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          46. + + + + + + + + + def + + + nonEmpty: Boolean + + +
            Definition Classes
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            +
          47. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          48. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          49. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + +
            Definition Classes
            List
            +
          50. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + +
            Definition Classes
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            +
          51. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + +
            Definition Classes
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          52. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + +
            Definition Classes
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            +
          53. + + + + + + + + + def + + + reverse: List[T] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.rev" + ) + +
            +
          54. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + +
            Definition Classes
            List
            +
          55. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + +
            Definition Classes
            List
            +
          56. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + +
            Definition Classes
            List
            +
          57. + + + + + + + + + def + + + size: BigInt + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "Int.int o List.length" + ) + +
            +
          58. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + +
            Definition Classes
            List
            +
          59. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + +
            Definition Classes
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          60. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + +
            Definition Classes
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            +
          61. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + +
            Definition Classes
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            +
          62. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          63. + + + + + + + + + def + + + tail: List[T] + + +
            Definition Classes
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            +
          64. + + + + + + + + + def + + + tailOption: Option[List[T]] + + +
            Definition Classes
            List
            +
          65. + + + + + + + + + def + + + take(i: BigInt): List[T] + + +
            Definition Classes
            List
            +
          66. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          67. + + + + + + + + + def + + + toSet: Set[T] + + +
            Definition Classes
            List
            +
          68. + + + + + + + + + def + + + unique: List[T] + + +
            Definition Classes
            List
            +
          69. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + +
            Definition Classes
            List
            +
          70. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          71. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          72. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          73. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + +
            Definition Classes
            List
            +
          74. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
            Definition Classes
            List
            Annotations
            + @function( + term = + "List.zip" + ) + +
            +
            75. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Product

          +
          +

          Inherited from Equals

          +
          +

          Inherited from List[T]

          +
          +

          Inherited from AnyRef

          +
          +

          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/collection/Queue$.html b/_static/stainless-library/stainless/collection/Queue$.html new file mode 100644 index 0000000000..779d4f4eed --- /dev/null +++ b/_static/stainless-library/stainless/collection/Queue$.html @@ -0,0 +1,639 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
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          +

          Packages

          + +
          +
          +
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          +
          o
           +

          stainless.collection

          +

          Queue + + + +

          +

          + Companion class Queue +

          +
          + +

          + + + object + + + Queue extends Serializable + +

          + + +
          Annotations
          + @library() + +
          + + Linear Supertypes + +
          Serializable, Serializable, AnyRef, Any
          +
          + + +
          +
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          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
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          + Inherited
          +           +
            +
          1. Queue
          2. Serializable
          3. Serializable
          4. AnyRef
          5. Any
            6. +
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          Value Members

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          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          5. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          6. + + + + + + + + + def + + + empty[A]: Queue[A] + + + +
          7. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          8. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          9. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          10. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          11. + + + + + + + + + def + + + hashCode(): Int + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          12. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          13. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          14. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          15. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          16. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
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            +
          17. + + + + + + + + + def + + + toString(): String + + +
            Definition Classes
            AnyRef → Any
            +
          18. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          19. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          20. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            21. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Serializable

          +
          +

          Inherited from AnyRef

          +
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          Inherited from Any

          +
          + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/_static/stainless-library/stainless/collection/Queue.html b/_static/stainless-library/stainless/collection/Queue.html new file mode 100644 index 0000000000..4a98cf45e5 --- /dev/null +++ b/_static/stainless-library/stainless/collection/Queue.html @@ -0,0 +1,723 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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          Packages

          + +
          +
          +
          + +
          +
          c
           +

          stainless.collection

          +

          Queue + + + +

          +

          + Companion object Queue +

          +
          + +

          + + + case class + + + Queue[A](front: List[A], rear: List[A]) extends Product with Serializable + +

          + + +
          Annotations
          + @library() + +
          + + Linear Supertypes + +
          Serializable, Serializable, Product, Equals, AnyRef, Any
          +
          + + +
          +
          +
          + + + + + +
          +
          +
          + Ordering +
            + +
          1. Alphabetic
            2. +
          2. By Inheritance
            3. +
          +
          +
          + Inherited
          +           +
            +
          1. Queue
          2. Serializable
          3. Serializable
          4. Product
          5. Equals
          6. AnyRef
          7. Any
            8. +
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            +
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          Instance Constructors

          +
          1. + + + + + + + + + new + + + Queue(front: List[A], rear: List[A]) + + + +
          +
          + + + + + +
          +

          Value Members

          +
            +
          1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          2. + + + + + + + + final + def + + + ##(): Int + + +
            Definition Classes
            AnyRef → Any
            +
          3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
            +
          4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
            Definition Classes
            Any
            +
          5. + + + + + + + + + def + + + asList: List[A] + + + +
          6. + + + + + + + + + def + + + clone(): AnyRef + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
          7. + + + + + + + + + def + + + enqueue(elem: A): Queue[A] + + + +
          8. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          9. + + + + + + + + + def + + + finalize(): Unit + + +
            Attributes
            protected[java.lang]
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + classOf[java.lang.Throwable] + ) + +
            +
          10. + + + + + + + + + val + + + front: List[A] + + + +
          11. + + + + + + + + final + def + + + getClass(): Class[_] + + +
            Definition Classes
            AnyRef → Any
            Annotations
            + @native() + +
            +
          12. + + + + + + + + + def + + + head: A + + + +
          13. + + + + + + + + + def + + + isAmortized: Boolean + + + +
          14. + + + + + + + + + def + + + isEmpty: Boolean + + + +
          15. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
            Definition Classes
            Any
            +
          16. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
            Definition Classes
            AnyRef
            +
          17. + + + + + + + + final + def + + + notify(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @native() + +
            +
          19. + + + + + + + + + val + + + rear: List[A] + + + +
          20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
            Definition Classes
            AnyRef
            +
          21. + + + + + + + + + def + + + tail: Queue[A] + + + +
          22. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + +
            +
          24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
            Definition Classes
            AnyRef
            Annotations
            + @throws( + + ... + ) + + @native() + +
            +
            25. +
          +
          + + + + +
          + +
          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Serializable

          +
          +

          Inherited from Product

          +
          +

          Inherited from Equals

          +
          +

          Inherited from AnyRef

          +
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          Inherited from Any

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          + +
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          Ungrouped

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            Close the stream; return true on success.

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            Test whether the stream is opened or not.

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            Open a new stream to write into filename, erasing any previous +content of the file or creating a new one if needed.

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            Close the stream; return true on success.

            Close the stream; return true on success.

            NOTE The stream must not be used afterward, even on failure. +

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            Test whether the stream is opened or not.

            Test whether the stream is opened or not.

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            Append a string to the stream and return true on success.

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            Append a character to the stream and return true on success.

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            Append an integer to the stream and return true on success.

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            Reads the next signed decimal integer

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            Definition Classes
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            Definition Classes
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          15. + + + + + + + + + def + + + map[C](f: (B) ⇒ C): Either[A, C] + + +
            Definition Classes
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            Definition Classes
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            Definition Classes
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          19. + + + + + + + + + def + + + swap: Right[B, A] + + +
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            Definition Classes
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          21. + + + + + + + + final + def + + + wait(): Unit + + +
            Definition Classes
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            + @throws( + + ... + ) + +
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          22. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
            Definition Classes
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            Definition Classes
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            24. +
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          Inherited from Serializable

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          Inherited from Serializable

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          Inherited from Product

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          Inherited from Either[A, B]

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          Map + + + +

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            Attributes
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            Attributes
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            Definition Classes
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          Inherited from Serializable

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          Inherited from Serializable

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          Inherited from AnyRef

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          Map + + + +

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          + + + case class + + + Map[A, B](theMap: scala.collection.immutable.Map[A, B]) extends Product with Serializable + +

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          4. + + + + + + + + + def + + + +(kv: (A, B)): Map[A, B] + + + +
          5. + + + + + + + + + def + + + ++(b: Map[A, B]): Map[A, B] + + + +
          6. + + + + + + + + + def + + + -(k: A): Map[A, B] + + + +
          7. + + + + + + + + + def + + + --(b: Set[A]): Map[A, B] + + + +
          8. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
            Definition Classes
            AnyRef → Any
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            Attributes
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            Close a proof.

            +
          22. + + + + + + + + + def + + + |[C](that: WithRel[B, C]): WithRel[B, C] + + +

            Close a proof.

            +
          23. + + + + + + + + + def + + + |[C](that: WithProof[B, C]): WithProof[B, C] + + +

            Close a proof.

            +
            24. +
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          Inherited from Serializable

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          + + + case class + + + WithRel[A, B](x: A, r: (A, B) ⇒ Boolean, prop: Boolean) extends Product with Serializable + +

          + + +

          * Helper classes for relational reasoning **

          Annotations
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          4. + + + + + + + + + def + + + ==|(proof: Boolean): WithProof[A, A] + + +

            Short-hand for equational reasoning.

            +
          5. + + + + + + + + + def + + + ^^(y: B): RelReasoning[B] + + +

            Continue with the next relation.

            +
          6. + + + + + + + + + def + + + ^^|(proof: Boolean): WithProof[A, B] + + +

            Add a proof.

            +
          7. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
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            * Helper classes for relational reasoning **

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            Relational reasoning.

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          Relational reasoning.

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We use `self` + // instead of `window` for `WebWorker` support. + var root = typeof self == 'object' && self.self === self && self || + typeof global == 'object' && global.global === global && global || + Function('return this')() || + {}; + + // Save bytes in the minified (but not gzipped) version: + var ArrayProto = Array.prototype, ObjProto = Object.prototype; + var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null; + + // Create quick reference variables for speed access to core prototypes. + var push = ArrayProto.push, + slice = ArrayProto.slice, + toString = ObjProto.toString, + hasOwnProperty = ObjProto.hasOwnProperty; + + // Modern feature detection. + var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined', + supportsDataView = typeof DataView !== 'undefined'; + + // All **ECMAScript 5+** native function implementations that we hope to use + // are declared here. + var nativeIsArray = Array.isArray, + nativeKeys = Object.keys, + nativeCreate = Object.create, + nativeIsView = supportsArrayBuffer && ArrayBuffer.isView; + + // Create references to these builtin functions because we override them. + var _isNaN = isNaN, + _isFinite = isFinite; + + // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed. + var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString'); + var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString', + 'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString']; + + // The largest integer that can be represented exactly. + var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1; + + // Some functions take a variable number of arguments, or a few expected + // arguments at the beginning and then a variable number of values to operate + // on. This helper accumulates all remaining arguments past the function’s + // argument length (or an explicit `startIndex`), into an array that becomes + // the last argument. Similar to ES6’s "rest parameter". + function restArguments(func, startIndex) { + startIndex = startIndex == null ? func.length - 1 : +startIndex; + return function() { + var length = Math.max(arguments.length - startIndex, 0), + rest = Array(length), + index = 0; + for (; index < length; index++) { + rest[index] = arguments[index + startIndex]; + } + switch (startIndex) { + case 0: return func.call(this, rest); + case 1: return func.call(this, arguments[0], rest); + case 2: return func.call(this, arguments[0], arguments[1], rest); + } + var args = Array(startIndex + 1); + for (index = 0; index < startIndex; index++) { + args[index] = arguments[index]; + } + args[startIndex] = rest; + return func.apply(this, args); + }; + } + + // Is a given variable an object? + function isObject(obj) { + var type = typeof obj; + return type === 'function' || type === 'object' && !!obj; + } + + // Is a given value equal to null? + function isNull(obj) { + return obj === null; + } + + // Is a given variable undefined? + function isUndefined(obj) { + return obj === void 0; + } + + // Is a given value a boolean? + function isBoolean(obj) { + return obj === true || obj === false || toString.call(obj) === '[object Boolean]'; + } + + // Is a given value a DOM element? + function isElement(obj) { + return !!(obj && obj.nodeType === 1); + } + + // Internal function for creating a `toString`-based type tester. + function tagTester(name) { + var tag = '[object ' + name + ']'; + return function(obj) { + return toString.call(obj) === tag; + }; + } + + var isString = tagTester('String'); + + var isNumber = tagTester('Number'); + + var isDate = tagTester('Date'); + + var isRegExp = tagTester('RegExp'); + + var isError = tagTester('Error'); + + var isSymbol = tagTester('Symbol'); + + var isArrayBuffer = tagTester('ArrayBuffer'); + + var isFunction = tagTester('Function'); + + // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old + // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236). + var nodelist = root.document && root.document.childNodes; + if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') { + isFunction = function(obj) { + return typeof obj == 'function' || false; + }; + } + + var isFunction$1 = isFunction; + + var hasObjectTag = tagTester('Object'); + + // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`. + // In IE 11, the most common among them, this problem also applies to + // `Map`, `WeakMap` and `Set`. + var hasStringTagBug = ( + supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8))) + ), + isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map)); + + var isDataView = tagTester('DataView'); + + // In IE 10 - Edge 13, we need a different heuristic + // to determine whether an object is a `DataView`. + function ie10IsDataView(obj) { + return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer); + } + + var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView); + + // Is a given value an array? + // Delegates to ECMA5's native `Array.isArray`. + var isArray = nativeIsArray || tagTester('Array'); + + // Internal function to check whether `key` is an own property name of `obj`. + function has$1(obj, key) { + return obj != null && hasOwnProperty.call(obj, key); + } + + var isArguments = tagTester('Arguments'); + + // Define a fallback version of the method in browsers (ahem, IE < 9), where + // there isn't any inspectable "Arguments" type. + (function() { + if (!isArguments(arguments)) { + isArguments = function(obj) { + return has$1(obj, 'callee'); + }; + } + }()); + + var isArguments$1 = isArguments; + + // Is a given object a finite number? + function isFinite$1(obj) { + return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj)); + } + + // Is the given value `NaN`? + function isNaN$1(obj) { + return isNumber(obj) && _isNaN(obj); + } + + // Predicate-generating function. Often useful outside of Underscore. + function constant(value) { + return function() { + return value; + }; + } + + // Common internal logic for `isArrayLike` and `isBufferLike`. + function createSizePropertyCheck(getSizeProperty) { + return function(collection) { + var sizeProperty = getSizeProperty(collection); + return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX; + } + } + + // Internal helper to generate a function to obtain property `key` from `obj`. + function shallowProperty(key) { + return function(obj) { + return obj == null ? void 0 : obj[key]; + }; + } + + // Internal helper to obtain the `byteLength` property of an object. + var getByteLength = shallowProperty('byteLength'); + + // Internal helper to determine whether we should spend extensive checks against + // `ArrayBuffer` et al. + var isBufferLike = createSizePropertyCheck(getByteLength); + + // Is a given value a typed array? + var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/; + function isTypedArray(obj) { + // `ArrayBuffer.isView` is the most future-proof, so use it when available. + // Otherwise, fall back on the above regular expression. + return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) : + isBufferLike(obj) && typedArrayPattern.test(toString.call(obj)); + } + + var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false); + + // Internal helper to obtain the `length` property of an object. + var getLength = shallowProperty('length'); + + // Internal helper to create a simple lookup structure. + // `collectNonEnumProps` used to depend on `_.contains`, but this led to + // circular imports. `emulatedSet` is a one-off solution that only works for + // arrays of strings. + function emulatedSet(keys) { + var hash = {}; + for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true; + return { + contains: function(key) { return hash[key] === true; }, + push: function(key) { + hash[key] = true; + return keys.push(key); + } + }; + } + + // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't + // be iterated by `for key in ...` and thus missed. Extends `keys` in place if + // needed. + function collectNonEnumProps(obj, keys) { + keys = emulatedSet(keys); + var nonEnumIdx = nonEnumerableProps.length; + var constructor = obj.constructor; + var proto = isFunction$1(constructor) && constructor.prototype || ObjProto; + + // Constructor is a special case. + var prop = 'constructor'; + if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop); + + while (nonEnumIdx--) { + prop = nonEnumerableProps[nonEnumIdx]; + if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) { + keys.push(prop); + } + } + } + + // Retrieve the names of an object's own properties. + // Delegates to **ECMAScript 5**'s native `Object.keys`. + function keys(obj) { + if (!isObject(obj)) return []; + if (nativeKeys) return nativeKeys(obj); + var keys = []; + for (var key in obj) if (has$1(obj, key)) keys.push(key); + // Ahem, IE < 9. + if (hasEnumBug) collectNonEnumProps(obj, keys); + return keys; + } + + // Is a given array, string, or object empty? + // An "empty" object has no enumerable own-properties. + function isEmpty(obj) { + if (obj == null) return true; + // Skip the more expensive `toString`-based type checks if `obj` has no + // `.length`. + var length = getLength(obj); + if (typeof length == 'number' && ( + isArray(obj) || isString(obj) || isArguments$1(obj) + )) return length === 0; + return getLength(keys(obj)) === 0; + } + + // Returns whether an object has a given set of `key:value` pairs. + function isMatch(object, attrs) { + var _keys = keys(attrs), length = _keys.length; + if (object == null) return !length; + var obj = Object(object); + for (var i = 0; i < length; i++) { + var key = _keys[i]; + if (attrs[key] !== obj[key] || !(key in obj)) return false; + } + return true; + } + + // If Underscore is called as a function, it returns a wrapped object that can + // be used OO-style. This wrapper holds altered versions of all functions added + // through `_.mixin`. Wrapped objects may be chained. + function _$1(obj) { + if (obj instanceof _$1) return obj; + if (!(this instanceof _$1)) return new _$1(obj); + this._wrapped = obj; + } + + _$1.VERSION = VERSION; + + // Extracts the result from a wrapped and chained object. + _$1.prototype.value = function() { + return this._wrapped; + }; + + // Provide unwrapping proxies for some methods used in engine operations + // such as arithmetic and JSON stringification. + _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value; + + _$1.prototype.toString = function() { + return String(this._wrapped); + }; + + // Internal function to wrap or shallow-copy an ArrayBuffer, + // typed array or DataView to a new view, reusing the buffer. + function toBufferView(bufferSource) { + return new Uint8Array( + bufferSource.buffer || bufferSource, + bufferSource.byteOffset || 0, + getByteLength(bufferSource) + ); + } + + // We use this string twice, so give it a name for minification. + var tagDataView = '[object DataView]'; + + // Internal recursive comparison function for `_.isEqual`. + function eq(a, b, aStack, bStack) { + // Identical objects are equal. `0 === -0`, but they aren't identical. + // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal). + if (a === b) return a !== 0 || 1 / a === 1 / b; + // `null` or `undefined` only equal to itself (strict comparison). + if (a == null || b == null) return false; + // `NaN`s are equivalent, but non-reflexive. + if (a !== a) return b !== b; + // Exhaust primitive checks + var type = typeof a; + if (type !== 'function' && type !== 'object' && typeof b != 'object') return false; + return deepEq(a, b, aStack, bStack); + } + + // Internal recursive comparison function for `_.isEqual`. + function deepEq(a, b, aStack, bStack) { + // Unwrap any wrapped objects. + if (a instanceof _$1) a = a._wrapped; + if (b instanceof _$1) b = b._wrapped; + // Compare `[[Class]]` names. + var className = toString.call(a); + if (className !== toString.call(b)) return false; + // Work around a bug in IE 10 - Edge 13. + if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) { + if (!isDataView$1(b)) return false; + className = tagDataView; + } + switch (className) { + // These types are compared by value. + case '[object RegExp]': + // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i') + case '[object String]': + // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is + // equivalent to `new String("5")`. + return '' + a === '' + b; + case '[object Number]': + // `NaN`s are equivalent, but non-reflexive. + // Object(NaN) is equivalent to NaN. + if (+a !== +a) return +b !== +b; + // An `egal` comparison is performed for other numeric values. + return +a === 0 ? 1 / +a === 1 / b : +a === +b; + case '[object Date]': + case '[object Boolean]': + // Coerce dates and booleans to numeric primitive values. Dates are compared by their + // millisecond representations. Note that invalid dates with millisecond representations + // of `NaN` are not equivalent. + return +a === +b; + case '[object Symbol]': + return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b); + case '[object ArrayBuffer]': + case tagDataView: + // Coerce to typed array so we can fall through. + return deepEq(toBufferView(a), toBufferView(b), aStack, bStack); + } + + var areArrays = className === '[object Array]'; + if (!areArrays && isTypedArray$1(a)) { + var byteLength = getByteLength(a); + if (byteLength !== getByteLength(b)) return false; + if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true; + areArrays = true; + } + if (!areArrays) { + if (typeof a != 'object' || typeof b != 'object') return false; + + // Objects with different constructors are not equivalent, but `Object`s or `Array`s + // from different frames are. + var aCtor = a.constructor, bCtor = b.constructor; + if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor && + isFunction$1(bCtor) && bCtor instanceof bCtor) + && ('constructor' in a && 'constructor' in b)) { + return false; + } + } + // Assume equality for cyclic structures. The algorithm for detecting cyclic + // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`. + + // Initializing stack of traversed objects. + // It's done here since we only need them for objects and arrays comparison. + aStack = aStack || []; + bStack = bStack || []; + var length = aStack.length; + while (length--) { + // Linear search. Performance is inversely proportional to the number of + // unique nested structures. + if (aStack[length] === a) return bStack[length] === b; + } + + // Add the first object to the stack of traversed objects. + aStack.push(a); + bStack.push(b); + + // Recursively compare objects and arrays. + if (areArrays) { + // Compare array lengths to determine if a deep comparison is necessary. + length = a.length; + if (length !== b.length) return false; + // Deep compare the contents, ignoring non-numeric properties. + while (length--) { + if (!eq(a[length], b[length], aStack, bStack)) return false; + } + } else { + // Deep compare objects. + var _keys = keys(a), key; + length = _keys.length; + // Ensure that both objects contain the same number of properties before comparing deep equality. + if (keys(b).length !== length) return false; + while (length--) { + // Deep compare each member + key = _keys[length]; + if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false; + } + } + // Remove the first object from the stack of traversed objects. + aStack.pop(); + bStack.pop(); + return true; + } + + // Perform a deep comparison to check if two objects are equal. + function isEqual(a, b) { + return eq(a, b); + } + + // Retrieve all the enumerable property names of an object. + function allKeys(obj) { + if (!isObject(obj)) return []; + var keys = []; + for (var key in obj) keys.push(key); + // Ahem, IE < 9. + if (hasEnumBug) collectNonEnumProps(obj, keys); + return keys; + } + + // Since the regular `Object.prototype.toString` type tests don't work for + // some types in IE 11, we use a fingerprinting heuristic instead, based + // on the methods. It's not great, but it's the best we got. + // The fingerprint method lists are defined below. + function ie11fingerprint(methods) { + var length = getLength(methods); + return function(obj) { + if (obj == null) return false; + // `Map`, `WeakMap` and `Set` have no enumerable keys. + var keys = allKeys(obj); + if (getLength(keys)) return false; + for (var i = 0; i < length; i++) { + if (!isFunction$1(obj[methods[i]])) return false; + } + // If we are testing against `WeakMap`, we need to ensure that + // `obj` doesn't have a `forEach` method in order to distinguish + // it from a regular `Map`. + return methods !== weakMapMethods || !isFunction$1(obj[forEachName]); + }; + } + + // In the interest of compact minification, we write + // each string in the fingerprints only once. + var forEachName = 'forEach', + hasName = 'has', + commonInit = ['clear', 'delete'], + mapTail = ['get', hasName, 'set']; + + // `Map`, `WeakMap` and `Set` each have slightly different + // combinations of the above sublists. + var mapMethods = commonInit.concat(forEachName, mapTail), + weakMapMethods = commonInit.concat(mapTail), + setMethods = ['add'].concat(commonInit, forEachName, hasName); + + var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map'); + + var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap'); + + var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set'); + + var isWeakSet = tagTester('WeakSet'); + + // Retrieve the values of an object's properties. + function values(obj) { + var _keys = keys(obj); + var length = _keys.length; + var values = Array(length); + for (var i = 0; i < length; i++) { + values[i] = obj[_keys[i]]; + } + return values; + } + + // Convert an object into a list of `[key, value]` pairs. + // The opposite of `_.object` with one argument. + function pairs(obj) { + var _keys = keys(obj); + var length = _keys.length; + var pairs = Array(length); + for (var i = 0; i < length; i++) { + pairs[i] = [_keys[i], obj[_keys[i]]]; + } + return pairs; + } + + // Invert the keys and values of an object. The values must be serializable. + function invert(obj) { + var result = {}; + var _keys = keys(obj); + for (var i = 0, length = _keys.length; i < length; i++) { + result[obj[_keys[i]]] = _keys[i]; + } + return result; + } + + // Return a sorted list of the function names available on the object. + function functions(obj) { + var names = []; + for (var key in obj) { + if (isFunction$1(obj[key])) names.push(key); + } + return names.sort(); + } + + // An internal function for creating assigner functions. + function createAssigner(keysFunc, defaults) { + return function(obj) { + var length = arguments.length; + if (defaults) obj = Object(obj); + if (length < 2 || obj == null) return obj; + for (var index = 1; index < length; index++) { + var source = arguments[index], + keys = keysFunc(source), + l = keys.length; + for (var i = 0; i < l; i++) { + var key = keys[i]; + if (!defaults || obj[key] === void 0) obj[key] = source[key]; + } + } + return obj; + }; + } + + // Extend a given object with all the properties in passed-in object(s). + var extend = createAssigner(allKeys); + + // Assigns a given object with all the own properties in the passed-in + // object(s). + // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign) + var extendOwn = createAssigner(keys); + + // Fill in a given object with default properties. + var defaults = createAssigner(allKeys, true); + + // Create a naked function reference for surrogate-prototype-swapping. + function ctor() { + return function(){}; + } + + // An internal function for creating a new object that inherits from another. + function baseCreate(prototype) { + if (!isObject(prototype)) return {}; + if (nativeCreate) return nativeCreate(prototype); + var Ctor = ctor(); + Ctor.prototype = prototype; + var result = new Ctor; + Ctor.prototype = null; + return result; + } + + // Creates an object that inherits from the given prototype object. + // If additional properties are provided then they will be added to the + // created object. + function create(prototype, props) { + var result = baseCreate(prototype); + if (props) extendOwn(result, props); + return result; + } + + // Create a (shallow-cloned) duplicate of an object. + function clone(obj) { + if (!isObject(obj)) return obj; + return isArray(obj) ? obj.slice() : extend({}, obj); + } + + // Invokes `interceptor` with the `obj` and then returns `obj`. + // The primary purpose of this method is to "tap into" a method chain, in + // order to perform operations on intermediate results within the chain. + function tap(obj, interceptor) { + interceptor(obj); + return obj; + } + + // Normalize a (deep) property `path` to array. + // Like `_.iteratee`, this function can be customized. + function toPath$1(path) { + return isArray(path) ? path : [path]; + } + _$1.toPath = toPath$1; + + // Internal wrapper for `_.toPath` to enable minification. + // Similar to `cb` for `_.iteratee`. + function toPath(path) { + return _$1.toPath(path); + } + + // Internal function to obtain a nested property in `obj` along `path`. + function deepGet(obj, path) { + var length = path.length; + for (var i = 0; i < length; i++) { + if (obj == null) return void 0; + obj = obj[path[i]]; + } + return length ? obj : void 0; + } + + // Get the value of the (deep) property on `path` from `object`. + // If any property in `path` does not exist or if the value is + // `undefined`, return `defaultValue` instead. + // The `path` is normalized through `_.toPath`. + function get(object, path, defaultValue) { + var value = deepGet(object, toPath(path)); + return isUndefined(value) ? defaultValue : value; + } + + // Shortcut function for checking if an object has a given property directly on + // itself (in other words, not on a prototype). Unlike the internal `has` + // function, this public version can also traverse nested properties. + function has(obj, path) { + path = toPath(path); + var length = path.length; + for (var i = 0; i < length; i++) { + var key = path[i]; + if (!has$1(obj, key)) return false; + obj = obj[key]; + } + return !!length; + } + + // Keep the identity function around for default iteratees. + function identity(value) { + return value; + } + + // Returns a predicate for checking whether an object has a given set of + // `key:value` pairs. + function matcher(attrs) { + attrs = extendOwn({}, attrs); + return function(obj) { + return isMatch(obj, attrs); + }; + } + + // Creates a function that, when passed an object, will traverse that object’s + // properties down the given `path`, specified as an array of keys or indices. + function property(path) { + path = toPath(path); + return function(obj) { + return deepGet(obj, path); + }; + } + + // Internal function that returns an efficient (for current engines) version + // of the passed-in callback, to be repeatedly applied in other Underscore + // functions. + function optimizeCb(func, context, argCount) { + if (context === void 0) return func; + switch (argCount == null ? 3 : argCount) { + case 1: return function(value) { + return func.call(context, value); + }; + // The 2-argument case is omitted because we’re not using it. + case 3: return function(value, index, collection) { + return func.call(context, value, index, collection); + }; + case 4: return function(accumulator, value, index, collection) { + return func.call(context, accumulator, value, index, collection); + }; + } + return function() { + return func.apply(context, arguments); + }; + } + + // An internal function to generate callbacks that can be applied to each + // element in a collection, returning the desired result — either `_.identity`, + // an arbitrary callback, a property matcher, or a property accessor. + function baseIteratee(value, context, argCount) { + if (value == null) return identity; + if (isFunction$1(value)) return optimizeCb(value, context, argCount); + if (isObject(value) && !isArray(value)) return matcher(value); + return property(value); + } + + // External wrapper for our callback generator. Users may customize + // `_.iteratee` if they want additional predicate/iteratee shorthand styles. + // This abstraction hides the internal-only `argCount` argument. + function iteratee(value, context) { + return baseIteratee(value, context, Infinity); + } + _$1.iteratee = iteratee; + + // The function we call internally to generate a callback. It invokes + // `_.iteratee` if overridden, otherwise `baseIteratee`. + function cb(value, context, argCount) { + if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context); + return baseIteratee(value, context, argCount); + } + + // Returns the results of applying the `iteratee` to each element of `obj`. + // In contrast to `_.map` it returns an object. + function mapObject(obj, iteratee, context) { + iteratee = cb(iteratee, context); + var _keys = keys(obj), + length = _keys.length, + results = {}; + for (var index = 0; index < length; index++) { + var currentKey = _keys[index]; + results[currentKey] = iteratee(obj[currentKey], currentKey, obj); + } + return results; + } + + // Predicate-generating function. Often useful outside of Underscore. + function noop(){} + + // Generates a function for a given object that returns a given property. + function propertyOf(obj) { + if (obj == null) return noop; + return function(path) { + return get(obj, path); + }; + } + + // Run a function **n** times. + function times(n, iteratee, context) { + var accum = Array(Math.max(0, n)); + iteratee = optimizeCb(iteratee, context, 1); + for (var i = 0; i < n; i++) accum[i] = iteratee(i); + return accum; + } + + // Return a random integer between `min` and `max` (inclusive). + function random(min, max) { + if (max == null) { + max = min; + min = 0; + } + return min + Math.floor(Math.random() * (max - min + 1)); + } + + // A (possibly faster) way to get the current timestamp as an integer. + var now = Date.now || function() { + return new Date().getTime(); + }; + + // Internal helper to generate functions for escaping and unescaping strings + // to/from HTML interpolation. + function createEscaper(map) { + var escaper = function(match) { + return map[match]; + }; + // Regexes for identifying a key that needs to be escaped. + var source = '(?:' + keys(map).join('|') + ')'; + var testRegexp = RegExp(source); + var replaceRegexp = RegExp(source, 'g'); + return function(string) { + string = string == null ? '' : '' + string; + return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string; + }; + } + + // Internal list of HTML entities for escaping. + var escapeMap = { + '&': '&', + '<': '<', + '>': '>', + '"': '"', + "'": ''', + '`': '`' + }; + + // Function for escaping strings to HTML interpolation. + var _escape = createEscaper(escapeMap); + + // Internal list of HTML entities for unescaping. + var unescapeMap = invert(escapeMap); + + // Function for unescaping strings from HTML interpolation. + var _unescape = createEscaper(unescapeMap); + + // By default, Underscore uses ERB-style template delimiters. Change the + // following template settings to use alternative delimiters. + var templateSettings = _$1.templateSettings = { + evaluate: /<%([\s\S]+?)%>/g, + interpolate: /<%=([\s\S]+?)%>/g, + escape: /<%-([\s\S]+?)%>/g + }; + + // When customizing `_.templateSettings`, if you don't want to define an + // interpolation, evaluation or escaping regex, we need one that is + // guaranteed not to match. + var noMatch = /(.)^/; + + // Certain characters need to be escaped so that they can be put into a + // string literal. + var escapes = { + "'": "'", + '\\': '\\', + '\r': 'r', + '\n': 'n', + '\u2028': 'u2028', + '\u2029': 'u2029' + }; + + var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g; + + function escapeChar(match) { + return '\\' + escapes[match]; + } + + // In order to prevent third-party code injection through + // `_.templateSettings.variable`, we test it against the following regular + // expression. It is intentionally a bit more liberal than just matching valid + // identifiers, but still prevents possible loopholes through defaults or + // destructuring assignment. + var bareIdentifier = /^\s*(\w|\$)+\s*$/; + + // JavaScript micro-templating, similar to John Resig's implementation. + // Underscore templating handles arbitrary delimiters, preserves whitespace, + // and correctly escapes quotes within interpolated code. + // NB: `oldSettings` only exists for backwards compatibility. + function template(text, settings, oldSettings) { + if (!settings && oldSettings) settings = oldSettings; + settings = defaults({}, settings, _$1.templateSettings); + + // Combine delimiters into one regular expression via alternation. + var matcher = RegExp([ + (settings.escape || noMatch).source, + (settings.interpolate || noMatch).source, + (settings.evaluate || noMatch).source + ].join('|') + '|$', 'g'); + + // Compile the template source, escaping string literals appropriately. + var index = 0; + var source = "__p+='"; + text.replace(matcher, function(match, escape, interpolate, evaluate, offset) { + source += text.slice(index, offset).replace(escapeRegExp, escapeChar); + index = offset + match.length; + + if (escape) { + source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'"; + } else if (interpolate) { + source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'"; + } else if (evaluate) { + source += "';\n" + evaluate + "\n__p+='"; + } + + // Adobe VMs need the match returned to produce the correct offset. + return match; + }); + source += "';\n"; + + var argument = settings.variable; + if (argument) { + // Insure against third-party code injection. (CVE-2021-23358) + if (!bareIdentifier.test(argument)) throw new Error( + 'variable is not a bare identifier: ' + argument + ); + } else { + // If a variable is not specified, place data values in local scope. + source = 'with(obj||{}){\n' + source + '}\n'; + argument = 'obj'; + } + + source = "var __t,__p='',__j=Array.prototype.join," + + "print=function(){__p+=__j.call(arguments,'');};\n" + + source + 'return __p;\n'; + + var render; + try { + render = new Function(argument, '_', source); + } catch (e) { + e.source = source; + throw e; + } + + var template = function(data) { + return render.call(this, data, _$1); + }; + + // Provide the compiled source as a convenience for precompilation. + template.source = 'function(' + argument + '){\n' + source + '}'; + + return template; + } + + // Traverses the children of `obj` along `path`. If a child is a function, it + // is invoked with its parent as context. Returns the value of the final + // child, or `fallback` if any child is undefined. + function result(obj, path, fallback) { + path = toPath(path); + var length = path.length; + if (!length) { + return isFunction$1(fallback) ? fallback.call(obj) : fallback; + } + for (var i = 0; i < length; i++) { + var prop = obj == null ? void 0 : obj[path[i]]; + if (prop === void 0) { + prop = fallback; + i = length; // Ensure we don't continue iterating. + } + obj = isFunction$1(prop) ? prop.call(obj) : prop; + } + return obj; + } + + // Generate a unique integer id (unique within the entire client session). + // Useful for temporary DOM ids. + var idCounter = 0; + function uniqueId(prefix) { + var id = ++idCounter + ''; + return prefix ? prefix + id : id; + } + + // Start chaining a wrapped Underscore object. + function chain(obj) { + var instance = _$1(obj); + instance._chain = true; + return instance; + } + + // Internal function to execute `sourceFunc` bound to `context` with optional + // `args`. Determines whether to execute a function as a constructor or as a + // normal function. + function executeBound(sourceFunc, boundFunc, context, callingContext, args) { + if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args); + var self = baseCreate(sourceFunc.prototype); + var result = sourceFunc.apply(self, args); + if (isObject(result)) return result; + return self; + } + + // Partially apply a function by creating a version that has had some of its + // arguments pre-filled, without changing its dynamic `this` context. `_` acts + // as a placeholder by default, allowing any combination of arguments to be + // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument. + var partial = restArguments(function(func, boundArgs) { + var placeholder = partial.placeholder; + var bound = function() { + var position = 0, length = boundArgs.length; + var args = Array(length); + for (var i = 0; i < length; i++) { + args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i]; + } + while (position < arguments.length) args.push(arguments[position++]); + return executeBound(func, bound, this, this, args); + }; + return bound; + }); + + partial.placeholder = _$1; + + // Create a function bound to a given object (assigning `this`, and arguments, + // optionally). + var bind = restArguments(function(func, context, args) { + if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function'); + var bound = restArguments(function(callArgs) { + return executeBound(func, bound, context, this, args.concat(callArgs)); + }); + return bound; + }); + + // Internal helper for collection methods to determine whether a collection + // should be iterated as an array or as an object. + // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength + // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094 + var isArrayLike = createSizePropertyCheck(getLength); + + // Internal implementation of a recursive `flatten` function. + function flatten$1(input, depth, strict, output) { + output = output || []; + if (!depth && depth !== 0) { + depth = Infinity; + } else if (depth <= 0) { + return output.concat(input); + } + var idx = output.length; + for (var i = 0, length = getLength(input); i < length; i++) { + var value = input[i]; + if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) { + // Flatten current level of array or arguments object. + if (depth > 1) { + flatten$1(value, depth - 1, strict, output); + idx = output.length; + } else { + var j = 0, len = value.length; + while (j < len) output[idx++] = value[j++]; + } + } else if (!strict) { + output[idx++] = value; + } + } + return output; + } + + // Bind a number of an object's methods to that object. Remaining arguments + // are the method names to be bound. Useful for ensuring that all callbacks + // defined on an object belong to it. + var bindAll = restArguments(function(obj, keys) { + keys = flatten$1(keys, false, false); + var index = keys.length; + if (index < 1) throw new Error('bindAll must be passed function names'); + while (index--) { + var key = keys[index]; + obj[key] = bind(obj[key], obj); + } + return obj; + }); + + // Memoize an expensive function by storing its results. + function memoize(func, hasher) { + var memoize = function(key) { + var cache = memoize.cache; + var address = '' + (hasher ? hasher.apply(this, arguments) : key); + if (!has$1(cache, address)) cache[address] = func.apply(this, arguments); + return cache[address]; + }; + memoize.cache = {}; + return memoize; + } + + // Delays a function for the given number of milliseconds, and then calls + // it with the arguments supplied. + var delay = restArguments(function(func, wait, args) { + return setTimeout(function() { + return func.apply(null, args); + }, wait); + }); + + // Defers a function, scheduling it to run after the current call stack has + // cleared. + var defer = partial(delay, _$1, 1); + + // Returns a function, that, when invoked, will only be triggered at most once + // during a given window of time. Normally, the throttled function will run + // as much as it can, without ever going more than once per `wait` duration; + // but if you'd like to disable the execution on the leading edge, pass + // `{leading: false}`. To disable execution on the trailing edge, ditto. + function throttle(func, wait, options) { + var timeout, context, args, result; + var previous = 0; + if (!options) options = {}; + + var later = function() { + previous = options.leading === false ? 0 : now(); + timeout = null; + result = func.apply(context, args); + if (!timeout) context = args = null; + }; + + var throttled = function() { + var _now = now(); + if (!previous && options.leading === false) previous = _now; + var remaining = wait - (_now - previous); + context = this; + args = arguments; + if (remaining <= 0 || remaining > wait) { + if (timeout) { + clearTimeout(timeout); + timeout = null; + } + previous = _now; + result = func.apply(context, args); + if (!timeout) context = args = null; + } else if (!timeout && options.trailing !== false) { + timeout = setTimeout(later, remaining); + } + return result; + }; + + throttled.cancel = function() { + clearTimeout(timeout); + previous = 0; + timeout = context = args = null; + }; + + return throttled; + } + + // When a sequence of calls of the returned function ends, the argument + // function is triggered. The end of a sequence is defined by the `wait` + // parameter. If `immediate` is passed, the argument function will be + // triggered at the beginning of the sequence instead of at the end. + function debounce(func, wait, immediate) { + var timeout, previous, args, result, context; + + var later = function() { + var passed = now() - previous; + if (wait > passed) { + timeout = setTimeout(later, wait - passed); + } else { + timeout = null; + if (!immediate) result = func.apply(context, args); + // This check is needed because `func` can recursively invoke `debounced`. + if (!timeout) args = context = null; + } + }; + + var debounced = restArguments(function(_args) { + context = this; + args = _args; + previous = now(); + if (!timeout) { + timeout = setTimeout(later, wait); + if (immediate) result = func.apply(context, args); + } + return result; + }); + + debounced.cancel = function() { + clearTimeout(timeout); + timeout = args = context = null; + }; + + return debounced; + } + + // Returns the first function passed as an argument to the second, + // allowing you to adjust arguments, run code before and after, and + // conditionally execute the original function. + function wrap(func, wrapper) { + return partial(wrapper, func); + } + + // Returns a negated version of the passed-in predicate. + function negate(predicate) { + return function() { + return !predicate.apply(this, arguments); + }; + } + + // Returns a function that is the composition of a list of functions, each + // consuming the return value of the function that follows. + function compose() { + var args = arguments; + var start = args.length - 1; + return function() { + var i = start; + var result = args[start].apply(this, arguments); + while (i--) result = args[i].call(this, result); + return result; + }; + } + + // Returns a function that will only be executed on and after the Nth call. + function after(times, func) { + return function() { + if (--times < 1) { + return func.apply(this, arguments); + } + }; + } + + // Returns a function that will only be executed up to (but not including) the + // Nth call. + function before(times, func) { + var memo; + return function() { + if (--times > 0) { + memo = func.apply(this, arguments); + } + if (times <= 1) func = null; + return memo; + }; + } + + // Returns a function that will be executed at most one time, no matter how + // often you call it. Useful for lazy initialization. + var once = partial(before, 2); + + // Returns the first key on an object that passes a truth test. + function findKey(obj, predicate, context) { + predicate = cb(predicate, context); + var _keys = keys(obj), key; + for (var i = 0, length = _keys.length; i < length; i++) { + key = _keys[i]; + if (predicate(obj[key], key, obj)) return key; + } + } + + // Internal function to generate `_.findIndex` and `_.findLastIndex`. + function createPredicateIndexFinder(dir) { + return function(array, predicate, context) { + predicate = cb(predicate, context); + var length = getLength(array); + var index = dir > 0 ? 0 : length - 1; + for (; index >= 0 && index < length; index += dir) { + if (predicate(array[index], index, array)) return index; + } + return -1; + }; + } + + // Returns the first index on an array-like that passes a truth test. + var findIndex = createPredicateIndexFinder(1); + + // Returns the last index on an array-like that passes a truth test. + var findLastIndex = createPredicateIndexFinder(-1); + + // Use a comparator function to figure out the smallest index at which + // an object should be inserted so as to maintain order. Uses binary search. + function sortedIndex(array, obj, iteratee, context) { + iteratee = cb(iteratee, context, 1); + var value = iteratee(obj); + var low = 0, high = getLength(array); + while (low < high) { + var mid = Math.floor((low + high) / 2); + if (iteratee(array[mid]) < value) low = mid + 1; else high = mid; + } + return low; + } + + // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions. + function createIndexFinder(dir, predicateFind, sortedIndex) { + return function(array, item, idx) { + var i = 0, length = getLength(array); + if (typeof idx == 'number') { + if (dir > 0) { + i = idx >= 0 ? idx : Math.max(idx + length, i); + } else { + length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1; + } + } else if (sortedIndex && idx && length) { + idx = sortedIndex(array, item); + return array[idx] === item ? idx : -1; + } + if (item !== item) { + idx = predicateFind(slice.call(array, i, length), isNaN$1); + return idx >= 0 ? idx + i : -1; + } + for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) { + if (array[idx] === item) return idx; + } + return -1; + }; + } + + // Return the position of the first occurrence of an item in an array, + // or -1 if the item is not included in the array. + // If the array is large and already in sort order, pass `true` + // for **isSorted** to use binary search. + var indexOf = createIndexFinder(1, findIndex, sortedIndex); + + // Return the position of the last occurrence of an item in an array, + // or -1 if the item is not included in the array. + var lastIndexOf = createIndexFinder(-1, findLastIndex); + + // Return the first value which passes a truth test. + function find(obj, predicate, context) { + var keyFinder = isArrayLike(obj) ? findIndex : findKey; + var key = keyFinder(obj, predicate, context); + if (key !== void 0 && key !== -1) return obj[key]; + } + + // Convenience version of a common use case of `_.find`: getting the first + // object containing specific `key:value` pairs. + function findWhere(obj, attrs) { + return find(obj, matcher(attrs)); + } + + // The cornerstone for collection functions, an `each` + // implementation, aka `forEach`. + // Handles raw objects in addition to array-likes. Treats all + // sparse array-likes as if they were dense. + function each(obj, iteratee, context) { + iteratee = optimizeCb(iteratee, context); + var i, length; + if (isArrayLike(obj)) { + for (i = 0, length = obj.length; i < length; i++) { + iteratee(obj[i], i, obj); + } + } else { + var _keys = keys(obj); + for (i = 0, length = _keys.length; i < length; i++) { + iteratee(obj[_keys[i]], _keys[i], obj); + } + } + return obj; + } + + // Return the results of applying the iteratee to each element. + function map(obj, iteratee, context) { + iteratee = cb(iteratee, context); + var _keys = !isArrayLike(obj) && keys(obj), + length = (_keys || obj).length, + results = Array(length); + for (var index = 0; index < length; index++) { + var currentKey = _keys ? _keys[index] : index; + results[index] = iteratee(obj[currentKey], currentKey, obj); + } + return results; + } + + // Internal helper to create a reducing function, iterating left or right. + function createReduce(dir) { + // Wrap code that reassigns argument variables in a separate function than + // the one that accesses `arguments.length` to avoid a perf hit. (#1991) + var reducer = function(obj, iteratee, memo, initial) { + var _keys = !isArrayLike(obj) && keys(obj), + length = (_keys || obj).length, + index = dir > 0 ? 0 : length - 1; + if (!initial) { + memo = obj[_keys ? _keys[index] : index]; + index += dir; + } + for (; index >= 0 && index < length; index += dir) { + var currentKey = _keys ? _keys[index] : index; + memo = iteratee(memo, obj[currentKey], currentKey, obj); + } + return memo; + }; + + return function(obj, iteratee, memo, context) { + var initial = arguments.length >= 3; + return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial); + }; + } + + // **Reduce** builds up a single result from a list of values, aka `inject`, + // or `foldl`. + var reduce = createReduce(1); + + // The right-associative version of reduce, also known as `foldr`. + var reduceRight = createReduce(-1); + + // Return all the elements that pass a truth test. + function filter(obj, predicate, context) { + var results = []; + predicate = cb(predicate, context); + each(obj, function(value, index, list) { + if (predicate(value, index, list)) results.push(value); + }); + return results; + } + + // Return all the elements for which a truth test fails. + function reject(obj, predicate, context) { + return filter(obj, negate(cb(predicate)), context); + } + + // Determine whether all of the elements pass a truth test. + function every(obj, predicate, context) { + predicate = cb(predicate, context); + var _keys = !isArrayLike(obj) && keys(obj), + length = (_keys || obj).length; + for (var index = 0; index < length; index++) { + var currentKey = _keys ? _keys[index] : index; + if (!predicate(obj[currentKey], currentKey, obj)) return false; + } + return true; + } + + // Determine if at least one element in the object passes a truth test. + function some(obj, predicate, context) { + predicate = cb(predicate, context); + var _keys = !isArrayLike(obj) && keys(obj), + length = (_keys || obj).length; + for (var index = 0; index < length; index++) { + var currentKey = _keys ? _keys[index] : index; + if (predicate(obj[currentKey], currentKey, obj)) return true; + } + return false; + } + + // Determine if the array or object contains a given item (using `===`). + function contains(obj, item, fromIndex, guard) { + if (!isArrayLike(obj)) obj = values(obj); + if (typeof fromIndex != 'number' || guard) fromIndex = 0; + return indexOf(obj, item, fromIndex) >= 0; + } + + // Invoke a method (with arguments) on every item in a collection. + var invoke = restArguments(function(obj, path, args) { + var contextPath, func; + if (isFunction$1(path)) { + func = path; + } else { + path = toPath(path); + contextPath = path.slice(0, -1); + path = path[path.length - 1]; + } + return map(obj, function(context) { + var method = func; + if (!method) { + if (contextPath && contextPath.length) { + context = deepGet(context, contextPath); + } + if (context == null) return void 0; + method = context[path]; + } + return method == null ? method : method.apply(context, args); + }); + }); + + // Convenience version of a common use case of `_.map`: fetching a property. + function pluck(obj, key) { + return map(obj, property(key)); + } + + // Convenience version of a common use case of `_.filter`: selecting only + // objects containing specific `key:value` pairs. + function where(obj, attrs) { + return filter(obj, matcher(attrs)); + } + + // Return the maximum element (or element-based computation). + function max(obj, iteratee, context) { + var result = -Infinity, lastComputed = -Infinity, + value, computed; + if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) { + obj = isArrayLike(obj) ? obj : values(obj); + for (var i = 0, length = obj.length; i < length; i++) { + value = obj[i]; + if (value != null && value > result) { + result = value; + } + } + } else { + iteratee = cb(iteratee, context); + each(obj, function(v, index, list) { + computed = iteratee(v, index, list); + if (computed > lastComputed || computed === -Infinity && result === -Infinity) { + result = v; + lastComputed = computed; + } + }); + } + return result; + } + + // Return the minimum element (or element-based computation). + function min(obj, iteratee, context) { + var result = Infinity, lastComputed = Infinity, + value, computed; + if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) { + obj = isArrayLike(obj) ? obj : values(obj); + for (var i = 0, length = obj.length; i < length; i++) { + value = obj[i]; + if (value != null && value < result) { + result = value; + } + } + } else { + iteratee = cb(iteratee, context); + each(obj, function(v, index, list) { + computed = iteratee(v, index, list); + if (computed < lastComputed || computed === Infinity && result === Infinity) { + result = v; + lastComputed = computed; + } + }); + } + return result; + } + + // Safely create a real, live array from anything iterable. + var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g; + function toArray(obj) { + if (!obj) return []; + if (isArray(obj)) return slice.call(obj); + if (isString(obj)) { + // Keep surrogate pair characters together. + return obj.match(reStrSymbol); + } + if (isArrayLike(obj)) return map(obj, identity); + return values(obj); + } + + // Sample **n** random values from a collection using the modern version of the + // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle). + // If **n** is not specified, returns a single random element. + // The internal `guard` argument allows it to work with `_.map`. + function sample(obj, n, guard) { + if (n == null || guard) { + if (!isArrayLike(obj)) obj = values(obj); + return obj[random(obj.length - 1)]; + } + var sample = toArray(obj); + var length = getLength(sample); + n = Math.max(Math.min(n, length), 0); + var last = length - 1; + for (var index = 0; index < n; index++) { + var rand = random(index, last); + var temp = sample[index]; + sample[index] = sample[rand]; + sample[rand] = temp; + } + return sample.slice(0, n); + } + + // Shuffle a collection. + function shuffle(obj) { + return sample(obj, Infinity); + } + + // Sort the object's values by a criterion produced by an iteratee. + function sortBy(obj, iteratee, context) { + var index = 0; + iteratee = cb(iteratee, context); + return pluck(map(obj, function(value, key, list) { + return { + value: value, + index: index++, + criteria: iteratee(value, key, list) + }; + }).sort(function(left, right) { + var a = left.criteria; + var b = right.criteria; + if (a !== b) { + if (a > b || a === void 0) return 1; + if (a < b || b === void 0) return -1; + } + return left.index - right.index; + }), 'value'); + } + + // An internal function used for aggregate "group by" operations. + function group(behavior, partition) { + return function(obj, iteratee, context) { + var result = partition ? [[], []] : {}; + iteratee = cb(iteratee, context); + each(obj, function(value, index) { + var key = iteratee(value, index, obj); + behavior(result, value, key); + }); + return result; + }; + } + + // Groups the object's values by a criterion. Pass either a string attribute + // to group by, or a function that returns the criterion. + var groupBy = group(function(result, value, key) { + if (has$1(result, key)) result[key].push(value); else result[key] = [value]; + }); + + // Indexes the object's values by a criterion, similar to `_.groupBy`, but for + // when you know that your index values will be unique. + var indexBy = group(function(result, value, key) { + result[key] = value; + }); + + // Counts instances of an object that group by a certain criterion. Pass + // either a string attribute to count by, or a function that returns the + // criterion. + var countBy = group(function(result, value, key) { + if (has$1(result, key)) result[key]++; else result[key] = 1; + }); + + // Split a collection into two arrays: one whose elements all pass the given + // truth test, and one whose elements all do not pass the truth test. + var partition = group(function(result, value, pass) { + result[pass ? 0 : 1].push(value); + }, true); + + // Return the number of elements in a collection. + function size(obj) { + if (obj == null) return 0; + return isArrayLike(obj) ? obj.length : keys(obj).length; + } + + // Internal `_.pick` helper function to determine whether `key` is an enumerable + // property name of `obj`. + function keyInObj(value, key, obj) { + return key in obj; + } + + // Return a copy of the object only containing the allowed properties. + var pick = restArguments(function(obj, keys) { + var result = {}, iteratee = keys[0]; + if (obj == null) return result; + if (isFunction$1(iteratee)) { + if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]); + keys = allKeys(obj); + } else { + iteratee = keyInObj; + keys = flatten$1(keys, false, false); + obj = Object(obj); + } + for (var i = 0, length = keys.length; i < length; i++) { + var key = keys[i]; + var value = obj[key]; + if (iteratee(value, key, obj)) result[key] = value; + } + return result; + }); + + // Return a copy of the object without the disallowed properties. + var omit = restArguments(function(obj, keys) { + var iteratee = keys[0], context; + if (isFunction$1(iteratee)) { + iteratee = negate(iteratee); + if (keys.length > 1) context = keys[1]; + } else { + keys = map(flatten$1(keys, false, false), String); + iteratee = function(value, key) { + return !contains(keys, key); + }; + } + return pick(obj, iteratee, context); + }); + + // Returns everything but the last entry of the array. Especially useful on + // the arguments object. Passing **n** will return all the values in + // the array, excluding the last N. + function initial(array, n, guard) { + return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n))); + } + + // Get the first element of an array. Passing **n** will return the first N + // values in the array. The **guard** check allows it to work with `_.map`. + function first(array, n, guard) { + if (array == null || array.length < 1) return n == null || guard ? void 0 : []; + if (n == null || guard) return array[0]; + return initial(array, array.length - n); + } + + // Returns everything but the first entry of the `array`. Especially useful on + // the `arguments` object. Passing an **n** will return the rest N values in the + // `array`. + function rest(array, n, guard) { + return slice.call(array, n == null || guard ? 1 : n); + } + + // Get the last element of an array. Passing **n** will return the last N + // values in the array. + function last(array, n, guard) { + if (array == null || array.length < 1) return n == null || guard ? void 0 : []; + if (n == null || guard) return array[array.length - 1]; + return rest(array, Math.max(0, array.length - n)); + } + + // Trim out all falsy values from an array. + function compact(array) { + return filter(array, Boolean); + } + + // Flatten out an array, either recursively (by default), or up to `depth`. + // Passing `true` or `false` as `depth` means `1` or `Infinity`, respectively. + function flatten(array, depth) { + return flatten$1(array, depth, false); + } + + // Take the difference between one array and a number of other arrays. + // Only the elements present in just the first array will remain. + var difference = restArguments(function(array, rest) { + rest = flatten$1(rest, true, true); + return filter(array, function(value){ + return !contains(rest, value); + }); + }); + + // Return a version of the array that does not contain the specified value(s). + var without = restArguments(function(array, otherArrays) { + return difference(array, otherArrays); + }); + + // Produce a duplicate-free version of the array. If the array has already + // been sorted, you have the option of using a faster algorithm. + // The faster algorithm will not work with an iteratee if the iteratee + // is not a one-to-one function, so providing an iteratee will disable + // the faster algorithm. + function uniq(array, isSorted, iteratee, context) { + if (!isBoolean(isSorted)) { + context = iteratee; + iteratee = isSorted; + isSorted = false; + } + if (iteratee != null) iteratee = cb(iteratee, context); + var result = []; + var seen = []; + for (var i = 0, length = getLength(array); i < length; i++) { + var value = array[i], + computed = iteratee ? iteratee(value, i, array) : value; + if (isSorted && !iteratee) { + if (!i || seen !== computed) result.push(value); + seen = computed; + } else if (iteratee) { + if (!contains(seen, computed)) { + seen.push(computed); + result.push(value); + } + } else if (!contains(result, value)) { + result.push(value); + } + } + return result; + } + + // Produce an array that contains the union: each distinct element from all of + // the passed-in arrays. + var union = restArguments(function(arrays) { + return uniq(flatten$1(arrays, true, true)); + }); + + // Produce an array that contains every item shared between all the + // passed-in arrays. + function intersection(array) { + var result = []; + var argsLength = arguments.length; + for (var i = 0, length = getLength(array); i < length; i++) { + var item = array[i]; + if (contains(result, item)) continue; + var j; + for (j = 1; j < argsLength; j++) { + if (!contains(arguments[j], item)) break; + } + if (j === argsLength) result.push(item); + } + return result; + } + + // Complement of zip. Unzip accepts an array of arrays and groups + // each array's elements on shared indices. + function unzip(array) { + var length = array && max(array, getLength).length || 0; + var result = Array(length); + + for (var index = 0; index < length; index++) { + result[index] = pluck(array, index); + } + return result; + } + + // Zip together multiple lists into a single array -- elements that share + // an index go together. + var zip = restArguments(unzip); + + // Converts lists into objects. Pass either a single array of `[key, value]` + // pairs, or two parallel arrays of the same length -- one of keys, and one of + // the corresponding values. Passing by pairs is the reverse of `_.pairs`. + function object(list, values) { + var result = {}; + for (var i = 0, length = getLength(list); i < length; i++) { + if (values) { + result[list[i]] = values[i]; + } else { + result[list[i][0]] = list[i][1]; + } + } + return result; + } + + // Generate an integer Array containing an arithmetic progression. A port of + // the native Python `range()` function. See + // [the Python documentation](https://docs.python.org/library/functions.html#range). + function range(start, stop, step) { + if (stop == null) { + stop = start || 0; + start = 0; + } + if (!step) { + step = stop < start ? -1 : 1; + } + + var length = Math.max(Math.ceil((stop - start) / step), 0); + var range = Array(length); + + for (var idx = 0; idx < length; idx++, start += step) { + range[idx] = start; + } + + return range; + } + + // Chunk a single array into multiple arrays, each containing `count` or fewer + // items. + function chunk(array, count) { + if (count == null || count < 1) return []; + var result = []; + var i = 0, length = array.length; + while (i < length) { + result.push(slice.call(array, i, i += count)); + } + return result; + } + + // Helper function to continue chaining intermediate results. + function chainResult(instance, obj) { + return instance._chain ? _$1(obj).chain() : obj; + } + + // Add your own custom functions to the Underscore object. + function mixin(obj) { + each(functions(obj), function(name) { + var func = _$1[name] = obj[name]; + _$1.prototype[name] = function() { + var args = [this._wrapped]; + push.apply(args, arguments); + return chainResult(this, func.apply(_$1, args)); + }; + }); + return _$1; + } + + // Add all mutator `Array` functions to the wrapper. + each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) { + var method = ArrayProto[name]; + _$1.prototype[name] = function() { + var obj = this._wrapped; + if (obj != null) { + method.apply(obj, arguments); + if ((name === 'shift' || name === 'splice') && obj.length === 0) { + delete obj[0]; + } + } + return chainResult(this, obj); + }; + }); + + // Add all accessor `Array` functions to the wrapper. + each(['concat', 'join', 'slice'], function(name) { + var method = ArrayProto[name]; + _$1.prototype[name] = function() { + var obj = this._wrapped; + if (obj != null) obj = method.apply(obj, arguments); + return chainResult(this, obj); + }; + }); + + // Named Exports + + var allExports = { + __proto__: null, + VERSION: VERSION, + restArguments: restArguments, + isObject: isObject, + isNull: isNull, + isUndefined: isUndefined, + isBoolean: isBoolean, + isElement: isElement, + isString: isString, + isNumber: isNumber, + isDate: isDate, + isRegExp: isRegExp, + isError: isError, + isSymbol: isSymbol, + isArrayBuffer: isArrayBuffer, + isDataView: isDataView$1, + isArray: isArray, + isFunction: isFunction$1, + isArguments: isArguments$1, + isFinite: isFinite$1, + isNaN: isNaN$1, + isTypedArray: isTypedArray$1, + isEmpty: isEmpty, + isMatch: isMatch, + isEqual: isEqual, + isMap: isMap, + isWeakMap: isWeakMap, + isSet: isSet, + isWeakSet: isWeakSet, + keys: keys, + allKeys: allKeys, + values: values, + pairs: pairs, + invert: invert, + functions: functions, + methods: functions, + extend: extend, + extendOwn: extendOwn, + assign: extendOwn, + defaults: defaults, + create: create, + clone: clone, + tap: tap, + get: get, + has: has, + mapObject: mapObject, + identity: identity, + constant: constant, + noop: noop, + toPath: toPath$1, + property: property, + propertyOf: propertyOf, + matcher: matcher, + matches: matcher, + times: times, + random: random, + now: now, + escape: _escape, + unescape: _unescape, + templateSettings: templateSettings, + template: template, + result: result, + uniqueId: uniqueId, + chain: chain, + iteratee: iteratee, + partial: partial, + bind: bind, + bindAll: bindAll, + memoize: memoize, + delay: delay, + defer: defer, + throttle: throttle, + debounce: debounce, + wrap: wrap, + negate: negate, + compose: compose, + after: after, + before: before, + once: once, + findKey: findKey, + findIndex: findIndex, + findLastIndex: findLastIndex, + sortedIndex: sortedIndex, + indexOf: indexOf, + lastIndexOf: lastIndexOf, + find: find, + detect: find, + findWhere: findWhere, + each: each, + forEach: each, + map: map, + collect: map, + reduce: reduce, + foldl: reduce, + inject: reduce, + reduceRight: reduceRight, + foldr: reduceRight, + filter: filter, + select: filter, + reject: reject, + every: every, + all: every, + some: some, + any: some, + contains: contains, + includes: contains, + include: contains, + invoke: invoke, + pluck: pluck, + where: where, + max: max, + min: min, + shuffle: shuffle, + sample: sample, + sortBy: sortBy, + groupBy: groupBy, + indexBy: indexBy, + countBy: countBy, + partition: partition, + toArray: toArray, + size: size, + pick: pick, + omit: omit, + first: first, + head: first, + take: first, + initial: initial, + last: last, + rest: rest, + tail: rest, + drop: rest, + compact: compact, + flatten: flatten, + without: without, + uniq: uniq, + unique: uniq, + union: union, + intersection: intersection, + difference: difference, + unzip: unzip, + transpose: unzip, + zip: zip, + object: object, + range: range, + chunk: chunk, + mixin: mixin, + 'default': _$1 + }; + + // Default Export + + // Add all of the Underscore functions to the wrapper object. + var _ = mixin(allExports); + // Legacy Node.js API. + _._ = _; + + return _; + +}))); +//# sourceMappingURL=underscore-umd.js.map diff --git a/_static/valid/AbstractRefinementMap.html b/_static/valid/AbstractRefinementMap.html new file mode 100644 index 0000000000..898e2de53b --- /dev/null +++ b/_static/valid/AbstractRefinementMap.html @@ -0,0 +1,35 @@ + + + +valid/AbstractRefinementMap.scala + + +

          AbstractRefinementMap.scala [raw]


          +
          import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+
+object AbstractRefinementMap {
+
+  case class ~>[A,B](private val f: A => B, ens: B => Boolean) {
+    require(forall((x: B) => ens.pre(x)) && forall((x: A) => f.pre(x) ==> ens(f(x))))
+
+    lazy val pre = f.pre
+
+    def apply(x: A): B = {
+      require(f.pre(x))
+      f(x)
+    } ensuring(ens)
+  }
+
+  def map[A, B](l: List[A], f: A ~> B): List[B] = {
+    require(forall((x:A) => l.contains(x) ==> f.pre(x)))
+    l match {
+      case Cons(x, xs) => Cons[B](f(x), map(xs, f))
+      case Nil() => Nil[B]()
+    }
+  } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) }
+}
+
+
          +

          back

          diff --git a/_static/valid/AbstractRefinementMap.scala b/_static/valid/AbstractRefinementMap.scala new file mode 100644 index 0000000000..48cb2ec848 --- /dev/null +++ b/_static/valid/AbstractRefinementMap.scala @@ -0,0 +1,26 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ + +object AbstractRefinementMap { + + case class ~>[A,B](private val f: A => B, ens: B => Boolean) { + require(forall((x: B) => ens.pre(x)) && forall((x: A) => f.pre(x) ==> ens(f(x)))) + + lazy val pre = f.pre + + def apply(x: A): B = { + require(f.pre(x)) + f(x) + } ensuring(ens) + } + + def map[A, B](l: List[A], f: A ~> B): List[B] = { + require(forall((x:A) => l.contains(x) ==> f.pre(x))) + l match { + case Cons(x, xs) => Cons[B](f(x), map(xs, f)) + case Nil() => Nil[B]() + } + } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) } +} + diff --git a/_static/valid/AddingPositiveNumbers.html b/_static/valid/AddingPositiveNumbers.html new file mode 100644 index 0000000000..d7122e0fab --- /dev/null +++ b/_static/valid/AddingPositiveNumbers.html @@ -0,0 +1,20 @@ + + + +valid/AddingPositiveNumbers.scala + + +

          AddingPositiveNumbers.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+object AddingPositiveNumbers {
+
+  //this should not overflow
+  def additionSound(x: BigInt, y: BigInt): BigInt = {
+    require(x >= 0 && y >= 0)
+    x + y
+  } ensuring(_ >= 0)
+
+}
+
          +

          back

          diff --git a/_static/valid/AddingPositiveNumbers.scala b/_static/valid/AddingPositiveNumbers.scala new file mode 100644 index 0000000000..84fca5dc63 --- /dev/null +++ b/_static/valid/AddingPositiveNumbers.scala @@ -0,0 +1,11 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +object AddingPositiveNumbers { + + //this should not overflow + def additionSound(x: BigInt, y: BigInt): BigInt = { + require(x >= 0 && y >= 0) + x + y + } ensuring(_ >= 0) + +} diff --git a/_static/valid/AssociativeList.html b/_static/valid/AssociativeList.html new file mode 100644 index 0000000000..bade03ed99 --- /dev/null +++ b/_static/valid/AssociativeList.html @@ -0,0 +1,60 @@ + + + +valid/AssociativeList.scala + + +

          AssociativeList.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object AssociativeList { 
+  sealed abstract class KeyValuePairAbs
+  case class KeyValuePair(key: Int, value: Int) extends KeyValuePairAbs
+
+  sealed abstract class List
+  case class Cons(head: KeyValuePairAbs, tail: List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptionInt
+  case class Some(i: Int) extends OptionInt
+  case class None() extends OptionInt
+
+  def domain(l: List): Set[Int] = l match {
+    case Nil() => Set.empty[Int]
+    case Cons(KeyValuePair(k,_), xs) => Set(k) ++ domain(xs)
+  }
+
+  def find(l: List, e: Int): OptionInt = l match {
+    case Nil() => None()
+    case Cons(KeyValuePair(k, v), xs) => if (k == e) Some(v) else find(xs, e)
+  }
+
+  def noDuplicates(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(KeyValuePair(k, v), xs) => find(xs, k) == None() && noDuplicates(xs)
+  }
+
+  def updateAll(l1: List, l2: List): List = (l2 match {
+    case Nil() => l1
+    case Cons(x, xs) => updateAll(updateElem(l1, x), xs)
+  }) ensuring(domain(_) == domain(l1) ++ domain(l2))
+
+  def updateElem(l: List, e: KeyValuePairAbs): List = (l match {
+    case Nil() => Cons(e, Nil())
+    case Cons(KeyValuePair(k, v), xs) => e match {
+      case KeyValuePair(ek, ev) => if (ek == k) Cons(KeyValuePair(ek, ev), xs) else Cons(KeyValuePair(k, v), updateElem(xs, e))
+    }
+  }) ensuring(res => e match {
+    case KeyValuePair(k, v) => domain(res) == domain(l) ++ Set[Int](k)
+  })
+
+  @induct
+  def readOverWrite(l: List, k1: Int, k2: Int, e: Int) : Boolean = {
+    find(updateElem(l, KeyValuePair(k2,e)), k1) == (if (k1 == k2) Some(e) else find(l, k1))
+  }.holds
+}
+
          +

          back

          diff --git a/_static/valid/AssociativeList.scala b/_static/valid/AssociativeList.scala new file mode 100644 index 0000000000..45ac711a12 --- /dev/null +++ b/_static/valid/AssociativeList.scala @@ -0,0 +1,51 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object AssociativeList { + sealed abstract class KeyValuePairAbs + case class KeyValuePair(key: Int, value: Int) extends KeyValuePairAbs + + sealed abstract class List + case class Cons(head: KeyValuePairAbs, tail: List) extends List + case class Nil() extends List + + sealed abstract class OptionInt + case class Some(i: Int) extends OptionInt + case class None() extends OptionInt + + def domain(l: List): Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(KeyValuePair(k,_), xs) => Set(k) ++ domain(xs) + } + + def find(l: List, e: Int): OptionInt = l match { + case Nil() => None() + case Cons(KeyValuePair(k, v), xs) => if (k == e) Some(v) else find(xs, e) + } + + def noDuplicates(l: List): Boolean = l match { + case Nil() => true + case Cons(KeyValuePair(k, v), xs) => find(xs, k) == None() && noDuplicates(xs) + } + + def updateAll(l1: List, l2: List): List = (l2 match { + case Nil() => l1 + case Cons(x, xs) => updateAll(updateElem(l1, x), xs) + }) ensuring(domain(_) == domain(l1) ++ domain(l2)) + + def updateElem(l: List, e: KeyValuePairAbs): List = (l match { + case Nil() => Cons(e, Nil()) + case Cons(KeyValuePair(k, v), xs) => e match { + case KeyValuePair(ek, ev) => if (ek == k) Cons(KeyValuePair(ek, ev), xs) else Cons(KeyValuePair(k, v), updateElem(xs, e)) + } + }) ensuring(res => e match { + case KeyValuePair(k, v) => domain(res) == domain(l) ++ Set[Int](k) + }) + + @induct + def readOverWrite(l: List, k1: Int, k2: Int, e: Int) : Boolean = { + find(updateElem(l, KeyValuePair(k2,e)), k1) == (if (k1 == k2) Some(e) else find(l, k1)) + }.holds +} diff --git a/_static/valid/AssociativityProperties.html b/_static/valid/AssociativityProperties.html new file mode 100644 index 0000000000..9455bffcdf --- /dev/null +++ b/_static/valid/AssociativityProperties.html @@ -0,0 +1,42 @@ + + + +valid/AssociativityProperties.scala + + +

          AssociativityProperties.scala [raw]


          +
          import stainless.lang._
+
+object AssociativityProperties {
+
+  def isAssociative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z)))
+  }
+
+  def isCommutative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A) => f(x, y) == f(y, x))
+  }
+
+  def isRotate[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x))
+  }
+
+  def assocPairs[A,B](f1: (A,A) => A, f2: (B,B) => B) = {
+    require(isAssociative(f1) && isAssociative(f2))
+    val fp = ((p1: (A,B), p2: (A,B)) => (f1(p1._1, p2._1), f2(p1._2, p2._2)))
+    isAssociative(fp)
+  }.holds
+
+  def assocRotate[A](f: (A,A) => A): Boolean = {
+    require(isCommutative(f) && isRotate(f))
+    isAssociative(f)
+  }.holds
+
+  def assocRotateInt(f: (BigInt, BigInt) => BigInt): Boolean = {
+    require(isCommutative(f) && isRotate(f))
+    isAssociative(f)
+  }.holds
+
+}
+
          +

          back

          diff --git a/_static/valid/AssociativityProperties.scala b/_static/valid/AssociativityProperties.scala new file mode 100644 index 0000000000..c92d44ae10 --- /dev/null +++ b/_static/valid/AssociativityProperties.scala @@ -0,0 +1,33 @@ +import stainless.lang._ + +object AssociativityProperties { + + def isAssociative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z))) + } + + def isCommutative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A) => f(x, y) == f(y, x)) + } + + def isRotate[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x)) + } + + def assocPairs[A,B](f1: (A,A) => A, f2: (B,B) => B) = { + require(isAssociative(f1) && isAssociative(f2)) + val fp = ((p1: (A,B), p2: (A,B)) => (f1(p1._1, p2._1), f2(p1._2, p2._2))) + isAssociative(fp) + }.holds + + def assocRotate[A](f: (A,A) => A): Boolean = { + require(isCommutative(f) && isRotate(f)) + isAssociative(f) + }.holds + + def assocRotateInt(f: (BigInt, BigInt) => BigInt): Boolean = { + require(isCommutative(f) && isRotate(f)) + isAssociative(f) + }.holds + +} diff --git a/_static/valid/BinarySearchTreeQuant.html b/_static/valid/BinarySearchTreeQuant.html new file mode 100644 index 0000000000..72c2c4ddd4 --- /dev/null +++ b/_static/valid/BinarySearchTreeQuant.html @@ -0,0 +1,53 @@ + + + +valid/BinarySearchTreeQuant.scala + + +

          BinarySearchTreeQuant.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.collection._
+
+object BSTSimpler {
+  sealed abstract class Tree
+  case class Node(left: Tree, value: BigInt, right: Tree) extends Tree
+  case class Leaf() extends Tree
+
+  def content(tree: Tree): Set[BigInt] = tree match {
+    case Leaf() => Set.empty[BigInt]
+    case Node(l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def isBST(tree: Tree) : Boolean = tree match {
+    case Leaf() => true
+    case Node(left, v, right) => {
+      isBST(left) && isBST(right) &&
+      forall((x:BigInt) => (content(left).contains(x) ==> x < v)) &&
+      forall((x:BigInt) => (content(right).contains(x) ==> v < x))
+    }
+  }
+
+  def emptySet(): Tree = Leaf()
+
+  def insert(tree: Tree, value: BigInt): Node = {
+    require(isBST(tree))
+    tree match {
+      case Leaf() => Node(Leaf(), value, Leaf())
+      case Node(l, v, r) => (if (v < value) {
+        Node(l, v, insert(r, value))
+      } else if (v > value) {
+        Node(insert(l, value), v, r)
+      } else {
+        Node(l, v, r)
+      })
+    }
+  } ensuring(res => isBST(res) && content(res) == content(tree) ++ Set(value))
+
+  def createRoot(v: BigInt): Node = {
+    Node(Leaf(), v, Leaf())
+  } ensuring (content(_) == Set(v))
+}
+
          +

          back

          diff --git a/_static/valid/BinarySearchTreeQuant.scala b/_static/valid/BinarySearchTreeQuant.scala new file mode 100644 index 0000000000..36f80d7d8b --- /dev/null +++ b/_static/valid/BinarySearchTreeQuant.scala @@ -0,0 +1,44 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.collection._ + +object BSTSimpler { + sealed abstract class Tree + case class Node(left: Tree, value: BigInt, right: Tree) extends Tree + case class Leaf() extends Tree + + def content(tree: Tree): Set[BigInt] = tree match { + case Leaf() => Set.empty[BigInt] + case Node(l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def isBST(tree: Tree) : Boolean = tree match { + case Leaf() => true + case Node(left, v, right) => { + isBST(left) && isBST(right) && + forall((x:BigInt) => (content(left).contains(x) ==> x < v)) && + forall((x:BigInt) => (content(right).contains(x) ==> v < x)) + } + } + + def emptySet(): Tree = Leaf() + + def insert(tree: Tree, value: BigInt): Node = { + require(isBST(tree)) + tree match { + case Leaf() => Node(Leaf(), value, Leaf()) + case Node(l, v, r) => (if (v < value) { + Node(l, v, insert(r, value)) + } else if (v > value) { + Node(insert(l, value), v, r) + } else { + Node(l, v, r) + }) + } + } ensuring(res => isBST(res) && content(res) == content(tree) ++ Set(value)) + + def createRoot(v: BigInt): Node = { + Node(Leaf(), v, Leaf()) + } ensuring (content(_) == Set(v)) +} diff --git a/_static/valid/ChooseWithWitness.html b/_static/valid/ChooseWithWitness.html new file mode 100644 index 0000000000..dacc364f12 --- /dev/null +++ b/_static/valid/ChooseWithWitness.html @@ -0,0 +1,60 @@ + + + +valid/ChooseWithWitness.scala + + +

          ChooseWithWitness.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ChooseWithWitness {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def createListOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        Cons(0, createListOfSize(i - 1))
+      }
+    } ensuring ( size(_) == i )
+
+    def listOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        assert(size(createListOfSize(i)) == i) // provides choose quantification with a matcher
+        choose[List] { (res: List) => size(res) == i }
+      }
+    } ensuring ( size(_) == i )
+
+    def listOfSize2(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i > 0) {
+        Cons(0, listOfSize(i-1))
+      } else {
+        Nil()
+      }
+    } ensuring ( size(_) == i )
+}
+
          +

          back

          diff --git a/_static/valid/ChooseWithWitness.scala b/_static/valid/ChooseWithWitness.scala new file mode 100644 index 0000000000..3d6c1c1d31 --- /dev/null +++ b/_static/valid/ChooseWithWitness.scala @@ -0,0 +1,51 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ChooseWithWitness { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def createListOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + Cons(0, createListOfSize(i - 1)) + } + } ensuring ( size(_) == i ) + + def listOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + assert(size(createListOfSize(i)) == i) // provides choose quantification with a matcher + choose[List] { (res: List) => size(res) == i } + } + } ensuring ( size(_) == i ) + + def listOfSize2(i: BigInt): List = { + require(i >= 0) + + if (i > 0) { + Cons(0, listOfSize(i-1)) + } else { + Nil() + } + } ensuring ( size(_) == i ) +} diff --git a/_static/valid/ConcRope.html b/_static/valid/ConcRope.html new file mode 100644 index 0000000000..29bc4359d4 --- /dev/null +++ b/_static/valid/ConcRope.html @@ -0,0 +1,470 @@ +

          ConcRope.scala [raw]


          +
          package conc
+// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL
+
+import stainless.collection._
+import stainless.lang._
+import ListSpecs._
+import stainless.annotation._
+
+object ConcRope {
+
+  def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y
+  def abs(x: BigInt): BigInt = if (x < 0) -x else x
+
+  sealed abstract class Conc[T] {
+
+    def isEmpty: Boolean = {
+      this == Empty[T]()
+    }
+
+    def isLeaf: Boolean = {
+      this match {
+        case Empty() => true
+        case Single(_) => true
+        case _ => false
+      }
+    }
+
+    def isNormalized: Boolean = this match {
+      case Append(_, _) => false
+      case _ => true
+    }
+
+    def valid: Boolean = {
+      concInv && balanced && appendInv
+    }
+
+    /**
+     * (a) left and right trees of conc node should be non-empty
+     * (b) they cannot be append nodes
+     */
+    def concInv: Boolean = this match {
+      case CC(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.isNormalized && r.isNormalized &&
+          l.concInv && r.concInv
+      case _ => true
+    }
+
+    def balanced: Boolean = {
+      this match {
+        case CC(l, r) =>
+          l.level - r.level >= -1 && l.level - r.level <= 1 &&
+            l.balanced && r.balanced
+        case _ => true
+      }
+    }
+
+    /**
+     * (a) Right subtree of an append node is not an append node
+     * (b) If the tree is of the form a@Append(b@Append(_,_),_) then
+     * 		a.right.level < b.right.level
+     * (c) left and right are not empty
+     */
+    def appendInv: Boolean = this match {
+      case Append(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.valid && r.valid &&
+          r.isNormalized &&
+          (l match {
+            case Append(_, lr) =>
+              lr.level > r.level
+            case _ =>
+              l.level > r.level
+          })
+      case _ => true
+    }
+
+    val level: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 0
+        case CC(l, r) =>
+          1 + max(l.level, r.level)
+        case Append(l, r) =>
+          1 + max(l.level, r.level)
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    val size: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 1
+        case CC(l, r) =>
+          l.size + r.size
+        case Append(l, r) =>
+          l.size + r.size
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    def toList: List[T] = {
+      this match {
+        case Empty() => Nil[T]()
+        case Single(x) => Cons(x, Nil[T]())
+        case CC(l, r) =>
+          l.toList ++ r.toList // note: left elements precede the right elements in the list
+        case Append(l, r) =>
+          l.toList ++ r.toList
+      }
+    } ensuring (res => res.size == this.size)
+  }
+
+  case class Empty[T]() extends Conc[T]
+  case class Single[T](x: T) extends Conc[T]
+  case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+  case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+
+  def lookup[T](xs: Conc[T], i: BigInt): T = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => x
+      case CC(l, r) =>
+        if (i < l.size) lookup(l, i)
+       else lookup(r, i - l.size)          
+      case Append(l, r) =>
+        if (i < l.size) lookup(l, i)
+        else lookup(r, i - l.size)          
+    }
+  } ensuring (res =>  instAppendIndexAxiom(xs, i) &&  // an auxiliary axiom instantiation that required for the proof
+    res == xs.toList(i)) // correctness
+    
+
+  def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = {
+    require(0 <= i && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case Append(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case _ => true
+    }
+  }.holds
+
+  def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => Single(y)
+      case CC(l, r) =>
+        if (i < l.size) CC(update(l, i, y), r)
+        else CC(l, update(r, i - l.size, y))
+      case Append(l, r) =>
+        if (i < l.size) {          
+          Append(update(l, i, y), r)
+        } else         
+          Append(l, update(r, i - l.size, y))
+    }
+  } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation
+    res.level == xs.level && // heights of the input and output trees are equal
+    res.valid && // tree invariants are preserved    
+    res.toList == xs.toList.updated(i, y) && // correctness
+    numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function     
+
+  def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case Append(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  /**
+   * A generic concat that applies to general concTrees
+   */  
+  def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid)    
+    concatNormalized(normalize(xs), normalize(ys))    
+  }
+
+  /**
+   * This concat applies only to normalized trees.
+   * This prevents concat from being recursive
+   */
+  def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized)
+    (xs, ys) match {
+      case (xs, Empty()) => xs
+      case (Empty(), ys) => ys
+      case _ =>
+        concatNonEmpty(xs, ys)
+    }
+  } ensuring (res => res.valid && // tree invariants
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    (res.toList == xs.toList ++ ys.toList) && // correctness
+    res.isNormalized //auxiliary properties    
+    )
+
+  def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized &&
+      !xs.isEmpty && !ys.isEmpty)
+
+    val diff = ys.level - xs.level
+    if (diff >= -1 && diff <= 1) 
+      CC(xs, ys)
+    else if (diff < -1) {
+      // ys is smaller than xs
+      xs match {
+        case CC(l, r) =>
+          if (l.level >= r.level) 
+            CC(l, concatNonEmpty(r, ys))
+          else {
+            r match {
+              case CC(rl, rr) =>
+                val nrr = concatNonEmpty(rr, ys)
+                if (nrr.level == xs.level - 3) {
+                  CC(l, CC(rl, nrr))
+                } else {
+                  CC(CC(l, rl), nrr)
+                }
+            }
+          }
+      }
+    } else {
+      ys match {
+        case CC(l, r) =>
+          if (r.level >= l.level) {
+            CC(concatNonEmpty(xs, l), r)
+          } else {
+            l match {
+              case CC(ll, lr) =>
+                val nll = concatNonEmpty(xs, ll)
+                if (nll.level == ys.level - 3) {                  
+                  CC(CC(nll, lr), r)
+                } else {                  
+                  CC(nll, CC(lr, r))
+                }
+            }
+          }
+      }
+    }
+  } ensuring (res =>  
+    appendAssocInst(xs, ys) && // instantiation of an axiom
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    res.balanced && res.appendInv && res.concInv && //this is should not be needed
+    res.valid && // tree invariant is preserved
+    res.toList == xs.toList ++ ys.toList && // correctness
+    res.isNormalized // auxiliary properties    
+    )
+
+  
+  def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    (xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation              
+          (r match {
+            case CC(rl, rr) =>
+              appendAssoc(rl.toList, rr.toList, ys.toList) &&
+                appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList)
+            case _ => true
+          })
+      case _ => true
+    }) &&
+      (ys match {
+        case CC(l, r) =>
+          appendAssoc(xs.toList, l.toList, r.toList) &&
+            (l match {
+              case CC(ll, lr) =>
+                appendAssoc(xs.toList, ll.toList, lr.toList) &&
+                  appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList)
+              case _ => true
+            })
+        case _ => true
+      })
+  }.holds
+
+  
+  def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && i >= 0 && i <= xs.size &&
+      xs.isNormalized) //note the precondition
+    xs match {
+      case Empty() => Single(y)
+      case Single(x) =>
+        if (i == 0)
+          CC(Single(y), xs)
+        else
+          CC(xs, Single(y))
+      case CC(l, r) if i < l.size =>
+        concatNonEmpty(insert(l, i, y), r)        
+      case CC(l, r) =>
+       concatNonEmpty(l, insert(r, i - l.size, y))      
+    }
+  } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom 
+    res.valid && res.isNormalized && // tree invariants            
+    res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree    
+    res.toList == insertAtIndex(xs.toList, i, y) // correctness    
+    )
+
+  /**
+   * Using a different version of insert than of the library
+   * because the library implementation in unnecessarily complicated.  
+   */
+  def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = {
+    require(0 <= i && i <= l.size)
+    l match {
+      case Nil() =>
+        Cons[T](y, Nil())
+      case _ if i == 0 =>
+        Cons[T](y, l)
+      case Cons(x, tail) =>
+        Cons[T](x, insertAtIndex(tail, i - 1, y))
+    }
+  }
+
+  // A lemma about `append` and `insertAtIndex`
+  def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = {
+    require(0 <= i && i <= l1.size + l2.size)
+    (l1 match {
+      case Nil() => true
+      case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y)
+    }) &&
+      // lemma
+      (insertAtIndex((l1 ++ l2), i, y) == (
+        if (i < l1.size) insertAtIndex(l1, i, y) ++ l2
+        else l1 ++ insertAtIndex(l2, (i - l1.size), y)))
+  }.holds
+
+  def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i <= xs.size)
+    xs match {
+      case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = {
+    require(xs.valid && xs.isNormalized)
+    xs match {
+      case Empty() =>
+        (Empty[T](), Empty[T]())
+      case s @ Single(x) =>
+        if (n <= 0) { 
+          (Empty[T](), s)
+        } else {
+          (s, Empty[T]())
+        }
+      case CC(l, r) =>
+        if (n < l.size) {
+          val (ll, lr) = split(l, n)          
+          (ll, concatNormalized(lr, r))
+        } else if (n > l.size) {
+          val (rl, rr) = split(r, n - l.size)          
+          (concatNormalized(l, rl), rr)
+        } else {
+          (l, r)
+        }
+    }
+  } ensuring (res  => instSplitAxiom(xs, n) && // instantiation of an axiom     
+    res._1.valid && res._2.valid && // tree invariants are preserved
+    res._1.isNormalized && res._2.isNormalized &&
+    xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree
+    res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness    
+    )
+
+  def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendTakeDrop(l.toList, r.toList, n)
+      case _ => true
+    }
+  }.holds
+
+  def append[T](xs: Conc[T], x: T): Conc[T] = {
+    require(xs.valid)
+    val ys = Single[T](x)
+    xs match {
+      case xs @ Append(_, _) =>
+        appendPriv(xs, ys)
+      case CC(_, _) =>
+        Append(xs, ys) //creating an append node
+      case Empty() => ys
+      case Single(_) => CC(xs, ys)
+    }
+  } ensuring (res => res.valid && //conctree invariants
+    res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness
+    res.level <= xs.level + 1 
+  )
+
+  /**
+   * This is a private method and is not exposed to the
+   * clients of conc trees
+   */
+  def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T]  = {
+    require(xs.valid && ys.valid &&
+      !ys.isEmpty && ys.isNormalized &&
+      xs.right.level >= ys.level)
+
+    if (xs.right.level > ys.level)
+      Append(xs, ys)
+    else {
+      val zs = CC(xs.right, ys)
+      xs.left match {
+        case l @ Append(_, _) => appendPriv(l, zs)          
+        case l if l.level <= zs.level => //note: here < is not possible           
+          CC(l, zs)
+        case l =>
+          Append(l, zs)
+      }
+    }
+  } ensuring (res => appendAssocInst2(xs, ys) && 
+    res.valid && //conc tree invariants
+    res.toList == xs.toList ++ ys.toList && //correctness invariants
+    res.level <= xs.level + 1 )
+
+  def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case Append(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case _ => true
+    }
+  }.holds
+
+  def numTrees[T](t: Conc[T]): BigInt = {
+    t match {
+      case Append(l, r) => numTrees(l) + 1
+      case _ => BigInt(1)
+    }
+  } ensuring (res => res >= 0)
+
+  def normalize[T](t: Conc[T]): Conc[T] = {
+    require(t.valid)
+    t match {
+      case Append(l @ Append(_, _), r) =>
+        wrap(l, r)
+      case Append(l, r) =>
+        concatNormalized(l, r)
+      case _ => t
+    }
+  } ensuring (res => res.valid &&
+    res.isNormalized &&
+    res.toList == t.toList && //correctness
+    res.size == t.size && res.level <= t.level //normalize preserves level and size  
+    )
+
+  def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid && ys.isNormalized &&
+      xs.right.level >= ys.level)
+    val nr  = concatNormalized(xs.right, ys)
+    xs.left match {
+      case l @ Append(_, _) => wrap(l, nr)      
+      case l =>
+        concatNormalized(l, nr)        
+    }
+  } ensuring (res => 
+    appendAssocInst2(xs, ys) && //some lemma instantiations   
+    res.valid &&
+    res.isNormalized &&
+    res.toList == xs.toList ++ ys.toList && //correctness
+    res.size == xs.size + ys.size && //other auxiliary properties
+    res.level <= xs.level    
+    ) 
+}
+
          diff --git a/_static/valid/ConcRope.scala b/_static/valid/ConcRope.scala new file mode 100644 index 0000000000..932bd11494 --- /dev/null +++ b/_static/valid/ConcRope.scala @@ -0,0 +1,468 @@ +package conc +// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL + +import stainless.collection._ +import stainless.lang._ +import ListSpecs._ +import stainless.annotation._ + +object ConcRope { + + def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y + def abs(x: BigInt): BigInt = if (x < 0) -x else x + + sealed abstract class Conc[T] { + + def isEmpty: Boolean = { + this == Empty[T]() + } + + def isLeaf: Boolean = { + this match { + case Empty() => true + case Single(_) => true + case _ => false + } + } + + def isNormalized: Boolean = this match { + case Append(_, _) => false + case _ => true + } + + def valid: Boolean = { + concInv && balanced && appendInv + } + + /** + * (a) left and right trees of conc node should be non-empty + * (b) they cannot be append nodes + */ + def concInv: Boolean = this match { + case CC(l, r) => + !l.isEmpty && !r.isEmpty && + l.isNormalized && r.isNormalized && + l.concInv && r.concInv + case _ => true + } + + def balanced: Boolean = { + this match { + case CC(l, r) => + l.level - r.level >= -1 && l.level - r.level <= 1 && + l.balanced && r.balanced + case _ => true + } + } + + /** + * (a) Right subtree of an append node is not an append node + * (b) If the tree is of the form a@Append(b@Append(_,_),_) then + * a.right.level < b.right.level + * (c) left and right are not empty + */ + def appendInv: Boolean = this match { + case Append(l, r) => + !l.isEmpty && !r.isEmpty && + l.valid && r.valid && + r.isNormalized && + (l match { + case Append(_, lr) => + lr.level > r.level + case _ => + l.level > r.level + }) + case _ => true + } + + val level: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 0 + case CC(l, r) => + 1 + max(l.level, r.level) + case Append(l, r) => + 1 + max(l.level, r.level) + }): BigInt + } ensuring (_ >= 0) + + val size: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 1 + case CC(l, r) => + l.size + r.size + case Append(l, r) => + l.size + r.size + }): BigInt + } ensuring (_ >= 0) + + def toList: List[T] = { + this match { + case Empty() => Nil[T]() + case Single(x) => Cons(x, Nil[T]()) + case CC(l, r) => + l.toList ++ r.toList // note: left elements precede the right elements in the list + case Append(l, r) => + l.toList ++ r.toList + } + } ensuring (res => res.size == this.size) + } + + case class Empty[T]() extends Conc[T] + case class Single[T](x: T) extends Conc[T] + case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] + case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T] + + def lookup[T](xs: Conc[T], i: BigInt): T = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => x + case CC(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + case Append(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + } + } ensuring (res => instAppendIndexAxiom(xs, i) && // an auxiliary axiom instantiation that required for the proof + res == xs.toList(i)) // correctness + + + def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = { + require(0 <= i && i < xs.size) + xs match { + case CC(l, r) => + appendIndex(l.toList, r.toList, i) + case Append(l, r) => + appendIndex(l.toList, r.toList, i) + case _ => true + } + }.holds + + def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => Single(y) + case CC(l, r) => + if (i < l.size) CC(update(l, i, y), r) + else CC(l, update(r, i - l.size, y)) + case Append(l, r) => + if (i < l.size) { + Append(update(l, i, y), r) + } else + Append(l, update(r, i - l.size, y)) + } + } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation + res.level == xs.level && // heights of the input and output trees are equal + res.valid && // tree invariants are preserved + res.toList == xs.toList.updated(i, y) && // correctness + numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function + + def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i < xs.size) + xs match { + case CC(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case Append(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + /** + * A generic concat that applies to general concTrees + */ + def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid) + concatNormalized(normalize(xs), normalize(ys)) + } + + /** + * This concat applies only to normalized trees. + * This prevents concat from being recursive + */ + def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized) + (xs, ys) match { + case (xs, Empty()) => xs + case (Empty(), ys) => ys + case _ => + concatNonEmpty(xs, ys) + } + } ensuring (res => res.valid && // tree invariants + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + (res.toList == xs.toList ++ ys.toList) && // correctness + res.isNormalized //auxiliary properties + ) + + def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized && + !xs.isEmpty && !ys.isEmpty) + + val diff = ys.level - xs.level + if (diff >= -1 && diff <= 1) + CC(xs, ys) + else if (diff < -1) { + // ys is smaller than xs + xs match { + case CC(l, r) => + if (l.level >= r.level) + CC(l, concatNonEmpty(r, ys)) + else { + r match { + case CC(rl, rr) => + val nrr = concatNonEmpty(rr, ys) + if (nrr.level == xs.level - 3) { + CC(l, CC(rl, nrr)) + } else { + CC(CC(l, rl), nrr) + } + } + } + } + } else { + ys match { + case CC(l, r) => + if (r.level >= l.level) { + CC(concatNonEmpty(xs, l), r) + } else { + l match { + case CC(ll, lr) => + val nll = concatNonEmpty(xs, ll) + if (nll.level == ys.level - 3) { + CC(CC(nll, lr), r) + } else { + CC(nll, CC(lr, r)) + } + } + } + } + } + } ensuring (res => + appendAssocInst(xs, ys) && // instantiation of an axiom + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + res.balanced && res.appendInv && res.concInv && //this is should not be needed + res.valid && // tree invariant is preserved + res.toList == xs.toList ++ ys.toList && // correctness + res.isNormalized // auxiliary properties + ) + + + def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = { + (xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation + (r match { + case CC(rl, rr) => + appendAssoc(rl.toList, rr.toList, ys.toList) && + appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList) + case _ => true + }) + case _ => true + }) && + (ys match { + case CC(l, r) => + appendAssoc(xs.toList, l.toList, r.toList) && + (l match { + case CC(ll, lr) => + appendAssoc(xs.toList, ll.toList, lr.toList) && + appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList) + case _ => true + }) + case _ => true + }) + }.holds + + + def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && i >= 0 && i <= xs.size && + xs.isNormalized) //note the precondition + xs match { + case Empty() => Single(y) + case Single(x) => + if (i == 0) + CC(Single(y), xs) + else + CC(xs, Single(y)) + case CC(l, r) if i < l.size => + concatNonEmpty(insert(l, i, y), r) + case CC(l, r) => + concatNonEmpty(l, insert(r, i - l.size, y)) + } + } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom + res.valid && res.isNormalized && // tree invariants + res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree + res.toList == insertAtIndex(xs.toList, i, y) // correctness + ) + + /** + * Using a different version of insert than of the library + * because the library implementation in unnecessarily complicated. + */ + def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = { + require(0 <= i && i <= l.size) + l match { + case Nil() => + Cons[T](y, Nil()) + case _ if i == 0 => + Cons[T](y, l) + case Cons(x, tail) => + Cons[T](x, insertAtIndex(tail, i - 1, y)) + } + } + + // A lemma about `append` and `insertAtIndex` + def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = { + require(0 <= i && i <= l1.size + l2.size) + (l1 match { + case Nil() => true + case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y) + }) && + // lemma + (insertAtIndex((l1 ++ l2), i, y) == ( + if (i < l1.size) insertAtIndex(l1, i, y) ++ l2 + else l1 ++ insertAtIndex(l2, (i - l1.size), y))) + }.holds + + def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i <= xs.size) + xs match { + case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = { + require(xs.valid && xs.isNormalized) + xs match { + case Empty() => + (Empty[T](), Empty[T]()) + case s @ Single(x) => + if (n <= 0) { + (Empty[T](), s) + } else { + (s, Empty[T]()) + } + case CC(l, r) => + if (n < l.size) { + val (ll, lr) = split(l, n) + (ll, concatNormalized(lr, r)) + } else if (n > l.size) { + val (rl, rr) = split(r, n - l.size) + (concatNormalized(l, rl), rr) + } else { + (l, r) + } + } + } ensuring (res => instSplitAxiom(xs, n) && // instantiation of an axiom + res._1.valid && res._2.valid && // tree invariants are preserved + res._1.isNormalized && res._2.isNormalized && + xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree + res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness + ) + + def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = { + xs match { + case CC(l, r) => + appendTakeDrop(l.toList, r.toList, n) + case _ => true + } + }.holds + + def append[T](xs: Conc[T], x: T): Conc[T] = { + require(xs.valid) + val ys = Single[T](x) + xs match { + case xs @ Append(_, _) => + appendPriv(xs, ys) + case CC(_, _) => + Append(xs, ys) //creating an append node + case Empty() => ys + case Single(_) => CC(xs, ys) + } + } ensuring (res => res.valid && //conctree invariants + res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness + res.level <= xs.level + 1 + ) + + /** + * This is a private method and is not exposed to the + * clients of conc trees + */ + def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + !ys.isEmpty && ys.isNormalized && + xs.right.level >= ys.level) + + if (xs.right.level > ys.level) + Append(xs, ys) + else { + val zs = CC(xs.right, ys) + xs.left match { + case l @ Append(_, _) => appendPriv(l, zs) + case l if l.level <= zs.level => //note: here < is not possible + CC(l, zs) + case l => + Append(l, zs) + } + } + } ensuring (res => appendAssocInst2(xs, ys) && + res.valid && //conc tree invariants + res.toList == xs.toList ++ ys.toList && //correctness invariants + res.level <= xs.level + 1 ) + + def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = { + xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case Append(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case _ => true + } + }.holds + + def numTrees[T](t: Conc[T]): BigInt = { + t match { + case Append(l, r) => numTrees(l) + 1 + case _ => BigInt(1) + } + } ensuring (res => res >= 0) + + def normalize[T](t: Conc[T]): Conc[T] = { + require(t.valid) + t match { + case Append(l @ Append(_, _), r) => + wrap(l, r) + case Append(l, r) => + concatNormalized(l, r) + case _ => t + } + } ensuring (res => res.valid && + res.isNormalized && + res.toList == t.toList && //correctness + res.size == t.size && res.level <= t.level //normalize preserves level and size + ) + + def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && ys.isNormalized && + xs.right.level >= ys.level) + val nr = concatNormalized(xs.right, ys) + xs.left match { + case l @ Append(_, _) => wrap(l, nr) + case l => + concatNormalized(l, nr) + } + } ensuring (res => + appendAssocInst2(xs, ys) && //some lemma instantiations + res.valid && + res.isNormalized && + res.toList == xs.toList ++ ys.toList && //correctness + res.size == xs.size + ys.size && //other auxiliary properties + res.level <= xs.level + ) +} diff --git a/_static/valid/FlatMap.html b/_static/valid/FlatMap.html new file mode 100644 index 0000000000..8025c50fbb --- /dev/null +++ b/_static/valid/FlatMap.html @@ -0,0 +1,61 @@ + + + +valid/FlatMap.scala + + +

          FlatMap.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.proof._
+import stainless.collection._
+
+object FlatMap {
+
+  def append[T](l1: List[T], l2: List[T]): List[T] = l1 match {
+    case Cons(head, tail) => Cons(head, append(tail, l2))
+    case Nil() => l2
+  }
+
+  def associative_append_lemma[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = {
+    append(append(l1, l2), l3) == append(l1, append(l2, l3))
+  }
+
+  def associative_append_lemma_induct[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = {
+    l1 match {
+      case Nil() => associative_append_lemma(l1, l2, l3)
+      case Cons(head, tail) => associative_append_lemma(l1, l2, l3) because associative_append_lemma_induct(tail, l2, l3)
+    }
+  }.holds
+
+  def flatMap[T,U](list: List[T], f: T => List[U]): List[U] = list match {
+    case Cons(head, tail) => append(f(head), flatMap(tail, f))
+    case Nil() => Nil()
+  }
+
+  def associative_lemma[T,U,V](list: List[T], f: T => List[U], g: U => List[V]): Boolean = {
+    flatMap(flatMap(list, f), g) == flatMap(list, (x: T) => flatMap(f(x), g))
+  }
+
+  def associative_lemma_induct[T,U,V](list: List[T], flist: List[U], glist: List[V], f: T => List[U], g: U => List[V]): Boolean = {
+    associative_lemma(list, f, g) because {
+      append(glist, flatMap(append(flist, flatMap(list, f)), g)) == append(append(glist, flatMap(flist, g)), flatMap(list, (x: T) => flatMap(f(x), g))) because
+      (glist match {
+        case Cons(ghead, gtail) =>
+          associative_lemma_induct(list, flist, gtail, f, g)
+        case Nil() => flist match {
+          case Cons(fhead, ftail) =>
+            associative_lemma_induct(list, ftail, g(fhead), f, g)
+          case Nil() => list match {
+            case Cons(head, tail) => associative_lemma_induct(tail, f(head), Nil(), f, g)
+            case Nil() => true
+          }
+        }
+      })
+    }
+  }.holds
+
+}
+
          +

          back

          diff --git a/_static/valid/FlatMap.scala b/_static/valid/FlatMap.scala new file mode 100644 index 0000000000..cb7c3f132b --- /dev/null +++ b/_static/valid/FlatMap.scala @@ -0,0 +1,52 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.proof._ +import stainless.collection._ + +object FlatMap { + + def append[T](l1: List[T], l2: List[T]): List[T] = l1 match { + case Cons(head, tail) => Cons(head, append(tail, l2)) + case Nil() => l2 + } + + def associative_append_lemma[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = { + append(append(l1, l2), l3) == append(l1, append(l2, l3)) + } + + def associative_append_lemma_induct[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = { + l1 match { + case Nil() => associative_append_lemma(l1, l2, l3) + case Cons(head, tail) => associative_append_lemma(l1, l2, l3) because associative_append_lemma_induct(tail, l2, l3) + } + }.holds + + def flatMap[T,U](list: List[T], f: T => List[U]): List[U] = list match { + case Cons(head, tail) => append(f(head), flatMap(tail, f)) + case Nil() => Nil() + } + + def associative_lemma[T,U,V](list: List[T], f: T => List[U], g: U => List[V]): Boolean = { + flatMap(flatMap(list, f), g) == flatMap(list, (x: T) => flatMap(f(x), g)) + } + + def associative_lemma_induct[T,U,V](list: List[T], flist: List[U], glist: List[V], f: T => List[U], g: U => List[V]): Boolean = { + associative_lemma(list, f, g) because { + append(glist, flatMap(append(flist, flatMap(list, f)), g)) == append(append(glist, flatMap(flist, g)), flatMap(list, (x: T) => flatMap(f(x), g))) because + (glist match { + case Cons(ghead, gtail) => + associative_lemma_induct(list, flist, gtail, f, g) + case Nil() => flist match { + case Cons(fhead, ftail) => + associative_lemma_induct(list, ftail, g(fhead), f, g) + case Nil() => list match { + case Cons(head, tail) => associative_lemma_induct(tail, f(head), Nil(), f, g) + case Nil() => true + } + } + }) + } + }.holds + +} diff --git a/_static/valid/FoldAssociative.html b/_static/valid/FoldAssociative.html new file mode 100644 index 0000000000..81f7fba43f --- /dev/null +++ b/_static/valid/FoldAssociative.html @@ -0,0 +1,113 @@ + + + +valid/FoldAssociative.scala + + +

          FoldAssociative.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless._
+import stainless.lang._
+import stainless.proof._
+
+object FoldAssociative {
+
+  sealed abstract class List
+  case class Cons(head: Int, tail: List) extends List
+  case class Nil() extends List
+
+  sealed abstract class Option
+  case class Some(x: Int) extends Option
+  case class None() extends Option
+
+  def foldRight[A](list: List, state: A, f: (Int, A) => A): A = list match {
+    case Cons(head, tail) =>
+      val tailState = foldRight(tail, state, f)
+      f(head, tailState)
+    case Nil() => state
+  }
+
+  def take(list: List, count: Int): List = {
+    require(count >= 0)
+    list match {
+      case Cons(head, tail) if count > 0 => Cons(head, take(tail, count - 1))
+      case _ => Nil()
+    }
+  }
+
+  def drop(list: List, count: Int): List = {
+    require(count >= 0)
+    list match {
+      case Cons(head, tail) if count > 0 => drop(tail, count - 1)
+      case _ => list
+    }
+  }
+
+  def append(l1: List, l2: List): List = {
+    l1 match {
+      case Cons(head, tail) => Cons(head, append(tail, l2))
+      case Nil() => l2
+    }
+  }
+
+  def lemma_split(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    foldRight(list, 0, f) == foldRight(l1, foldRight(l2, 0, f), f)
+  }
+
+  def lemma_split_induct(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    lemma_split(list, x) because (list match {
+      case Cons(head, tail) if x > 0 =>
+        lemma_split_induct(tail, x - 1)
+      case _ => true
+    })
+  }.holds
+
+  def lemma_reassociative(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+
+    foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f)
+  }
+
+  def lemma_reassociative_induct(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    lemma_reassociative(list, x) because (list match {
+      case Cons(head, tail) if x > 0 =>
+        lemma_reassociative_induct(tail, x - 1)
+      case _ => true
+    })
+  }.holds
+
+  def lemma_reassociative_presplit(l1: List, l2: List): Boolean = {
+    val f = (x: Int, s: Int) => x + s
+    val list = append(l1, l2)
+    foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f)
+  }
+
+  def lemma_reassociative_presplit_induct(l1: List, l2: List): Boolean = {
+    val f = (x: Int, s: Int) => x + s
+    val list = append(l1, l2)
+    lemma_reassociative_presplit(l1, l2) because (l1 match {
+      case Cons(head, tail) =>
+        lemma_reassociative_presplit_induct(tail, l2)
+      case Nil() => true
+    })
+  }.holds
+
+}
+
          +

          back

          diff --git a/_static/valid/FoldAssociative.scala b/_static/valid/FoldAssociative.scala new file mode 100644 index 0000000000..4c80b4ad98 --- /dev/null +++ b/_static/valid/FoldAssociative.scala @@ -0,0 +1,104 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless._ +import stainless.lang._ +import stainless.proof._ + +object FoldAssociative { + + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class Option + case class Some(x: Int) extends Option + case class None() extends Option + + def foldRight[A](list: List, state: A, f: (Int, A) => A): A = list match { + case Cons(head, tail) => + val tailState = foldRight(tail, state, f) + f(head, tailState) + case Nil() => state + } + + def take(list: List, count: Int): List = { + require(count >= 0) + list match { + case Cons(head, tail) if count > 0 => Cons(head, take(tail, count - 1)) + case _ => Nil() + } + } + + def drop(list: List, count: Int): List = { + require(count >= 0) + list match { + case Cons(head, tail) if count > 0 => drop(tail, count - 1) + case _ => list + } + } + + def append(l1: List, l2: List): List = { + l1 match { + case Cons(head, tail) => Cons(head, append(tail, l2)) + case Nil() => l2 + } + } + + def lemma_split(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + foldRight(list, 0, f) == foldRight(l1, foldRight(l2, 0, f), f) + } + + def lemma_split_induct(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + lemma_split(list, x) because (list match { + case Cons(head, tail) if x > 0 => + lemma_split_induct(tail, x - 1) + case _ => true + }) + }.holds + + def lemma_reassociative(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + + foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f) + } + + def lemma_reassociative_induct(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + lemma_reassociative(list, x) because (list match { + case Cons(head, tail) if x > 0 => + lemma_reassociative_induct(tail, x - 1) + case _ => true + }) + }.holds + + def lemma_reassociative_presplit(l1: List, l2: List): Boolean = { + val f = (x: Int, s: Int) => x + s + val list = append(l1, l2) + foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f) + } + + def lemma_reassociative_presplit_induct(l1: List, l2: List): Boolean = { + val f = (x: Int, s: Int) => x + s + val list = append(l1, l2) + lemma_reassociative_presplit(l1, l2) because (l1 match { + case Cons(head, tail) => + lemma_reassociative_presplit_induct(tail, l2) + case Nil() => true + }) + }.holds + +} diff --git a/_static/valid/Formulas.html b/_static/valid/Formulas.html new file mode 100644 index 0000000000..236168fdcc --- /dev/null +++ b/_static/valid/Formulas.html @@ -0,0 +1,61 @@ + + + +valid/Formulas.scala + + +

          Formulas.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless._
+
+object Formulas {
+  abstract class Expr
+  case class And(lhs: Expr, rhs: Expr) extends Expr
+  case class Or(lhs: Expr, rhs: Expr) extends Expr
+  case class Implies(lhs: Expr, rhs: Expr) extends Expr
+  case class Not(e : Expr) extends Expr
+  case class BoolLiteral(i: BigInt) extends Expr
+
+  def exists(e: Expr, f: Expr => Boolean): Boolean = {
+    f(e) || (e match {
+      case And(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Or(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Implies(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Not(e) => exists(e, f)
+      case _ => false
+    })
+  }
+
+  def existsImplies(e: Expr): Boolean = {
+    e.isInstanceOf[Implies] || (e match {
+      case And(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Or(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Implies(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Not(e) => existsImplies(e)
+      case _ => false
+    })
+  }
+
+  abstract class Value
+  case class BoolValue(b: Boolean) extends Value
+  case class IntValue(i: BigInt) extends Value
+  case object Error extends Value
+
+  def desugar(e: Expr): Expr = {
+    e match {
+      case And(lhs, rhs) => And(desugar(lhs), desugar(rhs))
+      case Or(lhs, rhs) => Or(desugar(lhs), desugar(rhs))
+      case Implies(lhs, rhs) =>
+        Or(Not(desugar(lhs)), desugar(rhs))
+      case Not(e) => Not(desugar(e))
+      case e => e
+    }
+  } ensuring { out =>
+    !existsImplies(out) &&
+    !exists(out, f => f.isInstanceOf[Implies])
+  }
+}
+
          +

          back

          diff --git a/_static/valid/Formulas.scala b/_static/valid/Formulas.scala new file mode 100644 index 0000000000..a5a350d827 --- /dev/null +++ b/_static/valid/Formulas.scala @@ -0,0 +1,52 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless._ + +object Formulas { + abstract class Expr + case class And(lhs: Expr, rhs: Expr) extends Expr + case class Or(lhs: Expr, rhs: Expr) extends Expr + case class Implies(lhs: Expr, rhs: Expr) extends Expr + case class Not(e : Expr) extends Expr + case class BoolLiteral(i: BigInt) extends Expr + + def exists(e: Expr, f: Expr => Boolean): Boolean = { + f(e) || (e match { + case And(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Or(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Implies(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Not(e) => exists(e, f) + case _ => false + }) + } + + def existsImplies(e: Expr): Boolean = { + e.isInstanceOf[Implies] || (e match { + case And(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Or(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Implies(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Not(e) => existsImplies(e) + case _ => false + }) + } + + abstract class Value + case class BoolValue(b: Boolean) extends Value + case class IntValue(i: BigInt) extends Value + case object Error extends Value + + def desugar(e: Expr): Expr = { + e match { + case And(lhs, rhs) => And(desugar(lhs), desugar(rhs)) + case Or(lhs, rhs) => Or(desugar(lhs), desugar(rhs)) + case Implies(lhs, rhs) => + Or(Not(desugar(lhs)), desugar(rhs)) + case Not(e) => Not(desugar(e)) + case e => e + } + } ensuring { out => + !existsImplies(out) && + !exists(out, f => f.isInstanceOf[Implies]) + } +} diff --git a/_static/valid/FunctionCaching.html b/_static/valid/FunctionCaching.html new file mode 100644 index 0000000000..e6bfc480c3 --- /dev/null +++ b/_static/valid/FunctionCaching.html @@ -0,0 +1,49 @@ + + + +valid/FunctionCaching.scala + + +

          FunctionCaching.scala [raw]


          +
          import stainless.lang._
+import stainless.collection._
+
+object FunctionCaching {
+
+  case class FunCache(var cached: Map[BigInt, BigInt])
+
+  def fun(x: BigInt)(implicit funCache: FunCache): BigInt = {
+    funCache.cached.get(x) match {
+      case None() => 
+        val res = 2*x + 42
+        funCache.cached = funCache.cached.updated(x, res)
+        res
+      case Some(cached) =>
+        cached
+    }
+  } ensuring(res => old(funCache).cached.get(x) match {
+    case None() => true
+    case Some(v) => v == res
+  })
+
+  def funProperlyCached(x: BigInt, trash: List[BigInt]): Boolean = {
+    implicit val cache = FunCache(Map())
+    val res1 = fun(x)
+    multipleCalls(trash, x)
+    val res2 = fun(x)
+    res1 == res2
+  } holds
+
+  def multipleCalls(args: List[BigInt], x: BigInt)(implicit funCache: FunCache): Unit = {
+    require(funCache.cached.get(x).forall(_ == 2*x + 42))
+    args match {
+      case Nil() => ()
+      case y::ys => 
+        fun(y)
+        multipleCalls(ys, x)
+    }
+  } ensuring(_ => funCache.cached.get(x).forall(_ == 2*x + 42))
+
+}
+
          +

          back

          diff --git a/_static/valid/FunctionCaching.scala b/_static/valid/FunctionCaching.scala new file mode 100644 index 0000000000..5e0984b3aa --- /dev/null +++ b/_static/valid/FunctionCaching.scala @@ -0,0 +1,40 @@ +import stainless.lang._ +import stainless.collection._ + +object FunctionCaching { + + case class FunCache(var cached: Map[BigInt, BigInt]) + + def fun(x: BigInt)(implicit funCache: FunCache): BigInt = { + funCache.cached.get(x) match { + case None() => + val res = 2*x + 42 + funCache.cached = funCache.cached.updated(x, res) + res + case Some(cached) => + cached + } + } ensuring(res => old(funCache).cached.get(x) match { + case None() => true + case Some(v) => v == res + }) + + def funProperlyCached(x: BigInt, trash: List[BigInt]): Boolean = { + implicit val cache = FunCache(Map()) + val res1 = fun(x) + multipleCalls(trash, x) + val res2 = fun(x) + res1 == res2 + } holds + + def multipleCalls(args: List[BigInt], x: BigInt)(implicit funCache: FunCache): Unit = { + require(funCache.cached.get(x).forall(_ == 2*x + 42)) + args match { + case Nil() => () + case y::ys => + fun(y) + multipleCalls(ys, x) + } + } ensuring(_ => funCache.cached.get(x).forall(_ == 2*x + 42)) + +} diff --git a/_static/valid/GuessNumber.html b/_static/valid/GuessNumber.html new file mode 100644 index 0000000000..4ace4ee467 --- /dev/null +++ b/_static/valid/GuessNumber.html @@ -0,0 +1,51 @@ + + + +valid/GuessNumber.scala + + +

          GuessNumber.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object GuessNumber {
+
+  case class State(var seed: BigInt)
+
+  def between(a: Int, x: Int, b: Int): Boolean = a <= x && x <= b
+
+  def random(min: Int, max: Int)(implicit state: State): Int = {
+    require(min <= max)
+    state.seed += 1
+    assert(between(min, min, max))
+    choose((x: Int) => between(min, x, max))
+  }
+  
+  def main()(implicit state: State): Unit = {
+    val choice = random(0, 10)
+
+    var guess = random(0, 10)
+    var top = 10
+    var bot = 0
+
+    (while(bot < top) {
+      if(isGreater(guess, choice)) {
+        top = guess-1
+        guess = random(bot, top)
+      } else if(isSmaller(guess, choice)) {
+        bot = guess+1
+        guess = random(bot, top)
+      }
+    }) invariant(guess >= bot && guess <= top && bot >= 0 && top <= 10 && bot <= top && choice >= bot && choice <= top &&
+                 true)
+    val answer = bot
+    assert(answer == choice)
+  }
+
+  def isGreater(guess: Int, choice: Int): Boolean = guess > choice
+  def isSmaller(guess: Int, choice: Int): Boolean = guess < choice
+
+}
+
          +

          back

          diff --git a/_static/valid/GuessNumber.scala b/_static/valid/GuessNumber.scala new file mode 100644 index 0000000000..c0ceca6696 --- /dev/null +++ b/_static/valid/GuessNumber.scala @@ -0,0 +1,42 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object GuessNumber { + + case class State(var seed: BigInt) + + def between(a: Int, x: Int, b: Int): Boolean = a <= x && x <= b + + def random(min: Int, max: Int)(implicit state: State): Int = { + require(min <= max) + state.seed += 1 + assert(between(min, min, max)) + choose((x: Int) => between(min, x, max)) + } + + def main()(implicit state: State): Unit = { + val choice = random(0, 10) + + var guess = random(0, 10) + var top = 10 + var bot = 0 + + (while(bot < top) { + if(isGreater(guess, choice)) { + top = guess-1 + guess = random(bot, top) + } else if(isSmaller(guess, choice)) { + bot = guess+1 + guess = random(bot, top) + } + }) invariant(guess >= bot && guess <= top && bot >= 0 && top <= 10 && bot <= top && choice >= bot && choice <= top && + true) + val answer = bot + assert(answer == choice) + } + + def isGreater(guess: Int, choice: Int): Boolean = guess > choice + def isSmaller(guess: Int, choice: Int): Boolean = guess < choice + +} diff --git a/_static/valid/Heaps.html b/_static/valid/Heaps.html new file mode 100644 index 0000000000..6e21ff6d9c --- /dev/null +++ b/_static/valid/Heaps.html @@ -0,0 +1,156 @@ + + + +valid/Heaps.scala + + +

          Heaps.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Heaps {
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Data type definitions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  case class Node(rank : BigInt, elem : Int, nodes : Heap)
+  
+  sealed abstract class Heap
+  private case class  Nodes(head : Node, tail : Heap) extends Heap
+  private case object Empty extends Heap
+  
+  sealed abstract class OptInt
+  case class Some(value : Int) extends OptInt
+  case object None extends OptInt
+  
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Abstraction functions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  def heapContent(h : Heap) : Set[Int] = h match {
+    case Empty => Set.empty[Int]
+    case Nodes(n, ns) => nodeContent(n) ++ heapContent(ns)
+  }
+  
+  def nodeContent(n : Node) : Set[Int] = n match {
+    case Node(_, e, h) => Set(e) ++ heapContent(h)
+  }
+  
+  /*~~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Helper/local functions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~~*/
+  private def reverse(h : Heap) : Heap = reverse0(h, Empty)
+  private def reverse0(h : Heap, acc : Heap) : Heap = (h match {
+    case Empty => acc
+    case Nodes(n, ns) => reverse0(ns, Nodes(n, acc))
+  }) ensuring(res => heapContent(res) == heapContent(h) ++ heapContent(acc))
+  
+  private def link(t1 : Node, t2 : Node) = (t1, t2) match {
+    case (Node(r, e1, ns1), Node(_, e2, ns2)) =>
+      if(e1 <= e2) {
+        Node(r + 1, e1, Nodes(t2, ns1))
+      } else {
+        Node(r + 1, e2, Nodes(t1, ns2))
+      }
+  }
+  
+  private def insertNode(t : Node, h : Heap) : Heap = (h match {
+    case Empty => Nodes(t, Empty)
+    case Nodes(t2, h2) =>
+      if(t.rank < t2.rank) {
+        Nodes(t, h)
+      } else {
+        insertNode(link(t, t2), h2)
+      }
+  }) ensuring(res => heapContent(res) == nodeContent(t) ++ heapContent(h))
+  
+  private def getMin(h : Heap) : (Node, Heap) = {
+    require(h != Empty)
+    h match {
+      case Nodes(t, Empty) => (t, Empty)
+      case Nodes(t, ts) =>
+        val (t0, ts0) = getMin(ts)
+        if(t.elem < t0.elem) {
+          (t, ts)
+        } else {
+          (t0, Nodes(t, ts0))
+        }
+    }
+  } ensuring(_ match {
+    case (n,h2) => nodeContent(n) ++ heapContent(h2) == heapContent(h)
+  })
+  
+  /*~~~~~~~~~~~~~~~~*/
+  /* Heap interface */
+  /*~~~~~~~~~~~~~~~~*/
+  def empty() : Heap = {
+    Empty
+  } ensuring(res => heapContent(res) == Set.empty[Int])
+  
+  def isEmpty(h : Heap) : Boolean = {
+    (h == Empty)
+  } ensuring(res => res == (heapContent(h) == Set.empty[Int]))
+  
+  def insert(e : Int, h : Heap) : Heap = {
+    insertNode(Node(0, e, Empty), h)
+  } ensuring(res => heapContent(res) == heapContent(h) ++ Set(e))
+  
+  def merge(h1 : Heap, h2 : Heap) : Heap = ((h1,h2) match {
+    case (_, Empty) => h1
+    case (Empty, _) => h2
+    case (Nodes(t1, ts1), Nodes(t2, ts2)) =>
+      if(t1.rank < t2.rank) {
+        Nodes(t1, merge(ts1, h2))
+      } else if(t2.rank < t1.rank) {
+        Nodes(t2, merge(h1, ts2))
+      } else {
+        insertNode(link(t1, t2), merge(ts1, ts2))
+      }
+  }) ensuring(res => heapContent(res) == heapContent(h1) ++ heapContent(h2))
+  
+  def findMin(h : Heap) : OptInt = (h match {
+    case Empty => None
+    case Nodes(Node(_, e, _), ns) =>
+      findMin(ns) match {
+        case None => Some(e)
+        case Some(e2) => Some(if(e < e2) e else e2)
+      }
+  }) ensuring(_ match {
+    case None => isEmpty(h)
+    case Some(v) => heapContent(h).contains(v)
+  })
+  
+  def deleteMin(h : Heap) : Heap = (h match {
+    case Empty => Empty
+    case ts : Nodes =>
+      val (Node(_, e, ns1), ns2) = getMin(ts)
+      merge(reverse(ns1), ns2)
+  }) ensuring(res => heapContent(res).subsetOf(heapContent(h)))
+  
+  def sanity0() : Boolean = {
+    val h0 : Heap = Empty
+    val h1 = insert(42, h0)
+    val h2 = insert(72, h1)
+    val h3 = insert(0, h2)
+    findMin(h0) == None &&
+    findMin(h1) == Some(42) &&
+    findMin(h2) == Some(42) &&
+    findMin(h3) == Some(0)
+  }.holds
+  
+  def sanity1() : Boolean = {
+    val h0 = insert(42, Empty)
+    val h1 = insert(0, Empty)
+    val h2 = merge(h0, h1)
+    findMin(h2) == Some(0)
+  }.holds
+  
+  def sanity3() : Boolean = {
+    val h0 = insert(42, insert(0, insert(12, Empty)))
+    val h1 = deleteMin(h0)
+    findMin(h1) == Some(12)
+  }.holds
+}
+
+
          +

          back

          diff --git a/_static/valid/Heaps.scala b/_static/valid/Heaps.scala new file mode 100644 index 0000000000..b16418adb3 --- /dev/null +++ b/_static/valid/Heaps.scala @@ -0,0 +1,147 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Heaps { + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Data type definitions */ + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + case class Node(rank : BigInt, elem : Int, nodes : Heap) + + sealed abstract class Heap + private case class Nodes(head : Node, tail : Heap) extends Heap + private case object Empty extends Heap + + sealed abstract class OptInt + case class Some(value : Int) extends OptInt + case object None extends OptInt + + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Abstraction functions */ + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + def heapContent(h : Heap) : Set[Int] = h match { + case Empty => Set.empty[Int] + case Nodes(n, ns) => nodeContent(n) ++ heapContent(ns) + } + + def nodeContent(n : Node) : Set[Int] = n match { + case Node(_, e, h) => Set(e) ++ heapContent(h) + } + + /*~~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Helper/local functions */ + /*~~~~~~~~~~~~~~~~~~~~~~~~*/ + private def reverse(h : Heap) : Heap = reverse0(h, Empty) + private def reverse0(h : Heap, acc : Heap) : Heap = (h match { + case Empty => acc + case Nodes(n, ns) => reverse0(ns, Nodes(n, acc)) + }) ensuring(res => heapContent(res) == heapContent(h) ++ heapContent(acc)) + + private def link(t1 : Node, t2 : Node) = (t1, t2) match { + case (Node(r, e1, ns1), Node(_, e2, ns2)) => + if(e1 <= e2) { + Node(r + 1, e1, Nodes(t2, ns1)) + } else { + Node(r + 1, e2, Nodes(t1, ns2)) + } + } + + private def insertNode(t : Node, h : Heap) : Heap = (h match { + case Empty => Nodes(t, Empty) + case Nodes(t2, h2) => + if(t.rank < t2.rank) { + Nodes(t, h) + } else { + insertNode(link(t, t2), h2) + } + }) ensuring(res => heapContent(res) == nodeContent(t) ++ heapContent(h)) + + private def getMin(h : Heap) : (Node, Heap) = { + require(h != Empty) + h match { + case Nodes(t, Empty) => (t, Empty) + case Nodes(t, ts) => + val (t0, ts0) = getMin(ts) + if(t.elem < t0.elem) { + (t, ts) + } else { + (t0, Nodes(t, ts0)) + } + } + } ensuring(_ match { + case (n,h2) => nodeContent(n) ++ heapContent(h2) == heapContent(h) + }) + + /*~~~~~~~~~~~~~~~~*/ + /* Heap interface */ + /*~~~~~~~~~~~~~~~~*/ + def empty() : Heap = { + Empty + } ensuring(res => heapContent(res) == Set.empty[Int]) + + def isEmpty(h : Heap) : Boolean = { + (h == Empty) + } ensuring(res => res == (heapContent(h) == Set.empty[Int])) + + def insert(e : Int, h : Heap) : Heap = { + insertNode(Node(0, e, Empty), h) + } ensuring(res => heapContent(res) == heapContent(h) ++ Set(e)) + + def merge(h1 : Heap, h2 : Heap) : Heap = ((h1,h2) match { + case (_, Empty) => h1 + case (Empty, _) => h2 + case (Nodes(t1, ts1), Nodes(t2, ts2)) => + if(t1.rank < t2.rank) { + Nodes(t1, merge(ts1, h2)) + } else if(t2.rank < t1.rank) { + Nodes(t2, merge(h1, ts2)) + } else { + insertNode(link(t1, t2), merge(ts1, ts2)) + } + }) ensuring(res => heapContent(res) == heapContent(h1) ++ heapContent(h2)) + + def findMin(h : Heap) : OptInt = (h match { + case Empty => None + case Nodes(Node(_, e, _), ns) => + findMin(ns) match { + case None => Some(e) + case Some(e2) => Some(if(e < e2) e else e2) + } + }) ensuring(_ match { + case None => isEmpty(h) + case Some(v) => heapContent(h).contains(v) + }) + + def deleteMin(h : Heap) : Heap = (h match { + case Empty => Empty + case ts : Nodes => + val (Node(_, e, ns1), ns2) = getMin(ts) + merge(reverse(ns1), ns2) + }) ensuring(res => heapContent(res).subsetOf(heapContent(h))) + + def sanity0() : Boolean = { + val h0 : Heap = Empty + val h1 = insert(42, h0) + val h2 = insert(72, h1) + val h3 = insert(0, h2) + findMin(h0) == None && + findMin(h1) == Some(42) && + findMin(h2) == Some(42) && + findMin(h3) == Some(0) + }.holds + + def sanity1() : Boolean = { + val h0 = insert(42, Empty) + val h1 = insert(0, Empty) + val h2 = merge(h0, h1) + findMin(h2) == Some(0) + }.holds + + def sanity3() : Boolean = { + val h0 = insert(42, insert(0, insert(12, Empty))) + val h1 = deleteMin(h0) + findMin(h1) == Some(12) + }.holds +} + diff --git a/_static/valid/InsertionSort.html b/_static/valid/InsertionSort.html new file mode 100644 index 0000000000..79cc64a131 --- /dev/null +++ b/_static/valid/InsertionSort.html @@ -0,0 +1,78 @@ + + + +valid/InsertionSort.scala + + +

          InsertionSort.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object InsertionSort {
+  sealed abstract class List
+  case class Cons(head:Int,tail:List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptInt
+  case class Some(value: Int) extends OptInt
+  case class None() extends OptInt
+
+  def size(l : List) : BigInt = (l match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def contents(l: List): Set[Int] = l match {
+    case Nil() => Set.empty
+    case Cons(x,xs) => contents(xs) ++ Set(x)
+  }
+
+  def min(l : List) : OptInt = l match {
+    case Nil() => None()
+    case Cons(x, xs) => min(xs) match {
+      case None() => Some(x)
+      case Some(x2) => if(x < x2) Some(x) else Some(x2)
+    }
+  }
+
+  def isSorted(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(x, Nil()) => true
+    case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys))
+  }
+
+  /* Inserting element 'e' into a sorted list 'l' produces a sorted list with
+   * the expected content and size */
+  def sortedIns(e: Int, l: List): List = {
+    require(isSorted(l))
+    l match {
+      case Nil() => Cons(e,Nil())
+      case Cons(x,xs) => if (x <= e) Cons(x,sortedIns(e, xs)) else Cons(e, l)
+    }
+  } ensuring(res => contents(res) == contents(l) ++ Set(e)
+                    && isSorted(res)
+                    && size(res) == size(l) + 1
+            )
+
+  /* Insertion sort yields a sorted list of same size and content as the input
+   * list */
+  def sort(l: List): List = (l match {
+    case Nil() => Nil()
+    case Cons(x,xs) => sortedIns(x, sort(xs))
+  }) ensuring(res => contents(res) == contents(l)
+                     && isSorted(res)
+                     && size(res) == size(l)
+             )
+
+  @ignore
+  def main(args: Array[String]): Unit = {
+    val ls: List = Cons(5, Cons(2, Cons(4, Cons(5, Cons(1, Cons(8,Nil()))))))
+
+    println(ls)
+    println(sort(ls))
+  }
+}
+
          +

          back

          diff --git a/_static/valid/InsertionSort.scala b/_static/valid/InsertionSort.scala new file mode 100644 index 0000000000..0acab72588 --- /dev/null +++ b/_static/valid/InsertionSort.scala @@ -0,0 +1,69 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object InsertionSort { + sealed abstract class List + case class Cons(head:Int,tail:List) extends List + case class Nil() extends List + + sealed abstract class OptInt + case class Some(value: Int) extends OptInt + case class None() extends OptInt + + def size(l : List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def contents(l: List): Set[Int] = l match { + case Nil() => Set.empty + case Cons(x,xs) => contents(xs) ++ Set(x) + } + + def min(l : List) : OptInt = l match { + case Nil() => None() + case Cons(x, xs) => min(xs) match { + case None() => Some(x) + case Some(x2) => if(x < x2) Some(x) else Some(x2) + } + } + + def isSorted(l: List): Boolean = l match { + case Nil() => true + case Cons(x, Nil()) => true + case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys)) + } + + /* Inserting element 'e' into a sorted list 'l' produces a sorted list with + * the expected content and size */ + def sortedIns(e: Int, l: List): List = { + require(isSorted(l)) + l match { + case Nil() => Cons(e,Nil()) + case Cons(x,xs) => if (x <= e) Cons(x,sortedIns(e, xs)) else Cons(e, l) + } + } ensuring(res => contents(res) == contents(l) ++ Set(e) + && isSorted(res) + && size(res) == size(l) + 1 + ) + + /* Insertion sort yields a sorted list of same size and content as the input + * list */ + def sort(l: List): List = (l match { + case Nil() => Nil() + case Cons(x,xs) => sortedIns(x, sort(xs)) + }) ensuring(res => contents(res) == contents(l) + && isSorted(res) + && size(res) == size(l) + ) + + @ignore + def main(args: Array[String]): Unit = { + val ls: List = Cons(5, Cons(2, Cons(4, Cons(5, Cons(1, Cons(8,Nil())))))) + + println(ls) + println(sort(ls)) + } +} diff --git a/_static/valid/ListOperations.html b/_static/valid/ListOperations.html new file mode 100644 index 0000000000..b643302da6 --- /dev/null +++ b/_static/valid/ListOperations.html @@ -0,0 +1,113 @@ + + + +valid/ListOperations.scala + + +

          ListOperations.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ListOperations {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    sealed abstract class IntPairList
+    case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList
+    case class IPNil() extends IntPairList
+
+    sealed abstract class IntPair
+    case class IP(fst: Int, snd: Int) extends IntPair
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def iplSize(l: IntPairList) : BigInt = (l match {
+      case IPNil() => BigInt(0)
+      case IPCons(_, xs) => 1 + iplSize(xs)
+    }) ensuring(_ >= 0)
+
+    def zip(l1: List, l2: List) : IntPairList = {
+      // try to comment this and see how pattern-matching becomes
+      // non-exhaustive and post-condition fails
+      require(size(l1) == size(l2))
+
+      l1 match {
+        case Nil() => IPNil()
+        case Cons(x, xs) => l2 match {
+          case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys))
+        }
+      }
+    } ensuring(iplSize(_) == size(l1))
+
+    def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0)
+    def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = {
+     require(acc >= 0)
+     l match {
+       case Nil() => acc
+       case Cons(_, xs) => sizeTailRecAcc(xs, acc+1)
+     }
+    } ensuring(res => res == size(l) + acc)
+
+    def sizesAreEquiv(l: List) : Boolean = {
+      size(l) == sizeTailRec(l)
+    }.holds
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def sizeAndContent(l: List) : Boolean = {
+      size(l) == BigInt(0) || content(l) != Set.empty[Int]
+    }.holds
+    
+    def drunk(l : List) : List = (l match {
+      case Nil() => Nil()
+      case Cons(x,l1) => Cons(x,Cons(x,drunk(l1)))
+    }) ensuring (size(_) == 2 * size(l))
+
+    def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l))
+    def reverse0(l1: List, l2: List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => reverse0(xs, Cons(x, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    def append(l1 : List, l2 : List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x,xs) => Cons(x, append(xs, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds
+
+    @induct
+    def appendAssoc(xs : List, ys : List, zs : List) : Boolean =
+      (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds
+
+    @induct
+    def sizeAppend(l1 : List, l2 : List) : Boolean =
+      (size(append(l1, l2)) == size(l1) + size(l2)).holds
+
+    @induct
+    def concat(l1: List, l2: List) : List = 
+      concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def concat0(l1: List, l2: List, l3: List) : List = (l1 match {
+      case Nil() => l2 match {
+        case Nil() => reverse(l3)
+        case Cons(y, ys) => {
+          concat0(Nil(), ys, Cons(y, l3))
+        }
+      }
+      case Cons(x, xs) => concat0(xs, l2, Cons(x, l3))
+    }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3))
+}
+
          +

          back

          diff --git a/_static/valid/ListOperations.scala b/_static/valid/ListOperations.scala new file mode 100644 index 0000000000..3a4383cc9b --- /dev/null +++ b/_static/valid/ListOperations.scala @@ -0,0 +1,104 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ListOperations { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class IntPairList + case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList + case class IPNil() extends IntPairList + + sealed abstract class IntPair + case class IP(fst: Int, snd: Int) extends IntPair + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def iplSize(l: IntPairList) : BigInt = (l match { + case IPNil() => BigInt(0) + case IPCons(_, xs) => 1 + iplSize(xs) + }) ensuring(_ >= 0) + + def zip(l1: List, l2: List) : IntPairList = { + // try to comment this and see how pattern-matching becomes + // non-exhaustive and post-condition fails + require(size(l1) == size(l2)) + + l1 match { + case Nil() => IPNil() + case Cons(x, xs) => l2 match { + case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys)) + } + } + } ensuring(iplSize(_) == size(l1)) + + def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0) + def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = { + require(acc >= 0) + l match { + case Nil() => acc + case Cons(_, xs) => sizeTailRecAcc(xs, acc+1) + } + } ensuring(res => res == size(l) + acc) + + def sizesAreEquiv(l: List) : Boolean = { + size(l) == sizeTailRec(l) + }.holds + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def sizeAndContent(l: List) : Boolean = { + size(l) == BigInt(0) || content(l) != Set.empty[Int] + }.holds + + def drunk(l : List) : List = (l match { + case Nil() => Nil() + case Cons(x,l1) => Cons(x,Cons(x,drunk(l1))) + }) ensuring (size(_) == 2 * size(l)) + + def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l)) + def reverse0(l1: List, l2: List) : List = (l1 match { + case Nil() => l2 + case Cons(x, xs) => reverse0(xs, Cons(x, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + def append(l1 : List, l2 : List) : List = (l1 match { + case Nil() => l2 + case Cons(x,xs) => Cons(x, append(xs, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds + + @induct + def appendAssoc(xs : List, ys : List, zs : List) : Boolean = + (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds + + @induct + def sizeAppend(l1 : List, l2 : List) : Boolean = + (size(append(l1, l2)) == size(l1) + size(l2)).holds + + @induct + def concat(l1: List, l2: List) : List = + concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def concat0(l1: List, l2: List, l3: List) : List = (l1 match { + case Nil() => l2 match { + case Nil() => reverse(l3) + case Cons(y, ys) => { + concat0(Nil(), ys, Cons(y, l3)) + } + } + case Cons(x, xs) => concat0(xs, l2, Cons(x, l3)) + }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3)) +} diff --git a/_static/valid/Mean.html b/_static/valid/Mean.html new file mode 100644 index 0000000000..7aeb602c83 --- /dev/null +++ b/_static/valid/Mean.html @@ -0,0 +1,22 @@ + + + +valid/Mean.scala + + +

          Mean.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Mean {
+
+  def mean(x: Int, y: Int): Int = {
+    require(x <= y && x >= 0 && y >= 0)
+    x + (y - x)/2
+  } ensuring(m => m >= x && m <= y)
+
+}
+
          +

          back

          diff --git a/_static/valid/Mean.scala b/_static/valid/Mean.scala new file mode 100644 index 0000000000..ec1108f4e5 --- /dev/null +++ b/_static/valid/Mean.scala @@ -0,0 +1,13 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Mean { + + def mean(x: Int, y: Int): Int = { + require(x <= y && x >= 0 && y >= 0) + x + (y - x)/2 + } ensuring(m => m >= x && m <= y) + +} diff --git a/_static/valid/MergeSort.html b/_static/valid/MergeSort.html new file mode 100644 index 0000000000..2e3c792880 --- /dev/null +++ b/_static/valid/MergeSort.html @@ -0,0 +1,136 @@ + + + +valid/MergeSort.scala + + +

          MergeSort.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object MergeSort {
+  // Data types
+  sealed abstract class List
+  case class Cons(head : Int, tail : List) extends List
+  case class Nil() extends List
+
+  sealed abstract class LList
+  case class LCons(head : List, tail : LList) extends LList
+  case class LNil() extends LList
+
+  def content(list : List) : Set[Int] = list match {
+    case Nil() => Set.empty[Int]
+    case Cons(x, xs) => Set(x) ++ content(xs)
+  }
+
+  def lContent(llist : LList) : Set[Int] = llist match {
+    case LNil() => Set.empty[Int]
+    case LCons(x, xs) => content(x) ++ lContent(xs)
+  }
+
+  def size(list : List) : BigInt = (list match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def isSorted(list : List) : Boolean = list match {
+    case Nil() => true
+    case Cons(_, Nil()) => true
+    case Cons(x1, Cons(x2, _)) if(x1 > x2) => false
+    case Cons(_, xs) => isSorted(xs)
+  }
+
+  def lIsSorted(llist : LList) : Boolean = llist match {
+    case LNil() => true
+    case LCons(x, xs) => isSorted(x) && lIsSorted(xs)
+  }
+
+  def abs(i : BigInt) : BigInt = {
+    if(i < 0) -i else i
+  } ensuring(_ >= 0)
+
+  def mergeSpec(list1 : List, list2 : List, res : List) : Boolean = {
+    isSorted(res) && content(res) == content(list1) ++ content(list2)
+  }
+
+  def mergeFast(list1 : List, list2 : List) : List = {
+    require(isSorted(list1) && isSorted(list2))
+
+    (list1, list2) match {
+      case (_, Nil()) => list1
+      case (Nil(), _) => list2
+      case (Cons(x, xs), Cons(y, ys)) =>
+        if(x <= y) {
+          Cons(x, mergeFast(xs, list2)) 
+        } else {
+          Cons(y, mergeFast(list1, ys))
+        }
+    }
+  } ensuring(res => mergeSpec(list1, list2, res))
+
+  def splitSpec(list : List, res : (List,List)) : Boolean = {
+    val s1 = size(res._1)
+    val s2 = size(res._2)
+    abs(s1 - s2) <= 1 && s1 + s2 == size(list) &&
+    content(res._1) ++ content(res._2) == content(list) 
+  }
+
+  def split(list : List) : (List,List) = (list match {
+    case Nil() => (Nil(), Nil())
+    case Cons(x, Nil()) => (Cons(x, Nil()), Nil())
+    case Cons(x1, Cons(x2, xs)) =>
+      val (s1,s2) = split(xs)
+      (Cons(x1, s1), Cons(x2, s2))
+  }) ensuring(res => splitSpec(list, res))
+
+  def sortSpec(in : List, out : List) : Boolean = {
+    content(out) == content(in) && isSorted(out)
+  }
+
+  // Not really quicksort, neither mergesort.
+  // Note: the `s` argument is just a witness for termination (always decreases),
+  // and not needed for functionality. Any decent optimizer will remove it ;-)
+  def weirdSort(s: BigInt, in : List) : List = {
+    require(s == size(in))
+    in match {
+      case Nil() => Nil()
+      case Cons(x, Nil()) => Cons(x, Nil())
+      case _ =>
+        val (s1,s2) = split(in)
+        mergeFast(weirdSort(size(s1), s1), weirdSort(size(s2), s2))
+    }
+  } ensuring(res => sortSpec(in, res))
+
+  def toLList(list : List) : LList = (list match {
+    case Nil() => LNil()
+    case Cons(x, xs) => LCons(Cons(x, Nil()), toLList(xs))
+  }) ensuring(res => lContent(res) == content(list) && lIsSorted(res))
+
+  def mergeMap(llist : LList) : LList = {
+    require(lIsSorted(llist))
+
+    llist match {
+      case LNil() => LNil()
+      case o @ LCons(x, LNil()) => o
+      case LCons(x, LCons(y, ys)) => LCons(mergeFast(x, y), mergeMap(ys))
+    }
+  } ensuring(res => lContent(res) == lContent(llist) && lIsSorted(res))
+
+  def mergeReduce(llist : LList) : List = {
+    require(lIsSorted(llist))
+
+    llist match {
+      case LNil() => Nil()
+      case LCons(x, LNil()) => x
+      case _ => mergeReduce(mergeMap(llist))
+    }
+  } ensuring(res => content(res) == lContent(llist) && isSorted(res))
+
+  def mergeSort(in : List) : List = {
+    mergeReduce(toLList(in))
+  } ensuring(res => sortSpec(in, res))
+}
+
          +

          back

          diff --git a/_static/valid/MergeSort.scala b/_static/valid/MergeSort.scala new file mode 100644 index 0000000000..b4cd205689 --- /dev/null +++ b/_static/valid/MergeSort.scala @@ -0,0 +1,127 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object MergeSort { + // Data types + sealed abstract class List + case class Cons(head : Int, tail : List) extends List + case class Nil() extends List + + sealed abstract class LList + case class LCons(head : List, tail : LList) extends LList + case class LNil() extends LList + + def content(list : List) : Set[Int] = list match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def lContent(llist : LList) : Set[Int] = llist match { + case LNil() => Set.empty[Int] + case LCons(x, xs) => content(x) ++ lContent(xs) + } + + def size(list : List) : BigInt = (list match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def isSorted(list : List) : Boolean = list match { + case Nil() => true + case Cons(_, Nil()) => true + case Cons(x1, Cons(x2, _)) if(x1 > x2) => false + case Cons(_, xs) => isSorted(xs) + } + + def lIsSorted(llist : LList) : Boolean = llist match { + case LNil() => true + case LCons(x, xs) => isSorted(x) && lIsSorted(xs) + } + + def abs(i : BigInt) : BigInt = { + if(i < 0) -i else i + } ensuring(_ >= 0) + + def mergeSpec(list1 : List, list2 : List, res : List) : Boolean = { + isSorted(res) && content(res) == content(list1) ++ content(list2) + } + + def mergeFast(list1 : List, list2 : List) : List = { + require(isSorted(list1) && isSorted(list2)) + + (list1, list2) match { + case (_, Nil()) => list1 + case (Nil(), _) => list2 + case (Cons(x, xs), Cons(y, ys)) => + if(x <= y) { + Cons(x, mergeFast(xs, list2)) + } else { + Cons(y, mergeFast(list1, ys)) + } + } + } ensuring(res => mergeSpec(list1, list2, res)) + + def splitSpec(list : List, res : (List,List)) : Boolean = { + val s1 = size(res._1) + val s2 = size(res._2) + abs(s1 - s2) <= 1 && s1 + s2 == size(list) && + content(res._1) ++ content(res._2) == content(list) + } + + def split(list : List) : (List,List) = (list match { + case Nil() => (Nil(), Nil()) + case Cons(x, Nil()) => (Cons(x, Nil()), Nil()) + case Cons(x1, Cons(x2, xs)) => + val (s1,s2) = split(xs) + (Cons(x1, s1), Cons(x2, s2)) + }) ensuring(res => splitSpec(list, res)) + + def sortSpec(in : List, out : List) : Boolean = { + content(out) == content(in) && isSorted(out) + } + + // Not really quicksort, neither mergesort. + // Note: the `s` argument is just a witness for termination (always decreases), + // and not needed for functionality. Any decent optimizer will remove it ;-) + def weirdSort(s: BigInt, in : List) : List = { + require(s == size(in)) + in match { + case Nil() => Nil() + case Cons(x, Nil()) => Cons(x, Nil()) + case _ => + val (s1,s2) = split(in) + mergeFast(weirdSort(size(s1), s1), weirdSort(size(s2), s2)) + } + } ensuring(res => sortSpec(in, res)) + + def toLList(list : List) : LList = (list match { + case Nil() => LNil() + case Cons(x, xs) => LCons(Cons(x, Nil()), toLList(xs)) + }) ensuring(res => lContent(res) == content(list) && lIsSorted(res)) + + def mergeMap(llist : LList) : LList = { + require(lIsSorted(llist)) + + llist match { + case LNil() => LNil() + case o @ LCons(x, LNil()) => o + case LCons(x, LCons(y, ys)) => LCons(mergeFast(x, y), mergeMap(ys)) + } + } ensuring(res => lContent(res) == lContent(llist) && lIsSorted(res)) + + def mergeReduce(llist : LList) : List = { + require(lIsSorted(llist)) + + llist match { + case LNil() => Nil() + case LCons(x, LNil()) => x + case _ => mergeReduce(mergeMap(llist)) + } + } ensuring(res => content(res) == lContent(llist) && isSorted(res)) + + def mergeSort(in : List) : List = { + mergeReduce(toLList(in)) + } ensuring(res => sortSpec(in, res)) +} diff --git a/_static/valid/PropositionalLogic.html b/_static/valid/PropositionalLogic.html new file mode 100644 index 0000000000..265a202cc6 --- /dev/null +++ b/_static/valid/PropositionalLogic.html @@ -0,0 +1,85 @@ + + + +valid/PropositionalLogic.scala + + +

          PropositionalLogic.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object PropositionalLogic { 
+
+  sealed abstract class Formula
+  case class And(lhs: Formula, rhs: Formula) extends Formula
+  case class Or(lhs: Formula, rhs: Formula) extends Formula
+  case class Implies(lhs: Formula, rhs: Formula) extends Formula
+  case class Not(f: Formula) extends Formula
+  case class Literal(id: Int) extends Formula
+
+  def simplify(f: Formula): Formula = (f match {
+    case And(lhs, rhs) => And(simplify(lhs), simplify(rhs))
+    case Or(lhs, rhs) => Or(simplify(lhs), simplify(rhs))
+    case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs))
+    case Not(f) => Not(simplify(f))
+    case Literal(_) => f
+  }) ensuring(isSimplified(_))
+
+  def isSimplified(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Implies(_,_) => false
+    case Not(f) => isSimplified(f)
+    case Literal(_) => true
+  }
+
+  def nnf(formula: Formula): Formula = (formula match {
+    case And(lhs, rhs) => And(nnf(lhs), nnf(rhs))
+    case Or(lhs, rhs) => Or(nnf(lhs), nnf(rhs))
+    case Implies(lhs, rhs) => Implies(nnf(lhs), nnf(rhs))
+    case Not(And(lhs, rhs)) => Or(nnf(Not(lhs)), nnf(Not(rhs)))
+    case Not(Or(lhs, rhs)) => And(nnf(Not(lhs)), nnf(Not(rhs)))
+    case Not(Implies(lhs, rhs)) => And(nnf(lhs), nnf(Not(rhs)))
+    case Not(Not(f)) => nnf(f)
+    case Not(Literal(_)) => formula
+    case Literal(_) => formula
+  }) ensuring(isNNF(_))
+
+  def isNNF(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Not(Literal(_)) => true
+    case Not(_) => false
+    case Literal(_) => true
+  }
+
+  def vars(f: Formula): Set[Int] = {
+    require(isNNF(f))
+    f match {
+      case And(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Or(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Implies(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Not(Literal(i)) => Set[Int](i)
+      case Literal(i) => Set[Int](i)
+    }
+  }
+
+  def fv(f : Formula) = { vars(nnf(f)) }
+
+  @induct
+  def nnfIsStable(f: Formula) : Boolean = {
+    require(isNNF(f))
+    nnf(f) == f
+  }.holds
+  
+  @induct
+  def simplifyIsStable(f: Formula) : Boolean = {
+    require(isSimplified(f))
+    simplify(f) == f
+  }.holds
+}
+
          +

          back

          diff --git a/_static/valid/PropositionalLogic.scala b/_static/valid/PropositionalLogic.scala new file mode 100644 index 0000000000..d1a4a4a460 --- /dev/null +++ b/_static/valid/PropositionalLogic.scala @@ -0,0 +1,76 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object PropositionalLogic { + + sealed abstract class Formula + case class And(lhs: Formula, rhs: Formula) extends Formula + case class Or(lhs: Formula, rhs: Formula) extends Formula + case class Implies(lhs: Formula, rhs: Formula) extends Formula + case class Not(f: Formula) extends Formula + case class Literal(id: Int) extends Formula + + def simplify(f: Formula): Formula = (f match { + case And(lhs, rhs) => And(simplify(lhs), simplify(rhs)) + case Or(lhs, rhs) => Or(simplify(lhs), simplify(rhs)) + case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs)) + case Not(f) => Not(simplify(f)) + case Literal(_) => f + }) ensuring(isSimplified(_)) + + def isSimplified(f: Formula): Boolean = f match { + case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Implies(_,_) => false + case Not(f) => isSimplified(f) + case Literal(_) => true + } + + def nnf(formula: Formula): Formula = (formula match { + case And(lhs, rhs) => And(nnf(lhs), nnf(rhs)) + case Or(lhs, rhs) => Or(nnf(lhs), nnf(rhs)) + case Implies(lhs, rhs) => Implies(nnf(lhs), nnf(rhs)) + case Not(And(lhs, rhs)) => Or(nnf(Not(lhs)), nnf(Not(rhs))) + case Not(Or(lhs, rhs)) => And(nnf(Not(lhs)), nnf(Not(rhs))) + case Not(Implies(lhs, rhs)) => And(nnf(lhs), nnf(Not(rhs))) + case Not(Not(f)) => nnf(f) + case Not(Literal(_)) => formula + case Literal(_) => formula + }) ensuring(isNNF(_)) + + def isNNF(f: Formula): Boolean = f match { + case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Not(Literal(_)) => true + case Not(_) => false + case Literal(_) => true + } + + def vars(f: Formula): Set[Int] = { + require(isNNF(f)) + f match { + case And(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Or(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Implies(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Not(Literal(i)) => Set[Int](i) + case Literal(i) => Set[Int](i) + } + } + + def fv(f : Formula) = { vars(nnf(f)) } + + @induct + def nnfIsStable(f: Formula) : Boolean = { + require(isNNF(f)) + nnf(f) == f + }.holds + + @induct + def simplifyIsStable(f: Formula) : Boolean = { + require(isSimplified(f)) + simplify(f) == f + }.holds +} diff --git a/_static/valid/QuickSort.html b/_static/valid/QuickSort.html new file mode 100644 index 0000000000..5fb43443e8 --- /dev/null +++ b/_static/valid/QuickSort.html @@ -0,0 +1,60 @@ + + + +valid/QuickSort.scala + + +

          QuickSort.scala [raw]


          +
          import stainless.proof._
+import stainless.lang._
+import stainless.collection._
+
+object QuickSort {
+
+  def isSorted(list: List[BigInt]): Boolean = {
+    list match {
+      case Cons(x, xs @ Cons(y, _)) => x <= y && isSorted(xs)
+      case _ => true
+    }
+  }
+
+  def appendSorted(l1: List[BigInt], l2: List[BigInt]): List[BigInt] = {
+    require(isSorted(l1) && isSorted(l2) && (l1.isEmpty || l2.isEmpty || l1.last <= l2.head))
+    l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => Cons(x, appendSorted(xs, l2))
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == l1.content ++ l2.content
+  }
+
+  def quickSort(list: List[BigInt]): List[BigInt] = {
+    decreases(list.size, BigInt(0))
+    list match {
+      case Nil() => Nil[BigInt]()
+      case Cons(x, xs) => par(x, Nil(), Nil(), xs)
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == list.content
+  }
+
+  def par(x: BigInt, l: List[BigInt], r: List[BigInt], ls: List[BigInt]): List[BigInt] = {
+    require(
+      forall((a: BigInt) => l.contains(a) ==> a <= x) &&
+      forall((a: BigInt) => r.contains(a) ==> x < a)
+    )
+    decreases(l.size + r.size + ls.size, ls.size + 1)
+
+    ls match {
+      case Nil() => appendSorted(quickSort(l), Cons(x, quickSort(r)))
+      case Cons(x2, xs2) => if (x2 <= x) par(x, Cons(x2, l), r, xs2) else par(x, l, Cons(x2, r), xs2)
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == l.content ++ r.content ++ ls.content + x
+  }
+}
+
          +

          back

          diff --git a/_static/valid/QuickSort.scala b/_static/valid/QuickSort.scala new file mode 100644 index 0000000000..9cd49876e8 --- /dev/null +++ b/_static/valid/QuickSort.scala @@ -0,0 +1,51 @@ +import stainless.proof._ +import stainless.lang._ +import stainless.collection._ + +object QuickSort { + + def isSorted(list: List[BigInt]): Boolean = { + list match { + case Cons(x, xs @ Cons(y, _)) => x <= y && isSorted(xs) + case _ => true + } + } + + def appendSorted(l1: List[BigInt], l2: List[BigInt]): List[BigInt] = { + require(isSorted(l1) && isSorted(l2) && (l1.isEmpty || l2.isEmpty || l1.last <= l2.head)) + l1 match { + case Nil() => l2 + case Cons(x, xs) => Cons(x, appendSorted(xs, l2)) + } + } ensuring { res => + isSorted(res) && + res.content == l1.content ++ l2.content + } + + def quickSort(list: List[BigInt]): List[BigInt] = { + decreases(list.size, BigInt(0)) + list match { + case Nil() => Nil[BigInt]() + case Cons(x, xs) => par(x, Nil(), Nil(), xs) + } + } ensuring { res => + isSorted(res) && + res.content == list.content + } + + def par(x: BigInt, l: List[BigInt], r: List[BigInt], ls: List[BigInt]): List[BigInt] = { + require( + forall((a: BigInt) => l.contains(a) ==> a <= x) && + forall((a: BigInt) => r.contains(a) ==> x < a) + ) + decreases(l.size + r.size + ls.size, ls.size + 1) + + ls match { + case Nil() => appendSorted(quickSort(l), Cons(x, quickSort(r))) + case Cons(x2, xs2) => if (x2 <= x) par(x, Cons(x2, l), r, xs2) else par(x, l, Cons(x2, r), xs2) + } + } ensuring { res => + isSorted(res) && + res.content == l.content ++ r.content ++ ls.content + x + } +} diff --git a/_static/valid/RedBlackTree.html b/_static/valid/RedBlackTree.html new file mode 100644 index 0000000000..308c69ad22 --- /dev/null +++ b/_static/valid/RedBlackTree.html @@ -0,0 +1,108 @@ + + + +valid/RedBlackTree.scala + + +

          RedBlackTree.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object RedBlackTree { 
+  sealed abstract class Color
+  case class Red() extends Color
+  case class Black() extends Color
+ 
+  sealed abstract class Tree
+  case class Empty() extends Tree
+  case class Node(color: Color, left: Tree, value: BigInt, right: Tree) extends Tree
+
+  sealed abstract class OptionInt
+  case class Some(v : BigInt) extends OptionInt
+  case class None() extends OptionInt
+
+  def content(t: Tree) : Set[BigInt] = t match {
+    case Empty() => Set.empty
+    case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def size(t: Tree) : BigInt = (t match {
+    case Empty() => BigInt(0)
+    case Node(_, l, v, r) => size(l) + 1 + size(r)
+  }) ensuring(_ >= 0)
+
+  /* We consider leaves to be black by definition */
+  def isBlack(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(),_,_,_) => true
+    case _ => false
+  }
+
+  def redNodesHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+    case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def redDescHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def blackBalanced(t : Tree) : Boolean = t match {
+    case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r)
+    case Empty() => true
+  }
+
+  def blackHeight(t : Tree) : BigInt = t match {
+    case Empty() => 1
+    case Node(Black(), l, _, _) => blackHeight(l) + 1
+    case Node(Red(), l, _, _) => blackHeight(l)
+  }
+
+  // <<insert element x into the tree t>>
+  def ins(x: BigInt, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    t match {
+      case Empty() => Node(Red(),Empty(),x,Empty())
+      case Node(c,a,y,b) =>
+        if      (x < y)  balance(c, ins(x, a), y, b)
+        else if (x == y) Node(c,a,y,b)
+        else             balance(c,a,y,ins(x, b))
+    }
+  } ensuring (res => content(res) == content(t) ++ Set(x) 
+                   && size(t) <= size(res) && size(res) <= size(t) + 1
+                   && redDescHaveBlackChildren(res)
+                   && blackBalanced(res))
+
+  def makeBlack(n: Tree): Tree = {
+    require(redDescHaveBlackChildren(n) && blackBalanced(n))
+    n match {
+      case Node(Red(),l,v,r) => Node(Black(),l,v,r)
+      case _ => n
+    }
+  } ensuring(res => redNodesHaveBlackChildren(res) && blackBalanced(res))
+
+  def add(x: BigInt, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    makeBlack(ins(x, t))
+  } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res) && blackBalanced(res))
+
+  def balance(c: Color, a: Tree, x: BigInt, b: Tree): Tree = {
+    Node(c,a,x,b) match {
+      case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(c,a,xV,b) => Node(c,a,xV,b)
+    }
+  } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res))
+}
+
          +

          back

          diff --git a/_static/valid/RedBlackTree.scala b/_static/valid/RedBlackTree.scala new file mode 100644 index 0000000000..94577704d6 --- /dev/null +++ b/_static/valid/RedBlackTree.scala @@ -0,0 +1,99 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object RedBlackTree { + sealed abstract class Color + case class Red() extends Color + case class Black() extends Color + + sealed abstract class Tree + case class Empty() extends Tree + case class Node(color: Color, left: Tree, value: BigInt, right: Tree) extends Tree + + sealed abstract class OptionInt + case class Some(v : BigInt) extends OptionInt + case class None() extends OptionInt + + def content(t: Tree) : Set[BigInt] = t match { + case Empty() => Set.empty + case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def size(t: Tree) : BigInt = (t match { + case Empty() => BigInt(0) + case Node(_, l, v, r) => size(l) + 1 + size(r) + }) ensuring(_ >= 0) + + /* We consider leaves to be black by definition */ + def isBlack(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(),_,_,_) => true + case _ => false + } + + def redNodesHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def redDescHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def blackBalanced(t : Tree) : Boolean = t match { + case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r) + case Empty() => true + } + + def blackHeight(t : Tree) : BigInt = t match { + case Empty() => 1 + case Node(Black(), l, _, _) => blackHeight(l) + 1 + case Node(Red(), l, _, _) => blackHeight(l) + } + + // <> + def ins(x: BigInt, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + t match { + case Empty() => Node(Red(),Empty(),x,Empty()) + case Node(c,a,y,b) => + if (x < y) balance(c, ins(x, a), y, b) + else if (x == y) Node(c,a,y,b) + else balance(c,a,y,ins(x, b)) + } + } ensuring (res => content(res) == content(t) ++ Set(x) + && size(t) <= size(res) && size(res) <= size(t) + 1 + && redDescHaveBlackChildren(res) + && blackBalanced(res)) + + def makeBlack(n: Tree): Tree = { + require(redDescHaveBlackChildren(n) && blackBalanced(n)) + n match { + case Node(Red(),l,v,r) => Node(Black(),l,v,r) + case _ => n + } + } ensuring(res => redNodesHaveBlackChildren(res) && blackBalanced(res)) + + def add(x: BigInt, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + makeBlack(ins(x, t)) + } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res) && blackBalanced(res)) + + def balance(c: Color, a: Tree, x: BigInt, b: Tree): Tree = { + Node(c,a,x,b) match { + case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(c,a,xV,b) => Node(c,a,xV,b) + } + } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res)) +} diff --git a/_static/valid/StableSorter.html b/_static/valid/StableSorter.html new file mode 100644 index 0000000000..bc8e1d335a --- /dev/null +++ b/_static/valid/StableSorter.html @@ -0,0 +1,124 @@ + + + +valid/StableSorter.scala + + +

          StableSorter.scala [raw]


          +
          import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+import stainless.proof._
+
+object StableSorter {
+
+  // Inserting into a stable list adds to the content and increases the length
+  def insert[T](t: T, l: List[T], key: T => BigInt): List[T] = {
+    l match {
+      case Nil() => t :: l
+      case Cons(hd, tl) if key(t) <= key(hd) => t :: l
+      case Cons(hd, tl) => hd :: insert(t, tl, key)
+    }
+  } ensuring { res => res.content == Set(t) ++ l.content && res.length == 1 + l.length }
+
+  // Sorting a list preserves the content and preserves the length
+  def sort[T](l: List[T], key: T => BigInt): List[T] = { l match {
+    case Nil() => l
+    case Cons(hd, tl) => {
+      val tlSorted = sort(tl, key)
+      insert(hd, tlSorted, key)
+    }
+  }} ensuring { res => res.content == l.content && res.length == l.length }
+
+  // To define stability, we first annotate the input list with the initial indices...
+  def annotateList[T](l: List[T], n: BigInt): List[(T, BigInt)] = {
+    l match {
+      case Nil() => Nil[(T, BigInt)]()
+      case Cons(hd, tl) => {
+        val tlAnn = annotateList(tl, n + 1)
+        hint((hd, n) :: tlAnn, trivProp2(annotateList(tl, n + 1), n))
+      }
+    }
+  } ensuring { res => l2AtLeast(res, n) }
+
+  // ... where:
+  def l2AtLeast[T](l: List[(T, BigInt)], n: BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => n <= hdIndex && l2AtLeast(tl, n)
+  }
+
+  // ... and the following trivial property holds:
+  @induct
+  def trivProp2[T](l: List[(T, BigInt)], n: BigInt): Boolean = {
+    require(l2AtLeast(l, n + 1))
+    l2AtLeast(l, n)
+  }.holds
+
+  // Next, we identify an appropriate value which is increasing in a stably sorted list:
+  def isStableSorted[T](l: List[(T, BigInt)], key: T => BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => isStableSortedAndAtLeast(tl, key, key(hd), hdIndex)
+  }
+
+  def isStableSortedAndAtLeast[T](
+    l: List[(T, BigInt)],
+    key: T => BigInt,
+    x: BigInt,
+    minIndex: BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => {
+      val hdSmall = x < key(hd) || x == key(hd) && minIndex <= hdIndex
+      val tlSorted = isStableSortedAndAtLeast(tl, key, key(hd), hdIndex)
+      hdSmall && tlSorted
+    }
+  }
+
+  // The insertion sort we initially defined is stable:
+  def sortStableProp[T](l: List[T], key: T => BigInt): Boolean = {
+    require(sortStablePropInt(l, 0, key))
+    val lAnn = annotateList(l, 0)
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val lAnnSorted = sort(lAnn, keyAnn)
+    isStableSorted(lAnnSorted, key)
+  }.holds
+
+  // To prove that insertion sort is stable, we first show that insertion is stable:
+  @induct
+  def insertStableProp[T](t: T, n: BigInt, l: List[(T, BigInt)], key: T => BigInt): Boolean = {
+    require(isStableSorted(l, key) && l2AtLeast(l, n))
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val res = insert((t, n), l, keyAnn)
+    isStableSorted(res, key) && l2AtLeast(res, n)
+  }.holds
+
+  // ... and complete the proof of stability.
+  def sortStablePropInt[T](l: List[T], n: BigInt, key: T => BigInt): Boolean = {
+    val lAnn = annotateList(l, n)
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val lAnnSorted = sort(lAnn, keyAnn)
+    lAnn match {
+      case Nil() => isStableSorted(lAnnSorted, key)
+      case Cons((hd, hdIndex), tlAnn) => {
+        val Cons(_, xs) = l
+        val tlAnnSorted = sort(tlAnn, keyAnn)
+        sortStablePropInt(xs, n + 1, key) &&
+        n == hdIndex &&
+        l2AtLeast(tlAnn, n) &&
+        l2AtLeast(tlAnnSorted, n + 1) &&
+        trivProp2(tlAnnSorted, n) &&
+        l2AtLeast(tlAnnSorted, n) &&
+        insertStableProp(hd, hdIndex, tlAnnSorted, key) &&
+        isStableSorted(lAnnSorted, key) &&
+        l2AtLeast(lAnnSorted, n)
+      }
+    }
+  }.holds
+
+  def hint[T](t: T, lemma: Boolean): T = {
+    require(lemma)
+    t
+  }
+
+}
+
          +

          back

          diff --git a/_static/valid/StableSorter.scala b/_static/valid/StableSorter.scala new file mode 100644 index 0000000000..699b853cf3 --- /dev/null +++ b/_static/valid/StableSorter.scala @@ -0,0 +1,115 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ +import stainless.proof._ + +object StableSorter { + + // Inserting into a stable list adds to the content and increases the length + def insert[T](t: T, l: List[T], key: T => BigInt): List[T] = { + l match { + case Nil() => t :: l + case Cons(hd, tl) if key(t) <= key(hd) => t :: l + case Cons(hd, tl) => hd :: insert(t, tl, key) + } + } ensuring { res => res.content == Set(t) ++ l.content && res.length == 1 + l.length } + + // Sorting a list preserves the content and preserves the length + def sort[T](l: List[T], key: T => BigInt): List[T] = { l match { + case Nil() => l + case Cons(hd, tl) => { + val tlSorted = sort(tl, key) + insert(hd, tlSorted, key) + } + }} ensuring { res => res.content == l.content && res.length == l.length } + + // To define stability, we first annotate the input list with the initial indices... + def annotateList[T](l: List[T], n: BigInt): List[(T, BigInt)] = { + l match { + case Nil() => Nil[(T, BigInt)]() + case Cons(hd, tl) => { + val tlAnn = annotateList(tl, n + 1) + hint((hd, n) :: tlAnn, trivProp2(annotateList(tl, n + 1), n)) + } + } + } ensuring { res => l2AtLeast(res, n) } + + // ... where: + def l2AtLeast[T](l: List[(T, BigInt)], n: BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => n <= hdIndex && l2AtLeast(tl, n) + } + + // ... and the following trivial property holds: + @induct + def trivProp2[T](l: List[(T, BigInt)], n: BigInt): Boolean = { + require(l2AtLeast(l, n + 1)) + l2AtLeast(l, n) + }.holds + + // Next, we identify an appropriate value which is increasing in a stably sorted list: + def isStableSorted[T](l: List[(T, BigInt)], key: T => BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => isStableSortedAndAtLeast(tl, key, key(hd), hdIndex) + } + + def isStableSortedAndAtLeast[T]( + l: List[(T, BigInt)], + key: T => BigInt, + x: BigInt, + minIndex: BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => { + val hdSmall = x < key(hd) || x == key(hd) && minIndex <= hdIndex + val tlSorted = isStableSortedAndAtLeast(tl, key, key(hd), hdIndex) + hdSmall && tlSorted + } + } + + // The insertion sort we initially defined is stable: + def sortStableProp[T](l: List[T], key: T => BigInt): Boolean = { + require(sortStablePropInt(l, 0, key)) + val lAnn = annotateList(l, 0) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val lAnnSorted = sort(lAnn, keyAnn) + isStableSorted(lAnnSorted, key) + }.holds + + // To prove that insertion sort is stable, we first show that insertion is stable: + @induct + def insertStableProp[T](t: T, n: BigInt, l: List[(T, BigInt)], key: T => BigInt): Boolean = { + require(isStableSorted(l, key) && l2AtLeast(l, n)) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val res = insert((t, n), l, keyAnn) + isStableSorted(res, key) && l2AtLeast(res, n) + }.holds + + // ... and complete the proof of stability. + def sortStablePropInt[T](l: List[T], n: BigInt, key: T => BigInt): Boolean = { + val lAnn = annotateList(l, n) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val lAnnSorted = sort(lAnn, keyAnn) + lAnn match { + case Nil() => isStableSorted(lAnnSorted, key) + case Cons((hd, hdIndex), tlAnn) => { + val Cons(_, xs) = l + val tlAnnSorted = sort(tlAnn, keyAnn) + sortStablePropInt(xs, n + 1, key) && + n == hdIndex && + l2AtLeast(tlAnn, n) && + l2AtLeast(tlAnnSorted, n + 1) && + trivProp2(tlAnnSorted, n) && + l2AtLeast(tlAnnSorted, n) && + insertStableProp(hd, hdIndex, tlAnnSorted, key) && + isStableSorted(lAnnSorted, key) && + l2AtLeast(lAnnSorted, n) + } + } + }.holds + + def hint[T](t: T, lemma: Boolean): T = { + require(lemma) + t + } + +} diff --git a/casestudies.html b/casestudies.html new file mode 100644 index 0000000000..0eccdae54c --- /dev/null +++ b/casestudies.html @@ -0,0 +1,430 @@ + + + + + + + Case Studies — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Case Studies

          +
          +

          Case Study #1: Proving invariants of actor systems

          +
          +

          Actor system model

          +

          Our model is loosely based on the modern definition of object-based actor systems, +and attempts to provide an idiomatic Scala API in the style of the Akka actor library.

          +

          In this framework, each actor is addressed by a reference, through which other actors +can asynchronously send messages. Each actor has an associated behavior, which holds +the state of the actor, if any, and determines

          +
            +

          1. the operations which will be performed upon receiving a message

            2. +

          2. what is the next behavior to associate with its reference

            3. +
          +

          A behavior can thus be seen as a data type holding some immutable values representing +the state, and a method which takes in a message, performs some computation which might +involve sending messages to other actors, and finally returns a new behavior.

          +

          State at the actor level is thus effectively handled in a functional way, by returning +a new behavior which holds the updated state. An actor system maintains a collection +of one-way channels (inboxes) between any two actors in the system.

          +

          An inbox is an ordered list of messages awaiting delivery, the head of the list being +the next message to deliver.

          +

          The system drives the execution by non-deterministically +picking a non-empty inbox, taking the first message of the list, and invoking the message +handler of the behavior associated with the destination reference.

          +

          It then collects the messages to send, and appends them to the appropriate inboxes, +and update the destination actor’s behavior with the behavior returned by the message handler.

          +
          +
          +

          Actor system implementation

          +
          +

          Imports

          +
          import stainless.lang._
+import stainless.collection._
+import stainless.annotation._
+
          +
          +
          +
          +

          Message

          +

          In our framework, messages are modeled as constructors of the abstract class Msg.

          +
          abstract class Msg
+
          +
          +
          +
          +

          Actor reference

          +

          Each actor is associated with a persistent reference, modeled as instances of the case class ActorRef. +Each reference has a name, and an underlying Akka akka.actor.ActorRef, marked as extern and pure (see Section Working With Existing Code for more information about extern fields).

          +
          case class ActorRef(
+  name: String,
+  @extern @pure
+  underlying: akka.actor.ActorRef
+) {
+
+  @inline
+  def !(msg: Msg)(implicit ctx: ActorContext): Unit = {
+    ctx.send(this, msg)
+  }
+}
+
          +
          +
          +
          +

          Actor Context

          +

          When a message is delivered to an actor, the latter is provided with a context, which holds a reference to itself, and a mutable list of messages to send. We mark this list as ghost to avoid having to persist in memory the list of all messages sent through the context.

          +
          case class ActorContext(
+  self: ActorRef,
+  @ghost
+  var toSend: List[(ActorRef, Msg)] = Nil()
+) {
+
+  def send(to: ActorRef, msg: Msg): Unit = {
+    toSend = (to, msg) :: toSend
+
+    sendUnderlying(to, msg)
+  }
+
+  @extern @pure
+  private def sendUnderlying(to: ActorRef, msg: Msg): Unit = {
+    to.underlying ! msg
+  }
+}
+
          +
          +
          +
          +

          Behavior

          +

          A behavior specifies both the current state of an actor, and how this one should process the next incoming message. In our framework, these are modeled as a subclass of the abstract class Behavior, which defines a single abstract method processMsg, to be overridden for each defined behavior.

          +

          Using the provided ActorContext, the implementation of the processMsg method can both access its own reference, and send messages. It is also required to return a new Behavior for handling subsequent messages.

          +
          sealed abstract class Behavior {
+  def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior
+}
+
          +
          +
          +
          +

          Actor System

          +

          The state of the actor system at a given point in time is modeled as a case class, holding the behavior associated with each actor reference, and the list of in-flight messages between any two actors.

          +

          It provides a step method which, whengiven two ActorRef, will deliver the next message (if any) in the corresponding channel.

          +

          Because the ActorSystem class is only used to model and prove properties about the underlying actor system, we mark the whole class as ghost in order to drop it from the resulting program.

          +
          @ghost
+case class ActorSystem(
+  behaviors: CMap[ActorRef, Behavior],
+  inboxes: CMap[(ActorRef, ActorRef), List[Msg]]
+) {
+
+  def step(from: ActorRef, to: ActorRef): ActorSystem = {
+    inboxes(from -> to) match {
+      case Nil() =>
+        this
+
+      case Cons(msg, msgs) =>
+        val (newBehavior, toSend) = deliverMessage(to, msg)
+
+        val newBehaviors = behaviors.updated(to, newBehavior)
+        val newInboxes = toSend.foldLeft(inboxes.updated(from -> to, msgs)) {
+          case (acc, (dest, m)) => acc.updated(to -> dest, m :: acc(to -> dest))
+        }
+
+        ActorSystem(newBehaviors, newInboxes)
+    }
+  }
+
+  private def deliverMessage(actor: ActorRef, msg: Msg): (Behavior, List[(ActorRef, Msg)]) = {
+    val behavior = behaviors(actor)
+
+    val ctx = ActorContext(actor, Nil())
+    val nextBehavior = behavior.processMsg(msg)(ctx)
+
+    (nextBehavior, ctx.toSend)
+  }
+}
+
          +
          +
          +
          +
          +

          Building a replicated counter

          +
          @extern
+def noSender = akka.actor.ActorRef.noSender
+
+val Primary = ActorRef("primary", noSender)
+val Backup  = ActorRef("backup", noSender)
+
+case object Inc extends Msg
+
+case class Counter(value: BigInt) {
+  require(value >= 0)
+
+  def increment: Counter = Counter(value + 1)
+
+  def <=(that: Counter): Boolean = this.value <= that.value
+}
+
+case class PrimBehav(backup: ActorRef, counter: Counter) extends Behavior {
+  require(backup.name == "backup")
+
+  override
+  def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior = msg match {
+    case Inc =>
+      backup ! Inc
+      PrimBehav(backup, counter.increment)
+
+    case _ => this
+  }
+}
+
+case class BackBehav(counter: Counter) extends Behavior {
+
+  override
+  def processMsg(msg: Msg)(implicit ctx: ActorContext): Behavior = msg match {
+    case Inc =>
+      BackBehav(counter.increment)
+
+    case _ => this
+  }
+}
+
          +
          +
          +

          Proving preservation of an invariant

          +

          After having defined an actor system with our framework, one might want to verify that this system preserves some invariant between each step of its execution. That is to say, given an invariant inv: ActorSystem → Boolean, for any ActorSystem s and any two ActorRef n and m, if inv(s) holds, then inv(s.step(n, m)) should hold as well. In other words:

          +

          \(\forall s: \texttt{ActorSystem}, n, m: \texttt{ActorRef}. \texttt{inv}(s) \implies \texttt{inv}(s.\texttt{step}(n, m))\)

          +

          We note that, because we are essentially doing a proof by induction over execution steps here, one needs also to ensure the invariant holds for some initial system. We show these two properties below:

          +
          @ghost
+def invariant(s: ActorSystem): Boolean = {
+  s.inboxes(Primary -> Primary).isEmpty &&
+  s.inboxes(Backup -> Primary).isEmpty &&
+  s.inboxes(Backup -> Backup).isEmpty &&
+  s.inboxes(Primary -> Backup).forall(_ == Inc) && {
+    (s.behaviors(Primary), s.behaviors(Backup)) match {
+      case (PrimBehav(_, p), BackBehav(b)) =>
+        p.value == b.value + s.inboxes(Primary -> Backup).length
+
+      case _ => false
+    }
+  }
+}
+
+@ghost
+def initialSystem = ActorSystem(
+  behaviors = CMap({
+    case `Primary` => PrimBehav(Counter(0))
+    case `Backup`  => BackBehav(Counter(0))
+  }),
+  inboxes = CMap(_ => List())
+)
+
+@ghost
+def initialInv = invariant(initialSystem).holds
+
+@ghost
+def validRef(ref: ActorRef): Boolean = ref == Primary || ref == Backup
+
+@ghost
+def theorem(s: ActorSystem, from: ActorRef, to: ActorRef): Boolean = {
+  require(invariant(s) && validRef(from) && validRef(to))
+  val newSystem = s.step(from, to)
+  invariant(newSystem)
+}.holds
+
          +
          +
          +
          +
          +

          Running the system with Akka

          +
          @ignore
+class ActorWrapper(initialBehavior: Behavior) extends akka.actor.Actor with akka.actor.ActorLogging {
+
+  private def handler(behavior: Behavior): PartialFunction[Any, Unit] = {
+    case msg: Msg =>
+      val me = ActorRef(context.self.path.name, context.self)
+      val ctx = ActorContext(me, Nil())
+      val newBehavior = behavior.processMsg(msg)(ctx)
+
+      log.info(s"Received: $msg, becoming $newBehavior")
+      context.become(handler(newBehavior), discardOld = true)
+  }
+
+  def receive = handler(initialBehavior)
+}
+
          +
          +
          @ignore
+def main(args: Array[String]): Unit = {
+  val initCounter = Counter(0)
+
+  val system = akka.actor.ActorSystem("Counter")
+
+  val backupRef = ActorRef(
+    "backup",
+    system.actorOf(
+      akka.actor.Props(new ActorWrapper(BackBehav(initCounter))),
+      name = "backup"
+    )
+  )
+
+  val primaryRef = ActorRef(
+    "primary",
+    system.actorOf(
+      akka.actor.Props(new ActorWrapper(PrimBehav(backupRef, initCounter))),
+      name = "primary"
+    )
+  )
+
+  implicit val ctx = ActorContext(primaryRef, Nil())
+
+  import system.dispatcher
+  import scala.concurrent.duration._
+  system.scheduler.schedule(500.millis, 1000.millis) {
+    primaryRef ! Inc
+  }
+}
+
          +
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/coq.html b/coq.html new file mode 100644 index 0000000000..ded14e3445 --- /dev/null +++ b/coq.html @@ -0,0 +1,185 @@ + + + + + + + Translation from Stainless to Coq — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Translation from Stainless to Coq

          +

          Initially based on a project done by Bence Czipó, this translation is an early experimental +stage.

          +

          The –coq option of Stainless replaces the standard verification checker +(which uses Inox) by a translation to Coq. Each function from the *.scala file +is translated to a Coq file, and obligations corresponding to assertions, +preconditions, and postconditions are solved using predefined tactics in Coq.

          +
          +

          Requirements

          +
            +

          • Coq 8.11.2

            • +

          • Coq Equations 1.2.2+8.11

            • +
          +

          These can be installed using opam as explained in the Equations +README.md.

          +
          +
          +

          Usage of the Coq option

          +

          First, clone the Stainless repository. In the slc-lib directory, run +./configure and make.

          +

          Then, assuming the Stainless binary stainless-scalac is in your path, run: +stainless-scalac --coq File.scala on the file of your choice. As an example, +consider the test function from the Arith.scala +file:

          +
          def test(a: BigInt, b: BigInt, c: BigInt): BigInt = {
+  require(a > b && c > BigInt(0))
+  c + a
+} ensuring( _ > c + b )
+
          +
          +

          Running stainless-scalac --coq frontends/benchmarks/coq/Arith.scala +generates the file tmp/test.v which contains the following Coq definition.

          +
          Definition test (a: Z) (b: Z) (c: Z) (contractHyp4: (ifthenelse (Z.gtb a b) bool
+        (fun _ => Z.gtb c (0)%Z )
+        (fun _ => false ) = true)) : {x___1: Z | (Z.gtb x___1 (Z.add c b) = true)} :=
+Z.add c a.
+
+Fail Next Obligation.
+
          +
          +

          The coqc executable in run on the file, and the status is reported by +Stainless. In the translation to Coq, the BigInt type is encoded as Z. +The precondition (require) is encoded as an extra argument contractHyp4, +and the postcondition is encoded as a refinement on the return type of test. +Here, the obligation related to the postcondition is solved automatically thanks +to the obligation tactic defined above in the tmp/test.v file. The statement +Fail Next Obligation. then succeeds because all obligations have been solved +(any command in Coq can be prefixed with Fail, and the resulting command +succeeds when the original command fails).

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/equivalence.html b/equivalence.html new file mode 100644 index 0000000000..c1850ba091 --- /dev/null +++ b/equivalence.html @@ -0,0 +1,211 @@ + + + + + + + Equivalence Checking — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Equivalence Checking

          +

          Stainless can prove equivalence of recursive programs using automated functional induction. Additionaly, it can treat many programs at once, reusing the information obtained throughout the process, to reason about subsequent programs. This paper explains the underlying algorithms.

          +

          To run the equivalence checker, use the --equivchk option of Stainless. The option --comparefuns specifies the names of candidate functions. The option --models specifies the names of reference functions.

          +
          +

          Example run

          +

          Consider the following three functions isSortedA (incorrect), isSortedB and isSortedC (both correct), that implement a check whether a given input list is sorted in a non-decreasing order:

          +
          def isSortedA(l: List[Int]): Boolean = {
+  def leq(cur: Int, next: Int): Boolean = cur < next
+  def iter(l: List[Int]): Boolean =
+    if (l.isEmpty) true
+    else if (l.tail.isEmpty) true
+    else leq(l.head, l.tail.head) && iter(l.tail)
+  if (l.size < 2) true
+  else l.head <= l.tail.head && iter(l.tail)
+}
+
          +
          +
          def isSortedB(l: List[Int]): Boolean = {
+  if (l.isEmpty)
+    true
+  else if (!l.tail.isEmpty && l.head > l.tail.head)
+    false
+  else
+    isSortedB(l.tail)
+}
+
          +
          +
          def isSortedC(l: List[Int]): Boolean = {
+  def chk(l: List[Int], p: Int, a: Boolean): Boolean = {
+    if (l.isEmpty) a
+    else if (l.head < p) false
+    else chk(l.tail, l.head, a)
+  }
+  if (l.isEmpty) true
+  else chk(l, l.head, true)
+}
+
          +
          +

          And the following reference function isSortedR:

          +
          def isSortedR(l: List[Int]): Boolean = {
+  def loop(p: Int, l: List[Int]): Boolean = l match {
+    case Nil() => true
+    case Cons(x, xs) if (p <= x) => loop(x, xs)
+    case _ => false
+  }
+  if (l.isEmpty) true
+  else loop(l.head, l.tail)
+}
+
          +
          +

          The following command invokes the equivalence checking (isSortedA, isSortedB, isSortedC and isSortedR are defined in frontends/benchmarks/equivalence/isSorted/isSorted.scala):

          +

          stainless frontends/benchmarks/equivalence/isSorted/isSorted.scala --equivchk=true --comparefuns=isSortedA,isSortedB,isSortedC --models=isSortedR --timeout=3

          +

          Stainless automatically generates all the equivalence lemmas and reports resulting equivalence clusters. This is done by checking for equivalence of each function from the --comparefuns list against the model functions from the --models list, until the proof of equivalence or a counterexample is found for one of the models.

          +

          The output of equivalence checking is a classification of candidate functions into the following categories:

          +
          +
            +

          • Wrong, if the signature is wrong;

            • +

          • Correct, if there is a reference program provably equivalent to this program;

            • +

          • Incorrect, if there is a counterexample that disproves the equivalence;

            • +

          • Unknown, when there is neither a proof nor a counterexample of equivalence.

            • +
          +
          +

          For our example run, we get the following output:

          +
          [  Info  ] Printing equivalence checking results:
+[  Info  ] List of functions that are equivalent to model IsSorted.isSortedB: IsSorted.isSortedC
+[  Info  ] List of functions that are equivalent to model IsSorted.isSortedR: IsSorted.isSortedB
+[  Info  ] List of erroneous functions: IsSorted.isSortedA
+[  Info  ] List of timed-out functions:
+[  Info  ] List of wrong functions:
+[  Info  ] Printing the final state:
+[  Info  ] Path for the function IsSorted.isSortedB: IsSorted.isSortedR
+[  Info  ] Path for the function IsSorted.isSortedC: IsSorted.isSortedB, IsSorted.isSortedR
+[  Info  ] Counterexample for the function IsSorted.isSortedA:
+[  Info  ]   l -> Cons[Int](-1357890535, Cons[Int](-1089455080, Cons[Int](-1089455080, Nil[Int]())))
+
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/faq.html b/faq.html new file mode 100644 index 0000000000..b8cd915db1 --- /dev/null +++ b/faq.html @@ -0,0 +1,220 @@ + + + + + + + FAQ: (Frequently) Asked Questions — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          FAQ: (Frequently) Asked Questions

          +

          If you have a question, you may also post it at http://stackoverflow.com +(try searching for the leon tag +or the stainless tag) +or contact one of the authors of this documentation.

          +

          Below we collect answers to some questions that came up.

          +
          +

          How does Stainless compare to other verification tools?

          +

          One can compare Stainless to proof assistants such as +Isabelle/HOL, +Coq, +Lean, +HOL4, or +ACL2 in terms of the complexity of some of the program properties it can prove, though it was originally conceived more as a program verifier, such as +Dafny or +Viper. +Stainless can be more automated when finding proofs of programs compared to proof assistants, and can also report counter-examples for invalid properties in many non-trivial cases, see counter-examples for bugs in benchmarks such as +ConcRope.scala, +ListOperations.scala, +Mean.scala, +PropositionalLogic.scala, +AssociativityProperties.scala, +InsertionSort.scala, +more example reports, or check some of our +regression tests. +On the other hand, proof assistants are much better at formalizing mathematics than Stainless, especially when it comes to libraries of formalized mathematics knowledge.

          +
          +
          +

          How does Stainless compare to fuzzing tools?

          +

          Formal software verification finds proofs that programs work under all scenarios of interest. Formal verification tools help developers construct such proofs, automatically searching for proofs using theorem proving and constraint solving (using, e.g. SMT solvers), and static analysis to discover program invariants. When it succeeds, formal verification is guaranteed to identify all software errors, including, for example, security vulnerabilities or cases when the computation produces a wrong numerical or symbolic result. Because it involves building proofs, this approach may require knowledge of proofs by induction and substitution of equals for equals, typically covered in computer science undergraduate university education. The best approach to obtain formally verified software is to perform formal verification while software is developed. If we try to apply formal verification after software is already written, we should be prepared to invest at least the amount of effort needed to rewrite it.

          +

          Testing can establish the presence of errors, but not their absence. Basic forms of testing can be easy to deploy, because running a program on a given input is a minimum requirement for software, but such testing is extremely limited. Suppose that we wish to test whether a program running on a smartphone performs multiplication of two machine numbers correctly. If we could check one test per nanosecond, we would still need many billions of years to enumerate all cases! This also illustrates how minuscule of a region of space around a given test a fuzzer can ever explore, despite an amazing speed at which some these fuzzing tools work. Formal software verification can cover all these cases with a single proof because it uses algebraic properties that are independent of the size of the data that software manipulates.

          +

          To avoid enumeration, advanced testing methods such as symbolic execution embrace constraint solvers originally developed for formal verification. These techniques reduce to formal verification when programs have no loops or recursion; otherwise they end up sampling a small fraction of program executions, so they do not result in a proof. To cover more than just absence of crashes and vulnerabilities, testing also requires insights into the purpose of software, the environment in which the software needs to execute and the expected outputs for given inputs.

          +
          +
          +

          Does Stainless use SMT solvers?

          +

          Stainless uses SMT solvers such as z3, CVC and Princess. The component that encodes formulas with executable higher-order functions into these solvers is Inox. Inox is designed to emit quantifier-free queries for these solvers, which increases its ability to generate counter-examples. The use of SMT solvers allows Stainless to achieve notable automation in reasoning about, for example, equality, case analysis, bitvectors, and algebraic data types.

          +
          +
          +

          What are the conditions required for Stainless to be applied to industry software?

          +

          It is best to deploy formal verification when starting to develop software. In this way, software and its specifications are developed hand in hand, much like one can define a class hierarchy and other types during the process of writing an object-oriented program. It is also possible to focus on one part of an existing software system and rewrite it in Stainless; such efforts have been shown to work in industry for software components in Scala, Java, and C. Software that has well-defined modular structure with clear responsibility of different modules is a good candidate for verification because one can expect that specifications at module boundaries will be non-controversial. In terms of developer skills, good knowledge of discrete mathematics, such as proofs by induction and algebra will make developers more effective at verification.

          +
          +
          +

          Can I use Stainless with Java?

          +

          Scala has excellent interoperability with Java, so external libraries can be used to build application where some parts are verified using Stainless. Stainless uses Scala syntax trees and does not support verification of Java itself. Whereas functional Scala works as a both specification and implementation language, Java does not appear to be a good language for specifications, so much that Java verification tools in the past introduced their own logical notation that developers then must learn in addition to Java.

          +
          +
          +

          Can I use Stainless with Rust?

          +

          Even though we had somewhat successful experiments translating Rust code into Stainless, we believe that, in the long term, it is more productive to use Scala as the starting point and generate low-level code. We are working on making this more practical in the future.

          +
          +
          +

          Proving properties of size

          +

          I have defined a size function on my algebraic data type.

          +
          sealed abstract class List
+case class Cons(head: Int, tail: List) extends List
+case object Nil extends List
+def size(l: List) : Int = (l match {
+  case Nil => 0
+  case Cons(_, t) => 1 + size(t)
+}) ensuring(_ >= 0)
+
          +
          +

          Stainless neither proves nor gives a counterexample. Why?

          +

          Answer: You should consider using BigInt, which +denotes unbounded mathematical integers, instead of Int, +which denotes 32-bit integers. If you replace Int with +BigInt in the result type of size, the function should +verify. Note that algebraic data types can be arbitrarily +large, so, if the input list had the size Int.MaxValue + 1 +(which is 2^32) then the addition 1 + size(t) would wrap +around and produce Int.MinValue (that is, -2^31), so the +ensuring clause would not hold.

          +
          +
          +

          Compiling Stainless programs to bytecode

          +

          If you don’t use special constructs such as choose or unbounded forall, you +should be able to compile Stainless programs to .class using scalac and +execute them directly on the JVM, or integrate them as part as other +Scala-based projects. See Section “Running Code with Stainless dependencies”.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/genc.html b/genc.html new file mode 100644 index 0000000000..7012d46e07 --- /dev/null +++ b/genc.html @@ -0,0 +1,602 @@ + + + + + + + Generating C Code — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Generating C Code

          +

          Stainless can generate from Scala code an equivalent and safe C99 code. Using the verification, repair and +synthesis features of Stainless this conversion can be made safely. Additionally, the produced code can be +compiled with any standard-compliant C99 compiler to target the desired hardware architecture +without extra dependencies. The initial description of GenC, which has evolved since then, can be found in Extending Safe C Support In Leon. +Furthermore, this Master Thesis Report explains how to achieve compliance under the MISRA C guidelines.

          +

          To convert a Scala program, please use the --genc option of Stainless.

          +

          The option --genc-output=file specifies the file name for GenC output (default: stainless.c).

          +
          +

          Note

          +

          Currently the memory model is limited to stack allocation and global state. Hence, no dynamic allocation +is done using malloc function family.

          +
          +
          +

          Requirements

          +

          The following is required from the Scala program fed to GenC:

          +
          +
            +

          • Functions compiled to C, and the types they use, +should be exclusively in the set of features described below, with the +exceptions of the (ghost) code used for verification conditions;

            • +

          • The program should be successfully verified with the --strict-arithmetic (enabled by default) +flag to ensure that arithmetic operations, array accesses, function +preconditions and so on, are safely converted into C code.

            • +
          +
          +

          The generated C code should be compiled with a C99-compliant compiler that +satisfies these extra conditions:

          +
          +
            +

          • CHAR_BITS is defined to be 8;

            • +

          • The int8_t, int16_t, int32_t, int64_t and uint8_t, uint16_t, uint32_t, uint64_t types are available (see Pure Scala for description);

            • +

          • Casting from unsigned to signed integer, and vice-versa, is not well supported at the moment.

            • +
          +
          +
          +
          +

          Export

          +

          Functions and classes can be marked with @cCode.export (import stainless.annotation._), +which affects GenC compilation in several ways. +First, the names of these functions and classes will not get mangled when generating the C code. +Second, the signatures of the functions, and the type definitions corresponding to exported classes, +will go into the header file (by default stainless.h). +Finally, preconditions of exported functions (which are meant to be called from external C code), +are transformed into runtime assertions.

          +
          +
          +

          Supported Features

          +

          The supported subset of Scala includes part of the core languages features, as well as some +imperative features, while ensuring the same expression execution order in both +languages.

          +
          +

          Types

          +

          The following raw types and their corresponding literals are supported:

          + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

          Scala

          C99

          Unit

          void

          Boolean

          bool

          Byte and Int8 (8-bit integer)

          int8_t

          Short and Int16 (16-bit integer)

          int16_t

          Int and Int32 (32-bit integer)

          int32_t

          Long and Int64 (64-bit integer)

          int64_t

          UInt8 (8-bit unsigned integer)

          uint8_t

          UInt16 (16-bit integer)

          uint16_t

          UInt32 (32-bit integer)

          uint32_t

          UInt64 (64-bit integer)

          uint64_t

          +

          Additionally, GenC has partial support for character and string literals made +of ASCII characters only but it has no API to manipulate strings at the moment: +Char is mapped to char and String is mapped to char*.

          +
          +

          Tuples

          +

          Using TupleN[T1, ..., TN] results in the creation of a C structure with the +same fields and matching types for every combination of any supported type +T1, ..., TN. The name of the generated structure will be unique and reflect +the sequence of types.

          +
          +
          +

          Arrays

          +

          Arrays are compiled by GenC into C structs that also store the length of the array. +For Array[Int] we get:

          +
          typedef struct {
+  int32_t* data;
+  int32_t length;
+} array_int32;
+
          +
          +
          +

          Note

          +

          Arrays live on the stack and therefore cannot be returned by functions. This limitation is +extended to other types having an array as field. In some cases, it is acceptable to use the +@cCode.inline annotation from Stainless’s library to workaround this limitation.

          +
          +

          For case classes containing arrays whose length is known at compile time, we avoid +using a struct wrapper for the array, and instead directly inline the array +in the struct of the case class. We trigger this optimized transformation +when the array length is specified in the case class invariant (with require) +as a conjunct. The left-hand-side needs to be a.length where a is the +array, and the right-hand-side needs to be a constant (or evaluate to a constant +at compile time).

          +

          See below for a case class with a fixed length array and its transformation in C:

          +
          val CONSTANT1: UInt16 = 5
+val CONSTANT2: UInt16 = 12
+val CONSTANT3: UInt16 = CONSTANT1 + CONSTANT2
+
+@cCode.export
+case class W(x: Int, a: Array[Int], y: Int) {
+  require(
+    a.length == CONSTANT3.toInt &&
+    0 <= x && x <= 1000 &&
+    0 <= y && y <= 1000
+  )
+}
+
          +
          +
          typedef struct {
+  int32_t x;
+  int32_t a[17];
+  int32_t y;
+} W;
+
          +
          +
          +
          +

          Classes

          +

          The support for classes is restricted to non-recursive ones so that instances +of such data-types live on the stack. The following language features are available:

          +
          +
            +

          • case class with mutable var fields;

            • +

          • generics:

            +
              +

            • similarly to Array[T] or tuples, each combination of type parameters +is mapped to a specific C structure;

              • +
            +
            • +

          • inheritance:

            +
              +

            • when all leaf classes have no fields, the class hierarchy is mapped to a +C enumeration,

              • +

            • otherwise, a tagged-union is used to represent the class hierarchy in C;

              • +
            +
            • +

          • external types:

            +
              +

            • see @cCode.typedef below.

              • +
            +
            • +
          +
          +
          +
          +
          +

          Functions

          +

          Functions with access to the variables in their respective scopes. The +following language features are available:

          +
          +
            +

          • top level, nested or member functions:

            +
              +

            • both val and var are supported for local variable with the limitations imposed by +the imperative phases of Stainless

              • +
            +
            • +

          • generics:

            +
              +

            • each combination of type parameters generates a different, specialised C function;

              • +
            +
            • +

          • overloading:

            +
              +

            • the Scala compiler is responsible for identifying the correct function at each call site;

              • +
            +
            • +

          • higher-order functions:

            +
              +

            • named functions that do not capture their environment can be used as value;

              • +
            +
            • +

          • external functions:

            +
              +

            • see @cCode.function below;

              • +
            +
            • +
          +
          +

          Since strings of characters are currently not (fully) available, in order to generate an executable +program, one has to define a main function without any argument, whose return type can be Int +or Unit:

          +
          @cCode.export
+def main(): Unit = {
+  // main code goes here
+}
+
          +
          +
          +
          +

          Constructs

          +

          The idiomatic if statements such as val b = if (x >= 0) true else false are converted into +a sequence of equivalent statements.

          +

          Imperative while loops are also supported.

          +

          Pattern matching is supported, with the exception of the Unapply +Patterns, as long as it is exempt of side effect.

          +

          Assertions, invariant, pre- and post-conditions are not translated into C99 and are simply ignored.

          +
          +
          +

          Operators

          +

          The following operators are supported:

          + ++++ + + + + + + + + + + + + + + + + + + + + + + +

          Category

          Operators

          Boolean operators

          &&, ||, !, !=, ==

          Comparision operators over integers

          <, <=, ==, !=, >=, >

          Comparision operators over instances of classes

          ==, !=

          Arithmetic operators over integers

          +, - (unary & binary), *, /, %

          Bitwise operators over integers

          &, |, ^, ~, <<, >>>

          +
          +
          +
          +

          Global State

          +

          At the moment, Stainless does not support global mutable variables declared in objects. +It is however possible to simulate global state by using classes marked with @cCode.global, +as shown in the Global.scala +example:

          +
          @cCode.global
+case class GlobalState(
+  val data: Array[Int] = Array.fill(100)(0),
+  var stable: Boolean = true,
+  var x: Int = 5,
+  var y: Int = 7,
+) {
+  require(
+    data.length == 100 && (
+      !stable || (
+        0 <= x && x <= 100 &&
+        0 <= y && y <= 100 &&
+        x + y == 12
+      )
+    )
+  )
+}
+
          +
          +
          +

          Note

          +

          In classes annotated with @cCode.global, only arrays with a fixed length are +allowed. Please check the paragraph about arrays to learn how to specify the array length.

          +
          +

          This annotation triggers some checks to make sure that indeed the GlobalState class +(the name of the class can be changed, and there can be multiple such classes) is used as a global +state:

          +
            +

          • Functions can take as argument at most one instance per each global class such as GlobalState.

            • +

          • There can be at most one instance created for each global class such as GlobalState +(in a function that doesn’t already take an instance of that class as argument).

            • +

          • A GlobalState instance can only be used for reads and assignments (e.g. it cannot be let bound, except for the declaration mentioned above).

            • +

          • The only global state that can be passed to other functions is the one we create or the one we received as a function argument.

            • +
          +

          These checks ensure that the fields of GlobalState can be compiled as global variables in C. +Consider the move function from the Global.scala +example:

          +
          def move()(implicit state: GlobalState): Unit = {
+  require(state.stable && state.y > 0)
+  state.stable = false
+  state.x += 1
+  state.y -= 1
+  state.data(state.y) = 1
+  state.stable = true
+  if (state.y > 0) move()
+}.ensuring(_ => state.stable)
+
          +
          +

          After compilation to C, we get the following function, with global declarations +stable, x, y, and data.

          +
          int32_t data[100] = { 0 };
+bool stable = true;
+int32_t x = 5;
+int32_t y = 7;
+
+void move() {
+    stable = false;
+    x = x + 1;
+    y = y - 1;
+    data[y] = 1;
+    stable = true;
+    if (y > 0) {
+        move();
+    }
+}
+
          +
          +

          Note that the initial values for the global variables correspond to the default values given +in the Stainless class declaration (default values are mandatory when using the @cCode.global +annotation). When creating a global state instance (the only one), we do not pass arguments, to +make sure that the instance is created using the default values:

          +
          @cCode.export
+def main() {
+  implicit val gs = GlobalState()
+  StdOut.print(gs.x)
+  StdOut.print(gs.y)
+  move()
+  StdOut.print(gs.data(6))
+  StdOut.print(gs.data(7))
+  StdOut.print(gs.x)
+  StdOut.println(gs.y)
+}
+
          +
          +

          Stainless supports two variants of the @cCode.global annotation, namely @cCode.globalUninitialized +and @cCode.globalExternal. The first one generates global declarations without initial +values. These global variables are thus initialized according to C semantics, and there can be +a mismatch between the global state instance created by the user, and the initial values in C. +The second one hides the global declarations, which can be useful when interacting with C code +that declares global variables outside of the Stainless program.

          +
          +
          +

          Custom Conversion

          +

          When it comes to function using system calls, such as I/Os, no automated conversion is possible. In +those situations the user can define his own implementation for functions, add manual conversion +from Scala types to C types or even drop some functions and types from the translation, with +@cCode.function, @cCode.typedef and @cCode.drop annotations from the package +stainless.annotation. Their usage is described below.

          +
          +

          Custom Function Implementation

          +

          In order to circumvent some current limitations of GenC, one can use @cCode.function(code, +includes) to define the corresponding implementation of any top-level function or method, usually +accompanied by @extern. Its usage is as follows:

          +
          +
            +

          • For convenience, the C implementation generated by code is represented using a String and +not an Abstract Syntax Tree. The user is responsible for the correctness of the provided C99 +code. Because GenC might rename the function, e.g. to deal with overloading, the special +__FUNCTION__ token should be used instead of the original name. Furthermore, the parameters +and return type should match the signature automatically generated by GenC.

            • +

          • The optional parameter includes can hold a colon separated list of required C99 include +header files.

            • +
          +
          +

          Here is a typical example:

          +
          // Print a 32-bit integer using the *correct*
+// format for printf in C99
+@cCode.function(
+  code = """
+    | void __FUNCTION__(int32_t x) {
+    |  printf("%"PRIi32, x);
+    | }
+    """,
+  includes = "inttypes.h:stdio.h"
+)
+def myprint(x: Int): Unit = {
+  print(x)
+}
+
          +
          +
          +
          +

          Custom Type Translation

          +

          When a whole type need to be represented using a special C type, the @cCode.typedef(alias, +include) annotation can be used. Here the include parameter is also optional, however it can +only refer to one header, as it is not expected to have a type defined in several headers. The +alias string must represent an existing and valid type.

          +

          Using an aliasing from S to C implies that every function that accept a S in the input +program must accept a C in the generated C code. Usually, using this annotation implicates +manually defining the implementation of functions using this type with @cCode.function.

          +

          Here is an example:

          +
          @cCode.typedef(alias = "FILE*", include = "stdio.h")
+case class MyFile( ...
+
          +
          +
          +
          +

          Ignore Function or Type

          +

          It is also possible to skip the translation of some functions or types that are only used as +implementation details in proofs, for example, using the @cCode.drop() annotation.

          +
          +
          +
          +

          API For Safe Low Level Programs

          +

          In this section we describe the APIs that can be used to make the bridge between some Scala +programming facilities and their low level, equivalent, C features.

          +
          +

          I/Os

          +

          Similarly to Scala’s scala.io.StdIn and scala.io.StdOut, Stainless provides stainless.io.StdIn and +stainless.io.StdOut. These two APIs are provided with equivalent C code for easy translation with +GenC, but are also shaped to allow users to write proofs in a non-deterministic environment.

          +

          Furthermore, Stainless provides stainless.io.FileInputStream to read data and +stainless.io.FileOutputStream to write data to a file with a C99 compatible API.

          +
          +

          Note

          +

          It is important that you close the stream after it was created or your C +application might leak resources.

          +
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/genindex.html b/genindex.html new file mode 100644 index 0000000000..1fd183a25e --- /dev/null +++ b/genindex.html @@ -0,0 +1,127 @@ + + + + + + Index — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          +
            +
          • »
            • +
          • Index
            • +
          • +
            • +
          +
          +
          +
          +
          + + +

          Index

          + +
          + +
          + + +
          +
          +
          + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/gettingstarted.html b/gettingstarted.html new file mode 100644 index 0000000000..1eca72444e --- /dev/null +++ b/gettingstarted.html @@ -0,0 +1,225 @@ + + + + + + + Verifying and Compiling Examples — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Verifying and Compiling Examples

          +
          +

          Verifying Examples

          +

          Stainless is currently available as either:

          +
            +

          • a command line tool, which exposes most of the functionality, available as a ZIP file (recommended) or via Docker.

            • +

          • via an SBT plugin.

            • +
          +

          See the installation documentation for more information.

          +

          It is henceforth assumed that there exists a stainless script in in your PATH.

          +

          To see the main options, use

          +
          $ stainless --help
+
          +
          +

          in your command line shell. +You may also wish to consult the available command-line options.

          +

          You can try some of the examples from frontends/benchmarks +distributed with Stainless:

          +
          $ stainless --solvers=smt-cvc5 frontends/benchmarks/verification/invalid/InsertionSort.scala
+
          +
          +

          and get something like this (some output cropped)

          +
          [  Info  ] Starting verification...
+[  Info  ] Verified: 3 / 19
+[Warning ]  - Result for 'postcondition' VC for buggySortedIns @37:38:
+[Warning ] l.isInstanceOf[Nil] || !(l.head <= e) || {
+[Warning ]   val res: List = Cons(l.head, buggySortedIns(e, l.tail))
+[Warning ]   assume({
+[Warning ]     val e: List = Cons(l.head, buggySortedIns(e, l.tail))
+[Warning ]     true
+[Warning ]   })
+[Warning ]   contents(res) == contents(l) ++ Set(e) && isSorted(res) && size(res) == size(l) + BigInt("1")
+[Warning ] }
+[Warning ] frontends/benchmarks/verification/invalid/InsertionSort.scala:37:38:  => INVALID
+                 case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l)
+                                                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+[Warning ] Found counter-example:
+[Warning ]   l: List -> Cons(-770374653, Cons(-771685886, Nil()))
+[Warning ]   e: Int  -> 1376322050
+[  Info  ] Verified: 3 / 19
+[Warning ]  - Result for 'postcondition' VC for buggySortedIns @37:73:
+[Warning ] l.isInstanceOf[Nil] || l.head <= e || {
+[Warning ]   val res: List = Cons(e, l)
+[Warning ]   contents(res) == contents(l) ++ Set(e) && isSorted(res) && size(res) == size(l) + BigInt("1")
+[Warning ] }
+[Warning ] frontends/benchmarks/verification/invalid/InsertionSort.scala:37:73:  => INVALID
+                 case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l)
+                                                                                   ^^^^^^^^^^
+[Warning ] Found counter-example:
+[Warning ]   l: List -> Cons(691483681, Cons(512, Nil()))
+[Warning ]   e: Int  -> -1263292350
+[  Info  ] Verified: 17 / 19
+[  Info  ]   ┌───────────────────┐
+[  Info  ] ╔═╡ stainless summary ╞══════════════════════════════════════════════════════════════════════════════════════════════╗
+[  Info  ] ║ └───────────────────┘                                                                                              ║
+[  Info  ] ║ InsertionSort.scala:33:7:    buggySortedIns  non-negative measure                  valid             U:smt-z3  0,1 ║
+[  Info  ] ║ InsertionSort.scala:35:5:    buggySortedIns  body assertion: match exhaustiveness  trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:35:5:    buggySortedIns  postcondition                         trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:36:21:   buggySortedIns  postcondition                         valid             U:smt-z3  0,1 ║
+[  Info  ] ║ InsertionSort.scala:37:38:   buggySortedIns  postcondition                         invalid           U:smt-z3  0,3 ║
+[  Info  ] ║ InsertionSort.scala:37:45:   buggySortedIns  measure decreases                     valid             U:smt-z3  0,1 ║
+[  Info  ] ║ InsertionSort.scala:37:73:   buggySortedIns  postcondition                         invalid           U:smt-z3  0,1 ║
+[  Info  ] ║ InsertionSort.scala:20:7:    contents        non-negative measure                  valid from cache            0,0 ║
+[  Info  ] ║ InsertionSort.scala:20:37:   contents        body assertion: match exhaustiveness  trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:22:24:   contents        measure decreases                     valid             U:smt-z3  0,0 ║
+[  Info  ] ║ InsertionSort.scala:25:7:    isSorted        non-negative measure                  valid             U:smt-z3  0,0 ║
+[  Info  ] ║ InsertionSort.scala:25:36:   isSorted        body assertion: match exhaustiveness  trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:28:44:   isSorted        measure decreases                     valid             U:smt-z3  0,1 ║
+[  Info  ] ║ InsertionSort.scala:15:7:    size            non-negative measure                  valid from cache            0,0 ║
+[  Info  ] ║ InsertionSort.scala:15:34:   size            body assertion: match exhaustiveness  trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:15:34:   size            postcondition                         trivial                     0,0 ║
+[  Info  ] ║ InsertionSort.scala:16:19:   size            postcondition                         valid             U:smt-z3  0,0 ║
+[  Info  ] ║ InsertionSort.scala:17:25:   size            postcondition                         valid             U:smt-z3  0,0 ║
+[  Info  ] ║ InsertionSort.scala:17:29:   size            measure decreases                     valid from cache            0,0 ║
+[  Info  ] ╟┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄╢
+[  Info  ] ║ total: 19   valid: 17   (3 from cache, 6 trivial) invalid: 2    unknown: 0    time:    0,81                        ║
+[  Info  ] ╚════════════════════════════════════════════════════════════════════════════════════════════════════════════════════╝
+[  Info  ] Verification pipeline summary:
+[  Info  ]   cache, anti-aliasing, smt-z3
+[  Info  ] Shutting down executor service.
+
          +
          +
          +
          +

          Compiling and Executing Examples

          +

          Scala code written with Stainless library dependencies can be compiled and run using the +library sources available on the Stainless github repository, +along with the scala compiler and runner script.

          +

          See the installation documentation for more information.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/ghost.html b/ghost.html new file mode 100644 index 0000000000..c34b7bc8a4 --- /dev/null +++ b/ghost.html @@ -0,0 +1,279 @@ + + + + + + + Ghost Context — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Ghost Context

          +
          +

          Introduction

          +

          When verifying code, one often needs to introduce lemmas, auxiliary functions, +additional fields and parameters, and contracts, whose only function is to specify +and prove that some properties are satisfied by the program.

          +
          import stainless.lang._
+import stainless.lang.collection._
+import stainless.lang.annotation._
+
+def isSorted(list: List[BigInt]): Boolean = list match {
+  case Nil()                            => true
+  case Cons(_, Nil())                   => true
+  case Cons(x1, Cons(x2, _)) if x1 > x2 => false
+  case Cons(_, xs)                      => isSorted(xs)
+}
+
+def sort(list: List[BigInt]): List[BigInt] = {
+  /* ... */
+} ensuring { res =>
+  res.contents == list.contents &&
+  isSorted(res) &&
+  res.size == l.size
+}
+
          +
          +

          One can alleviate this issue by adding the following import:

          +
          import stainless.lang.StaticChecks._
+
          +
          +
          +
          +

          Ghost annotation

          +
          +
          +

          Correctness check

          +

          As part of the verification pipeline, Stainless will check that it never +encounters a ghost expression outside of a ghost context. Should +the check fail, verification will fail and compilation will be aborted.

          +

          A ghost expression is any of:

          +
            +

          • Call to a ghost method

            • +

          • Selection of a ghost field

            • +

          • Instantiation of a ghost class

            • +

          • Reference to a ghost variable

            • +
          +

          A ghost context as any of:

          +
            +

          • Body of a ghost method

            • +

          • Argument to a ghost parameter (method or class constructor)

            • +

          • Assignment to a ghost variable

            • +

          • Anywhere where a value of type Unit is expected

            • +
          +
          +
          +

          Ghost expression elimination

          +

          If the correctness check described in the previous section succeeds, the sbt plugin +will then proceed to eliminate ghost methods and expressions from the programs.

          +
          +
          +

          Case study

          +
          import stainless.lang._
+import stainless.lang.StaticChecks._
+import stainless.collection._
+import stainless.annotation._
+
+import java.util.ArrayDeque
+
+object MessageQueue {
+
+  case class MsgQueue[A](
+    @extern @pure
+    queue: ArrayDeque[A],
+    @ghost
+    var msgs: List[A]
+  ) {
+    def put(msg: A): Unit = {
+
+      msgs = msg :: msgs
+      _put(msg)
+    }
+
+    @extern @pure
+    private def _put(msg: A): Unit = {
+      queue.addFirst(msg)
+    }
+
+    def take(): Option[A] = {
+      val result = _take()
+      msgs = msgs.tailOption.getOrElse(Nil())
+      result
+    } ensuring { res =>
+      res == old(this).msgs.headOption
+    }
+
+    @extern @pure
+    private def _take(): Option[A] = {
+      Option(queue.pollFirst())
+    } ensuring { res =>
+      res == msgs.headOption
+    }
+
+    @extern @pure
+    def isEmpty: Boolean = {
+      queue.size() == 0
+    } ensuring { res =>
+      res == msgs.isEmpty
+    }
+  }
+
+  object MsgQueue {
+    @extern @pure
+    def empty[A]: MsgQueue[A] = {
+      MsgQueue(new ArrayDeque(), Nil())
+    } ensuring { res =>
+      res.isEmpty && res.msgs.isEmpty
+    }
+  }
+
+  def test = {
+    val queue = MsgQueue.empty[String]
+
+    queue.put("World")
+    queue.put("Hello")
+
+    assert(!queue.isEmpty)
+
+    val a = queue.take()
+    assert(a == Some("Hello"))
+
+    val b = queue.take()
+    assert(b == Some("World"))
+    assert(queue.isEmpty)
+
+    val c = queue.take()
+    assert(!c.isDefined)
+  }
+}
+
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/imperative.html b/imperative.html new file mode 100644 index 0000000000..be724f120f --- /dev/null +++ b/imperative.html @@ -0,0 +1,625 @@ + + + + + + + Imperative — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Imperative

          +

          To complement the core Pure Scala language, Stainless +proposes a few extensions to that core language.

          +

          On the technical side, these extensions do not have specific treatment in the +back-end of Stainless. Instead, they are desugared into Pure Scala +constructs during a preprocessing phase in the Stainless front-end.

          +

          These transformations are partly documented in the EPFL PhD thesis of Régis Blanc.

          +
          +

          Imperative Code

          +

          Stainless lets you introduce local variables in functions, and use Scala assignments +syntax.

          +
          def foo(x: Int): Int = {
+  var a = x
+  var b = 42
+  a = a + b
+  b = a
+  b
+}
+
          +
          +

          The above example illustrates three new features introduced by imperative support:

          +
            +

          1. Declaring a variable in a local scope

            2. +

          2. Blocks of expressions

            3. +

          3. Assignments

            4. +
          +

          You can use Scala variables with a few restrictions. The variables can only be +declared and used locally, no variable declaration outside of a function body. +There is also support for variables in case classes constructors. Imperative support +introduces the possibility to use sequences of expressions (blocks) – a +feature not available in Pure Scala, where your only +option is a sequence of val which essentially introduce nested let +declarations.

          +
          +
          +

          While loops

          +

          You can use the while keyword. While loops usually combine the ability to +declare variables and make a sequence of assignments in order to compute +something useful:

          +
          def foo(x: Int): Int = {
+  var res = 0
+  var i = 0
+  while(i < 10) {
+    res = res + i
+    i = i + 1
+  }
+  res
+}
+
          +
          +

          Stainless will automatically generate a postcondition to the while loop, using +the negation of the loop condition. It will automatically prove that +verification condition and you should see an invariant postcondition marked +as valid.

          +

          Stainless internally handles loops as a function with a postcondition. For the end-user, it +means that Stainless is only going to rely on the postcondition of the loop to prove properties +of code relying on loops. Usually that invariant is too weak to prove anything remotely +useful and you will need to annotate the loop with a stronger invariant.

          +

          You can annotate a loop with an invariant as follows:

          +
          var res = 0
+var i = 0
+(while(i < 10) {
+  res = res + i
+  i = i + 1
+}) invariant(i >= 0 && res >= i)
+
          +
          +

          The strange syntax comes from some Scala magic in order to make the keyword +invariant a valid keyword. Stainless is defining an implicit conversion from +Unit to an InvariantFunction object that provides an invariant +method. The invariant method takes a boolean expression as a parameter and +its semantics is to hold at the following points during the execution of the loop:

          +
            +

          1. When first entering the loop: initialization.

            2. +

          2. After each complete execution of the body.

            3. +

          3. On exiting the loop.

            4. +
          +

          Stainless will generate verification conditions invariant inductive and +invariant postcondition to verify points (2) and (3) above. It will also +generate a precondition corresponding to the line of the while loop. This +verification condition is used to prove the invariant on initialization of the +loop.

          +
          +
          +

          Arrays

          +

          PureScala supports functional arrays, that is, the operations apply and +updated which do not modify an array but only returns some result. In +particular, updated returns a new copy of the array.

          +
          def f(a: Array[Int]): Array[Int] = {
+  a.updated(0, a(1))
+}
+
          +
          +

          However, using functional arrays is not the most natural way to work with +arrays, and arrays are often used in imperative implementations of algorithms. +We add the usual update operation on arrays:

          +
          val a = Array(1,2,3,4)
+a(1) //2
+a(1) = 10
+a(1) //10
+
          +
          +

          Stainless simply rewrite arrays using update operation as the assignment of function arrays +using updated. This leverages the built-in algorithm for functional arrays +and relies on the elimination procedure for assignments. Concretely, it would +transform the above on the following equivalent implementation:

          +
          var a = Array(1,2,3,4)
+a(1) //2
+a = a.updated(1, 10)
+a(1) //10
+
          +
          +

          Stainless also has a swap operation in stainless.lang, which is equivalent to two updates.

          +
          def swap[@mutable T](a1: Array[T], i1: Int, a2: Array[T], i2: Int): Unit
+
          +
          +
          +
          +

          Mutable Objects

          +

          A restricted form of mutable classes is supported via case classes with var +arguments:

          +
          case class A(var x: Int)
+def f(): Int = {
+  val a = new A(10)
+  a.x = 13
+  a.x
+}
+
          +
          +

          Mutable case classes are behaving similarly to Array, and are handled with a +rewriting, where each field updates becomes essentially a copy of the object with +the modified parameter changed.

          +
          +
          +

          Aliasing

          +

          With mutable data structures comes the problem of aliasing. In Stainless, we +maintain the invariant that in any scope, there is at most one pointer to some +mutable structure. Stainless will issue an error if you try to create an alias to +some mutable structure in the same scope:

          +
          val a = Array(1,2,3,4)
+val b = a //error: illegal aliasing
+b(0) = 10
+assert(a(0) == 10)
+
          +
          +

          However, Stainless correctly supports aliasing mutable structures when passing it +as a parameter to a function (assuming its scope is not shared with the call +site, i.e. not a nested function). Essentially you can do:

          +
          case class A(var x: Int)
+def updateA(a: A): Unit = {
+  a.x = 14
+}
+def f(): Unit = {
+  val a = A(10)
+  updateA(a)
+  assert(a.x == 14)
+}
+
          +
          +

          The function updateA will have the side effect of updating its argument +a and this will be visible at the call site.

          +
          +
          +

          Annotations for Imperative Programming

          +

          We introduce the special function old that can be used in postconditions to +talk about the value of a variable before the execution of the block. When you refer to a variable +or mutable structure in a post-condition, Stainless will always consider the current value of +the object, so that in the case of a post-condition this would refer to the final value of the +object. Using old, you can refer to the original value of the variable and check some +properties:

          +
          case class A(var x: Int)
+def inc(a: A): Unit = {
+  a.x = a.x + 1
+} ensuring(_ => a.x == old(a).x + 1)
+
          +
          +

          old can be wrapped around any identifier that is affected by the body. You can also use +old for variables in scope, in the case of nested functions:

          +
          def f(): Int = {
+  var x = 0
+  def inc(): Unit = {
+    x = x + 1
+  } ensuring(_ => x == old(x) + 1)
+
+  inc(); inc();
+  assert(x == 2)
+}
+
          +
          +

          Another useful and similar construct is snapshot that semantically makes a deep copy of a mutable object. +Contrarily to old, snapshot allows to refer to the state of an object prior to its mutation within +the body of the function, as long as it is used in a ghost context.

          +

          For instance:

          +
          def updateArray(a: Array[BigInt], i: Int, x: BigInt): Unit = {
+  require(0 <= i && i < a.length - 1)
+  require(a(i) == 0 && a(i + 1) == 0)
+  @ghost val a0 = snapshot(a)
+  a(i) = x
+  // a0 is unaffected by the update of a
+  // Note: using StaticChecks assert, which introduces a ghost context
+  assert(a0(i) == 0 && a(i) == x)
+  @ghost val a1 = snapshot(a)
+  a(i + 1) = 2 * x
+  assert(a1(i + 1) == 0 && a(i + 1) == 2 * x)
+}
+
          +
          +
          +
          +

          Extern functions and abstract methods

          +

          @extern functions and abstract methods of non-sealed trait taking mutable objects as parameters are treated as-if +they were applying arbitrary modifications to them. +For instance, the assertions in the following snippet are invalid:

          +
          @extern
+def triple(mc: MutableClass): BigInt = ???
+
+trait UnsealedTrait {
+  def quadruple(mc: MutableClass): BigInt
+}
+
+def test1(mc: MutableClass): Unit = {
+  val i = mc.i
+  triple(mc)
+  assert(i == mc.i) // Invalid, mc.i could be anything
+}
+
+def test2(ut: UnsealedTrait, mc: MutableClass): Unit = {
+  val i = mc.i
+  ut.quadruple(mc)
+  assert(i == mc.i) // Invalid as well
+}
+
          +
          +

          Annotating such methods or functions with @pure tells Stainless to assume the parameters are not mutated:

          +
          case class MutableClass(var i: BigInt)
+
+@pure @extern
+def triple(mc: MutableClass): BigInt = ???
+
+trait UnsealedTrait {
+  @pure
+  def quadruple(mc: MutableClass): BigInt
+}
+
+def test1(mc: MutableClass): Unit = {
+  val i = mc.i
+  triple(mc)
+  assert(i == mc.i) // Ok
+}
+
+def test2(ut: UnsealedTrait, mc: MutableClass): Unit = {
+  val i = mc.i
+  ut.quadruple(mc)
+  assert(i == mc.i) // Ok
+}
+
          +
          +

          Note that Stainless will enforce purity for visible implementations of quadruple.

          +

          Sometimes, a method or @extern function may mutate some parameters but not all of them. +In such cases, the untouched parameters can be annotated with @pure:

          +
          case class MutableClass(var i: BigInt)
+
+@extern
+def sum(@pure mc1: MutableClass, mc2: MutableClass): BigInt = ???
+
+trait UnsealedTrait {
+  def doubleSum(@pure mc1: MutableClass, mc2: MutableClass): BigInt
+}
+
+def test1(mc1: MutableClass, mc2: MutableClass): Unit = {
+  val i1 = mc1.i
+  val i2 = mc2.i
+  sum(mc1, mc2)
+  assert(i1 == mc1.i) // Ok
+  assert(i2 == mc2.i) // Invalid, mc2.i may have any value
+}
+
+def test2(ut: UnsealedTrait, mc1: MutableClass, mc2: MutableClass): Unit = {
+  val i1 = mc1.i
+  val i2 = mc2.i
+  ut.doubleSum(mc1, mc2)
+  assert(i1 == mc1.i) // Ok
+  assert(i2 == mc2.i) // Invalid
+}
+
          +
          +
          +
          +

          Trait Variables

          +

          Traits are allowed to declare variables, with the restriction that these cannot be +assigned a default value.

          +
          trait MutableBox[A] {
+  var value: A
+}
+
          +
          +

          Such abstract variables must be overridden at some point by either:

          +
            +

          1. a mutable field of a case class

            2. +
          +
          case class Box[A](var value: A) extends MutableBox[A]
+
          +
          +
            +

          1. a pair of getter/setter

            2. +
          +
          case class WriteOnceBox[A](
+  var underlying: A,
+  var written: Boolean = false
+) extends MutableBox[A] {
+
+  def value: A = underlying
+
+  def value_=(newValue: A): Unit = {
+    if (!written) {
+      underlying = newValue
+      written = true
+    }
+  }
+}
+
          +
          +

          Note: a setter is not required to actually perform any mutation, and the following +is a perfectly valid sub-class of MutableBox:

          +
          case class ImmutableBox[A](underlying: A) extends MutableBox[A] {
+  def value: A = underlying
+  def value_=(newValue: A): Unit = ()
+}
+
          +
          +
          +
          +

          Return keyword

          +

          Stainless partially supports the return keyword. For verification, an internal +phase of Stainless (called ReturnElimination) injects a data-structure named +ControlFlow to simulate the control flow of programs with returns.

          +
          sealed abstract class ControlFlow[Ret, Cur]
+case class Return[Ret, Cur](value: Ret)  extends ControlFlow[Ret, Cur]
+case class Proceed[Ret, Cur](value: Cur) extends ControlFlow[Ret, Cur]
+
          +
          +

          Here is a function taken from ControlFlow2.scala:

          +
          def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = {
+  if (a && b) {
+    return 1
+  }
+
+  val y = x match {
+    case None()       => return 0
+    case Some(x) if a => return x + 1
+    case Some(x) if b => return x + 2
+    case Some(x)      => x
+  };
+
+  -y
+}
+
          +
          +

          The program transformation can be inspected by running:

          +
          +
          stainless ControlFlow2.scala --batched --debug=trees --debug-objects=foo --debug-phases=ReturnElimination
+
          +
          +
          +

          We get the following output (with cf identifiers renamed for clarity; you can +use the --print-ids option so that Stainless expressions get displayed with +unique identifiers, at the cost of readability):

          +
          +
          def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = {
+  val cf0: ControlFlow[BigInt, Unit] = if (a && b) {
+    Return[BigInt, Unit](1)
+  } else {
+    Proceed[BigInt, Unit](())
+  }
+  cf0 match {
+    case Return(retValue) =>
+      retValue
+    case Proceed(proceedValue) =>
+      val cf1: ControlFlow[BigInt, BigInt] = x match {
+        case None()       => Return[BigInt, BigInt](0)
+        case Some(x) if a => Return[BigInt, BigInt](x + 1)
+        case Some(x) if b => Return[BigInt, BigInt](x + 2)
+        case Some(x)      => Proceed[BigInt, BigInt](x)
+      }
+      cf1 match {
+        case Return(retValue) =>
+          retValue
+        case Proceed(proceedValue) =>
+          -proceedValue
+      }
+  }
+}
+
          +
          +
          +

          Stainless also supports return in while loops, and transforms them to local functions, also in +the ReturnElimination phase. Here is a function taken from ReturnInWhile.scala.

          +
          +
          def returnN(n: Int): Int = {
+  require(n >= 0)
+  var i = 0
+  (while (true) {
+    decreases(n - i)
+    if (i == n) return i
+    i += 1
+  }).invariant(0 <= i && i <= n)
+
+  assert(false, "unreachable code")
+  0
+}.ensuring((res: Int) => res == n)
+
          +
          +
          +

          After transformation, we get a recursive (local) function named returnWhile +that returns a control flow element to indicate whether the loop terminated +normally or returned. We check that the invariant clause of the while loop is +indeed an invariant by adding it to the pre and postconditions of the generated +returnWhile function. When the while loop returns, we check in addition that +the postcondition of the top-level holds (see comment).

          +
          +
          def returnN(n: Int): Int = {
+  require(n >= 0)
+
+  var i: Int = 0
+  val cf0: ControlFlow[Int, Unit] = {
+    def returnNWhile: ControlFlow[Int, Unit] = {
+      require(0 <= i && i <= n)
+      decreases(n - i)
+      {
+        val cf1: ControlFlow[Int, Unit] = if (i == n) {
+          Return[Int, Unit](i)
+        } else {
+          Proceed[Int, Unit](())
+        }
+        cf1 match {
+          case Return(retValue) => Return[Int, Unit](retValue)
+          case Proceed(proceedValue) =>
+            Proceed[Int, Unit]({
+              i = (i + 1)
+              ()
+            })
+        }
+      } match {
+        case Return(retValue) =>
+          Return[Int, Unit](retValue)
+        case Proceed(proceedValue) =>
+          if (true) {
+            returnNWhile
+          } else {
+            Proceed[Int, Unit](())
+          }
+      }
+    } ensuring {
+      (cfWhile: ControlFlow[Int, Unit]) => cfWhile match {
+        case Return(retValue) =>
+          // we check the postcondition `retValue == n` of the top-level function
+          retValue == n &&
+          0 <= i && i <= n
+        case Proceed(proceedValue) =>
+          ¬true && 0 <= i && i <= n
+      }
+    }
+    if (true) {
+      returnNWhile
+    } else {
+      Proceed[Int, Unit](())
+    }
+  }
+  cf0 match {
+    case Return(retValue) => retValue
+    case Proceed(proceedValue) =>
+      assert(false, "unreachable code")
+      0
+  }
+} ensuring {
+  (res: Int) => res == n
+}
+
          +
          +
          +

          Finally, return is also supported for local function definitions, with the same transformation. +It is however not supported for anonymous functions.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 0000000000..c6752a5ce8 --- /dev/null +++ b/index.html @@ -0,0 +1,295 @@ + + + + + + + Stainless documentation — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Stainless documentation

          +

          Contents:

          +
          + +
          + +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/installation.html b/installation.html new file mode 100644 index 0000000000..d96806cee4 --- /dev/null +++ b/installation.html @@ -0,0 +1,473 @@ + + + + + + + Installing Stainless — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Installing Stainless

          +
          +

          General Requirement

          +
            +

          • Java 17 JRE +It suffices to have headless OpenJDK JRE 17 (e.g. one that one gets with apt install openjdk-17-jre-headless on Debian/Ubuntu). +Make sure that java -version reports a version starting with 1.17, such as openjdk version "1.17 or java version "1.17.

            • +
          +

          Stainless bundles Scala compiler front-end and runs it before it starts compilation. We recommend using the Scala 3 front end (originally named dotty), though Scala 2 is also available.

          +
          + +
          +

          Running Code with Stainless dependencies

          +

          Using sources:

          +
            +

          1. Clone the sources from https://github.com/epfl-lara/stainless

            2. +

          2. Create a folder to put compiled Scala objects: mkdir -p ~/.scala_objects

            3. +

          3. Compile your code (here in MyFile.scala, though you can have more than one file) while referring to the Stainless library sources: scalac -d ~/.scala_objects $(find /path/to/stainless/frontends/library/stainless/ -name "*.scala") MyFile.scala

            4. +

          4. Run your code (replace MyMainClass with the name of your main object): scala -cp ~/.scala_objects MyMainClass

            5. +
          +

          Using jar:

          +

          You can package the Stainless library into a jar to avoid the need to compile it every time:

          +
          $ cd path/to/stainless/
+$ sbt stainless-library/packageBin
+
          +
          +

          Add the generated Stainless library jar file when invoking the compiler with scalac and the JVM with scala or java. For instance:

          +
          $ mkdir -p ~/.scala_objects
+$ scalac -d ~/.scala_objects -cp /path/to/stainless/frontends/library/target/scala-2.13/stainless-library_2.13-X.Y.Z-A-BCDEFGHI.jar MyFile1.scala MyFile2.scala # and so on
+$ scala -cp ~/.scala_objects:/path/to/stainless/frontends/library/target/scala-2.13/stainless-library_2.13-X.Y.Z-A-BCDEFGHI.jar MyMainClass
+
          +
          +

          where X.Y.Z is the Stainless version and A-BCDEFGHI is some hash (which can be autocompleted by the terminal).

          +
          +
          +

          External Solver Binaries

          +

          If no external SMT solvers (such as Z3 or cvc5) are found, Stainless will use the bundled Scala-based Princess solver

          +

          To improve performance, we highly recommend that you install the following two additional external SMT solvers as binaries for your platform:

          + +

          You can enable these solvers using --solvers=smt-z3 and --solvers=smt-cvc5 flags.

          +

          Solver binaries that you install should match your operating system and your architecture. We recommend that you install these solvers as a binary and have their binaries available in the $PATH (as z3 or cvc5).

          +

          Note that somewhat lower version numbers of solvers should work as well and might even have different sets of soundness-related issues.

          +

          You can use multiple solvers in portfolio mode, as with the options --timeout=15 --solvers=smt-z3,smt-cvc5, where verification succeeds if at least one of the solvers proves (within the given number of seconds) each the verification conditions. We suggest to order the solvers starting from the one most likely to succeed quickly.

          +

          For final verification runs of highly critical software, we recommend that (instead of the portfolio mode) you obtain several solvers and their versions, then try a single solver at a time and ensure that each verification run succeeds (thus applying N-version programming to SMT solver implementations).

          +
          +

          Install Z3 4.12.2

          +
            +

          1. Download Z3 4.12.2 from https://github.com/Z3Prover/z3/releases/tag/z3-4.12.2

            2. +

          2. Unzip the downloaded archive

            3. +

          3. Copy the z3 binary found in the bin/ directory of the inflated archive to a directory in your $PATH, eg., /usr/local/bin.

            4. +

          4. Make sure z3 can be found, by opening a new terminal window and typing:

            5. +
          +
          $ z3 --version
+
          +
          +
            +

          1. The output should read:

            2. +
          +
          Z3 version 4.12.2 - 64 bit`
+
          +
          +
          +
          +

          Install cvc5 1.0.8

          +
            +

          1. Download cvc5 1.0.8 from https://github.com/cvc5/cvc5/releases/tag/cvc5-1.0.8 for your platform.

            2. +

          2. Copy or link the downloaded binary under name cvc5 to a directory in your $PATH, eg., /usr/local/bin.

            3. +
          +
            +

          1. Make sure cvc5 can be found, by opening a new terminal window and typing:

            2. +
          +
          $ cvc5 --version | head
+
          +
          +
            +

          1. The output should begin with:

            2. +
          +
          This is cvc5 version 1.0.8
+
          +
          +
          +
          +
          +

          Build from Source on Linux & macOS

          +

          To build Stainless, we use sbt. In a typical configuration, sbt universal:stage in the root of the source tree should work, yet, +in an attempt to be more reproducible and independent from SBT cache and path, the instructions below assume that the directory called stainless does not exist, they instruct sbt to use a relative path for its bootstrap, and do not require adding sbt to your path.

          +

          Install SBT

          +

          Follow the instructions at http://www.scala-sbt.org/ to install sbt 1.7.3 (or somewhat later version).

          +

          Check out sources

          +

          Get the sources of Stainless by cloning the official Stainless repository:

          +
          $ git clone https://github.com/epfl-lara/stainless.git
+Cloning into 'stainless'...
+
          +
          +

          Run SBT

          +

          The following instructions will invoke SBT while using a stainless sub-directory to download files.

          +
          $ cd stainless
+$ sbt universal:stage
+
          +
          +

          Where to find generated files

          +

          The compilation will automatically generate the bash script stainless-dotty (and the Scala2 one stainless-scalac).

          +

          You may want to introduce a soft-link from to a file called stainless:

          +
          $ ln -s frontends/dotty/target/universal/stage/bin/stainless-dotty stainless
+
          +
          +

          and, for the Scala2 version of the front end,

          +
          +

          $ ln -s frontends/scalac/target/universal/stage/bin/stainless-scalac stainless-scalac-old

          +
          +

          Analogous scripts work for various platforms and allow additional control over the execution, such as passing JVM arguments or system properties:

          +
          $ stainless -Dscalaz3.debug.load=true -J-Xmx6G --help
+
          +
          +

          Note that Stainless is organized as a structure of several projects. The main project lives in core while the two available frontends can be found in frontends/dotty (and frontends/scalac). From a user point of view, this should most of the time be transparent and the build command should take care of everything.

          +
          +
          +

          Build from Source on Windows 10

          +

          Before following the infrequently updated instructions in this section, considering running Ubuntu on Windows 10 (through e.g. WSL) and following the instructions for Linux.

          +

          Get the sources of Stainless by cloning the official Stainless repository. You will need a Git shell for windows, e.g. Git for Windows. +On Windows, please do not use sbt universal:stage as this generates a Windows batch file which is unusable, because it contains commands that are too long for Windows. +Instead, please use sbt stainless-scalac-standalone/assembly as follows:

          +
          $ git clone https://github.com/epfl-lara/stainless.git
+Cloning into 'stainless'...
+// ...
+$ cd stainless
+$ sbt stainless-scalac-standalone/assembly
+// takes about 1 minutes
+
          +
          +

          Running Stainless can then be done with the command: java -jar frontends\stainless-dotty-standalone\target\scala-3.3.3\stainless-dotty-standalone-{VERSION}.jar, where VERSION denotes Stainless version.

          +
          +
          +

          Running Tests

          +

          Stainless comes with a test suite. Use the following commands to +invoke different test suites:

          +
          $ sbt test
+$ sbt it:test
+
          +
          +

          It’s also possible to run tests in isolation, for example, the following command runs Extraction tests on all files in termination/looping:

          +
          $ sbt 'it:testOnly *ExtractionSuite* -- -z "in termination/looping"'
+
          +
          +
          +
          +

          Building Stainless Documentation

          +

          Stainless documentation is available at https://epfl-lara.github.io/stainless/ . +To build the documentation locally, you will need Sphinx ( +http://sphinx-doc.org/ ), a restructured text toolkit that +was originally developed to support Python documentation.

          +
            +

          • On Ubuntu 18, you can use sudo apt install sphinx-common

            • +
          +

          The documentation resides in the core/src/sphinx/ directory and can be built using the provided Makefile. To do this, in a Linux shell, +type make html, and open in your web browser the generated top-level local HTML file, by default stored in +core/src/sphinx/_build/html/index.html. Also, you can open the *.rst documentation files in a text editor, as they are human-readable in their source form as well.

          +

          Note for project maintainers: to build documentation on GitHub Pages, use make gh-pages in the same Makefile, or adapt it to you needs.

          +
          +
          +

          Using IDEs with –no-colors option. Emacs illustration

          +

          Using command line option --no-colors asks stainless to produce clear 7-bit ASCII output with error messages in a standardized format:

          +
          FileName.scala:LineNo:ColNo: text of the error message
+
          +
          +

          This helps IDEs to pick up line numbers and show error location in the source file.

          +

          In emacs editor, you can invoke ansi-term and compilation-shell-minor-mode. Then, run

          +
          stainless --no-colors <InputFilesAndOptions>
+
          +
          +

          You may also consider using the --watch option.

          +

          You should now be able to click on a message for verification condition to jump to the appropriate position in the appropriate file, as well as to use emacs commands previous-error and next-error to navigate through errors and other verification-condition outcomes.

          +

          Here is a very simple illustration that introduces an interactive comp-ansi-term command that creates new window with ansi-term and minor compilation mode:

          +
          (setq comp-terminal-current-number 1)
+(defun create-numbered-comp-terminal ()
+  (ansi-term "/bin/bash")
+  (rename-buffer (concat "q" (number-to-string comp-terminal-current-number)) 1)
+  (setq comp-terminal-current-number (+ comp-terminal-current-number 1))
+  (compilation-shell-minor-mode)
+)
+(defun comp-ansi-term (arg)
+  "Run ansi-term with bash and compilation-shell-minor-mode in buffer named q_N for increasing N" (interactive "P")
+  (create-numbered-comp-terminal)
+  (split-window-vertically)
+  (previous-buffer)
+  (other-window 1)
+)
+
          +
          +

          The following globally binds the above command to the F3 key and binds F7 and F8 to commands for navigating reports:

          +
          (global-set-key [f3] 'comp-ansi-term)
+(global-set-key [f7] 'previous-error)
+(global-set-key [f8] 'next-error)
+
          +
          +

          For more information, please consult the documentation for emacs.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/internals.html b/internals.html new file mode 100644 index 0000000000..db76d93298 --- /dev/null +++ b/internals.html @@ -0,0 +1,132 @@ + + + + + + + Stainless’ Internals — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Stainless’ Internals

          +

          The main component of Stainless and the dataflow in its pipeline:

          +_images/pipeline.svg +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/intro.html b/intro.html new file mode 100644 index 0000000000..7240d621dc --- /dev/null +++ b/intro.html @@ -0,0 +1,254 @@ + + + + + + + Introduction — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Introduction

          +

          The Stainless verification framework aims to help developers build +verified Scala software. It encourages using a small set of core +Scala features and provides unique verification functionality. +In particular, Stainless can

          +
            +

          • verify statically that your program conforms to a given +specification and that it cannot crash at run-time

            • +

          • provide useful counterexamples when an implementation does +not satisfy its specification

            • +

          • verify that your program will terminate on all inputs

            • +
          +
          +

          Stainless and Scala

          +

          Stainless attempts to strike a delicate balance between the +convenience of use on the one hand and the simplicity of +reasoning on the other hand. Stainless supports verification +of Scala programs by applying a succession of semantic-preserving +transformations to the Pure Scala fragment until +it fits into the fragment supported by +Inox. +The Pure Scala fragment is at the core of +the functional programming paradigm and should sound familiar to +users of Scala, Haskell, ML, and fragments +present in interactive theorem provers such as Isabelle and Coq. Thus, +if you do not already know Scala, learning the Stainless subset should +be easier as it is a smaller language. Moreover, thanks to the use of +a Scala front end, Stainless supports implicits and for +comprehensions (which also serve as a syntax for monads in Scala). +Stainless also comes with a simple library of useful data types, which +are designed to work well with automated reasoning and Stainless’s +language fragment.

          +

          In addition to this pure fragment, Stainless supports certain +imperative features. +Features thus introduced are handled by +a translation into Pure Scala concepts. They are often more +than just syntactic sugar, because some of them require +significant modification of the original program, such as +introducing additional parameters to a set of functions. As +an intended aspect of its current design, Stainless’s language +currently does not provide a default encoding of +e.g. concurrency with a shared mutable heap, though it might +support more manageable forms of concurrency in the future.

          +

          If you would like to use Stainless now, check the +Installing Stainless section and follow Verifying and Compiling Examples and Tutorial. +To learn more about the functionality that Stainless provides, read on below.

          +
          +
          +

          Software Verification

          +

          The Stainless program verifier collects a list of top-level functions, +and verifies the validity of their contracts. Essentially, for each function, +it will (try to) prove that the postcondition always holds, assuming a given +precondition does hold. A simple example:

          +
          def factorial(n: BigInt): BigInt = {
+  require(n >= 0)
+  if(n == 0) {
+    BigInt(1)
+  } else {
+    n * factorial(n - 1)
+  }
+} ensuring(res => res >= 0)
+
          +
          +

          Stainless generates a postcondition verification condition for the above +function, corresponding to the predicate parameter to the ensuring +expression. It attempts to prove it using a combination of an internal +algorithm and external automated theorem proving. Stainless will return one of the +following:

          +
            +

          • The postcondition is valid. In that case, Stainless was able to prove that for any +input to the function satisfying the precondition, the postcondition will always hold.

            • +

          • The postcondition is invalid. It means that Stainless disproved the postcondition and +that there exists at least one input satisfying the precondition such that the +postcondition does not hold. Stainless will always return a concrete counterexample, very +useful when trying to understand why a function is not satisfying its contract.

            • +

          • The postcondition is unknown. It means Stainless is unable to prove or find a +counterexample. It usually happens after a timeout or an internal error occurring in +the external theorem prover.

            • +
          +

          Stainless will also verify for each call site that the precondition of the invoked +function cannot be violated.

          +

          Stainless supports verification of a significant part of the Scala language, described in +Pure Scala and Imperative.

          +
          +
          +

          Program Termination

          +

          A “verified” function in stainless is guaranteed to never crash, however, it can +still lead to an infinite evaluation. Stainless therefore provides a termination +checker that complements the verification of safety properties.

          +

          For each function in the program, Stainless will try to automatically infer a +decreasing metric associated with this function to prove termination. The +termination checker will then report one of the following:

          +
            +

          • The function terminates. In this case, Stainless was able to prove that for +all inputs (satisfying the function’s precondition), evaluation of the function +under those inputs is guaranteed to terminate.

            • +

          • The function loops. In this case, Stainless was able to construct an input +to the function such that evaluation under that input will be looping.

            • +

          • The function maybe loops. In the case where recursive functions are passed +around as first-class functions, Stainless will sometimes over-approximate the +potential call sites and report loops that may never occur.

            • +

          • Termination of the function is unknown. In this case, Stainless was neither +able to prove nor disprove termination of the relevant function. Automated +termination proving is a hard problem and such cases are thus to be expected.

            • +
          +

          In cases where automated termination checking fails, Stainless provides the user +with the ability to manually specify a measure under which termination should +occur through the decreases construct. For example, the +McCarthy 91 function +can be shown terminating as follows:

          +
          def M(n: BigInt): BigInt = {
+  decreases(stainless.math.max(101 - n, 0))
+  if (n > 100) n - 10 else M(M(n + 11))
+} ensuring (_ == (if (n > 100) n - 10 else BigInt(91)))
+
          +
          +

          It is also possible to add a pre-condition (require(...)) before decreases.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/laws.html b/laws.html new file mode 100644 index 0000000000..9530da1ce3 --- /dev/null +++ b/laws.html @@ -0,0 +1,694 @@ + + + + + + + Specifying Algebraic Properties — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Specifying Algebraic Properties

          +
          +

          Introduction

          +

          Many datatypes that programmers deal with on a day-to-day basis often provide +the same set of operations, for example:

          +
            +

          • They can be tested for equality to some other value

            • +

          • They can be ordered (partially or totally)

            • +

          • They can be composed together

            • +

          • They can be added or multiplied together

            • +

          • They have an inverse with respect to some operation

            • +
          +

          Because those are very common properties, it is often useful to be able to +abstract over them. In fact, each of these properties corresponds to an +algebraic structure, and is governed by the set of laws which allow the +programmer to reason at a higher level of abstraction, and to be able +to rely on the behavior specified by the laws associated with the structure.

          +

          While these properties can be modeled and implemented using Java interfaces, +modern programming languages such as Scala or Haskell provide a better +mechanism for expressing the properties: typeclasses.

          +
          +
          +

          Typeclasses

          +

          Typeclasses were introduced by Wadler & Blott [WB89] as an extension +to the Hindley/Milner type system to implement a certain kind of overloading, +known as ad-hoc polymorphism.

          +

          A typeclass is identified by its name, and is associated with a set of +(usually polymorphic) functions signatures, its methods.

          +

          It can then be instantiated at various types, given that the user is able +to provide a concrete implementation for each method. A user can then apply +these methods to any type for which there is a corresponding instance, which +essentially corresponds to overloading.

          +

          Using typeclasses, one can model algebraic properties of datatypes in a fairly natural way. +Here is for example, the definition and implementation of a Monoid, ie. a typeclass +for datatypes which can be mashed together associatively, and which have an +identity element w.r.t. to this operation:

          +
          abstract class Monoid[A] {
+  def empty: A
+  def append(x: A, y: A): A
+
+  @law
+  def law_leftIdentity(x: A) = {
+    append(empty, x) == x
+  }
+
+  @law
+  def law_rightIdentity(x: A) = {
+    append(x, empty) == x
+  }
+
+  @law
+  def law_associativity(x: A, y: A, z: A) = {
+    append(x, append(y, z)) == append(append(x, y), z)
+  }
+}
+
+implicit val bigIntAdditiveMonoid: Monoid[BigInt] = new Monoid[BigInt] {
+  override def empty: BigInt = 0
+  override def append(x: BigInt, y: BigInt): BigInt = x + y
+}
+
          +
          +

          Here, the abstract class specifies the two abstract operations which are required, +but also the associated laws that the implementation of these operations must +satisfy for the datatype to form a valid monoid.

          +

          Stainless will then ensure that the implementation of Monoid for the BigInt type satisfy +those laws. In this case, the above definition of bigIntAdditiveMonoid will generate the +following verification conditions:

          +
            ┌───────────────────┐
+╔═╡ stainless summary ╞══════════════════════════════════════════════════════════════════════╗
+║ └───────────────────┘                                                                      ║
+║ law_associativity     law              valid   nativez3   ../../test.scala:25:3     0.052  ║
+║ law_leftIdentity      law              valid   nativez3   ../../test.scala:25:3     0.037  ║
+║ law_rightIdentity     law              valid   nativez3   ../../test.scala:25:3     0.029  ║
+╟--------------------------------------------------------------------------------------------╢
+║ total: 9    valid: 9    (0 from cache) invalid: 0    unknown: 0    time:   0.729           ║
+╚════════════════════════════════════════════════════════════════════════════════════════════╝
+
          +
          +

          Armed with the knowledge that our Monoid will always be lawful, one can now fearlessly write +the foldMap function, and get the expected result:

          +
          def foldMap[A, M](xs: List[A])(f: A => M)(implicit M: Monoid[M]): M = xs match {
+  case Nil() => M.empty
+  case Cons(y, ys) => M.append(f(y), foldMap(ys)(f))
+}
+
+def sumBigInt(xs: List[BigInt]): BigInt = {
+  foldMap(xs)(x => x)
+}
+
          +
          +

          Sometimes, Stainless will not be able to automatically prove that an instance is lawful, +for example when the property of interest involves a recursive definition over an inductive +data type, as in the following code:

          +
          sealed abstract class Nat {
+  def +(m: Nat): Nat = this match {
+    case Zero => m
+    case Succ(n) => Succ(n + m)
+  }
+
+  def *(m: Nat): Nat = this match {
+    case Zero => Zero
+    case Succ(n) => n * m + m
+  }
+}
+
+final case object Zero extends Nat
+final case class Succ(prev: Nat) extends Nat
+
+final val One = Succ(Zero)
+
+implicit def natAdditiveMonoid: Monoid[Nat] = new Monoid[Nat] {
+  def empty: nat = Zero
+  def append(x: Nat, y: Nat): Nat = x + y
+}
+
          +
          +

          To help Stainless out, one needs to prove that Zero indeed the right identity of +, +as well as the associativity of the latter.

          +
          @induct
+def lemma_rightIdentity_plus(x: Nat): Boolean = {
+  x + Zero == x
+}.holds
+
+@induct
+def lemma_associativity_plus(x: Nat, y: Nat, z: Nat): Boolean = {
+  x + (y + z) == (x + y) + z
+}.holds
+
          +
          +

          One can then override the law of interest, and instantiate the lemma over the relevant parameters:

          +
          implicit def natAdditiveMonoid: Monoid[Nat] = new Monoid[Nat] {
+  def empty: nat = Zero
+  def append(x: Nat, y: Nat): Nat = x + y
+
+  override def law_rightIdentity(x: Nat) = {
+    super.law_rightIdentity(x) because lemma_rightIdentity_plus(x)
+  }
+
+  override def law_associativity(x: Nat, y: Nat, z: Nat) = {
+    super.law_associativity(x, y, z) because lemma_associativity_plus(x, y, z)
+  }
+}
+
          +
          +

          With these modifications, the example goes through without a hitch.

          +
          +
          +

          Typeclass inheritance

          +

          Some algebraic structures can be defined as some other algebraic structure plus some additional +operations and/or laws, eg. a monoid can be seen as a semigroup with identity.

          +

          In Scala, typeclasses allow to represent such relationship between algebraic structures by mean of inheritance.

          +

          Let’s take for example the Ord typeclass, which describes totally ordered datatypes.

          +

          This class is defined as follows:

          +
          trait Eq[A] {
+  def equals(x: A, y: A): Boolean
+}
+
+trait Ord[A] extends Eq[A] {
+  def lessThanEq(x: A, y: A): Boolean
+
+  def lessThan(x: A, y: A): Boolean = lessThanEq(x, y) && !equals(x, y)
+}
+
          +
          +

          This can also be read as: if A is an instance of Ord, then it also is a instance of Eq.

          +
          +
          +

          Associated methods

          +

          On top of abstract operations, a typeclass can also introduces concrete methods which +do not need to (but can) be re-defined by the programmer at instance declaration time, +just like the lessThan method of the Ord class above.

          +

          While such methods could be defined as a standalone function with an Ord constraint, +having it be a part of the class allows users to override it with e.g. a more efficient +implementation specific to the datatype they are instantiating the class for, as shown below:

          +
          case object BigIntOrd extends Ord[BigInt] {
+  def equal(x: BigInt, y: BigInt) = x == y
+  def lessThanEq(x: BigInt, y: BigInt) = x <= y
+
+  override def lessThan(x: BigInt, y: BigInt) x < y
+}
+
          +
          +
          +
          +

          Coherence

          +

          Let’s now look at an issue that might arise when working with typeclasses in Scala.

          +
          abstract class Monoid[A] {
+  def empty: A
+  def combine(x: A, y: A): A
+}
+
+implicit val bigIntAddMonoid: Monoid[BigInt] = new Monoid[BigInt] {
+  override def empty: BigInt = 0
+  override def combine(x: BigInt, y: BigInt): BigInt = x + y
+}
+
+implicit val bigIntProdMonoid: Monoid[BigInt] = new Monoid[BigInt] {
+  override def empty: BigInt = 1
+  override def combine(x: BigInt, y: BigInt): BigInt = x * y
+}
+
+def fold[A](list: List[A])(implicit M: Monoid[A]): A = {
+  list.foldRight(M.empty)(M.combine)
+}
+
+val list: List[BigInt] = List(2, 3)
+val res: BigInt = fold(list) // ?
+
          +
          +

          Here, the Scala compiler bails out with an ambiguous implicits error but for good reasons this time. +Indeed, depending on which instance of Monoid[BigInt] it picks, res can either be equal to 5 or 6. +This issue arise because the two instances above are overlapping, which has the effect of making the +type system incoherent. For a type system to be coherent, “every valid typing derivation for a program +must lead to a resulting program that has the same dynamic semantics”, which is clearly not the case here. +While in this specific example, the compiler will rightfully reject the program, this might always be +possible as one could import a different instance in scope in two different modules, and then a third module +might assume that these modules actually make use of the same instance, silently breaking the program. +Imagine trying to merge two Sets that have been created with two different Ord instances in scope.

          +

          Haskell partially solves this problem by enforcing that instances defined in the same module do not overlap, +that is to say that the compiler would reject the program above. We deem Haskell’s approach only partial as +it allows the programmer to define two or more overlapping instances, provided that they are not defined in the same module. +A program is then only rejected when the programmer makes imports such overlapping instances in scope and +attempts to make use of them. This decision stems from the will to allow linking together two different +libraries which both define a class instance for the same type.

          +

          Because Stainless operates under a closed-world assumption, we could go further and disallow overlapping +instances altogether, but this has not been implemented yet.

          +

          One might still want to provide both an additive and multiplicative Monoid instance for integers. +To this end, one can wrap values of type BigInt with two different wrapper classes for which +we will define the respective instances:

          +
          case class Sum(value: BigInt)     extends AnyVal
+case class Product(value: BigInt) extends AnyVal
+
+implicit val bigIntSumMonoid: Monoid[Sum] = new Monoid[Sum] {
+  override def empty: Sum = Sum(0)
+  override def combine(x: Int, y: Int): Sum = Sum(x.value + y.value)
+}
+
+implicit val bigIntProductMonoid: Monoid[Product] = new Monoid[Product] {
+  override def empty: Product = Product(1)
+  override def combine(x: Int, y: Int): Product = Product(x.value * y.value)
+}
+
          +
          +
          def foldMap[A, B](list: List[A])(f: A => B)(implicit M: Monoid[B]): B = {
+  list.map(f).foldRight(M.empty)(M.combine)
+}
+
          +
          +

          It then becomes possible to unambiguously pick which instance to use depending on the semantics one wants:

          +
          val list: List[BigInt] = List(2, 3)
+
+val sum: BigInt     = foldMap(list)(Sum(_)).value     // 5
+val product: BigInt = foldMap(list)(Product(_)).value // 6
+
          +
          +
          +
          +

          Under the hood

          +

          In this section we describe how laws are encoded within Stainless.

          +

          Let’s take as an example the Semigroup+Monoid hierarchy, slightly +amended to exercise at once all the features described above.

          +
          abstract class Semigroup[A] {
+  def append(x: A, y: A): A
+
+  @law
+  def law_associativity(x: A, y: A, z: A): Boolean = {
+    append(x, append(y, z)) == append(append(x, y), z)
+  }
+}
+
+abstract class Monoid[A] extends Semigroup[A] {
+  def empty: A
+
+  @law
+  def law_leftIdentity(x: A): Boolean = {
+    append(empty, x) == x
+  }
+
+  @law
+  def law_rightIdentity(x: A): Boolean = {
+    append(x, empty) == x
+  }
+
+  override def law_associativity(x: A, y: A, z: A): Boolean = {
+    // We refine the Semigroup associativity law with a dummy
+    // predicate `refineLaw` to demonstrate this feature.
+    super.law_associativity(x, y, z) && refineLaw(x, y, z)
+  }
+}
+
+def refineLaw[A](x: A, y: A, z: A): Boolean = true
+
          +
          +

          Together with a simple implementation for BigInt:

          +
          def bigIntAdditiveMonoid: Monoid[BigInt] = new Monoid[BigInt] {
+  def empty: BigInt = 0
+  def append(x: BigInt, y: BigInt): BigInt = x + y
+
+  override def law_rightIdentity(x: BigInt): Boolean = {
+    // no manual proof is needed in this case, but we include
+    // a dummy one for the sake of this example.
+    someProof
+  }
+}
+
+def someProof: Boolean = true
+
          +
          +

          Here is the internal Stainless AST pretty much right after extraction +from the Scala compiler.

          +

          Each symbol (class, method, variable) is annotated with its internal identifier +(ie. the number after the $ sign at the end of its name) which will prove useful +for reading the code after the next phase, as it introduces new symbols with the same +name but different identifiers.

          +
          abstract class Semigroup$0[A$85] {
+
+  @abstract
+  def append$3(x$108: A$85, y$24: A$85): A$85 = <empty tree>[A$85]
+
+  @law
+  def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = {
+    this.append$3(x$109, this.append$3(y$25, z$11)) ==
+    this.append$3(this.append$3(x$109, y$25), z$11)
+   }
+}
+
+abstract class Monoid$0[A$86] extends Semigroup$0[A$86] {
+
+  @abstract
+  def empty$6: A$86 = <empty tree>[A$86]
+
+  @law
+  def law_leftIdentity$0(x$110: A$86): Boolean =
+   this.append$3(this.empty$6, x$110) == x$110
+
+  @law
+  def law_rightIdentity$0(x$111: A$86): Boolean =
+   this.append$3(x$111, this.empty$6) == x$111
+
+  def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean =
+    super.law_associativity$0(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12)
+}
+
+def refineLaw$0[A$87](x$113: A$87, y$27: A$87, z$13: A$87): Boolean = true
+
+case class $anon$0() extends Monoid$0[BigInt] {
+  def empty$7: BigInt = 0
+  def append$4(x$112: BigInt, y$26: BigInt): BigInt = x$112 + y$26
+
+  def law_rightIdentity$1(x$113: BigInt): Boolean = someProof$0
+}
+
+def bigIntAdditiveMonoid$0: Monoid$0[BigInt] = $anon$0()
+
+def someProof$0: Boolean = true
+
          +
          +

          The code above maps in straightforward way to the original code.

          +

          Let’s now take a look at the output of the Laws phase. This is +the phase which desugars the law definitions and their overrides +into methods with explicit postconditions.

          +
          abstract class Semigroup$0[A$85] {
+
+  @abstract
+  def append$3(x$108: A$85, y$24: A$85): A$85 = <empty tree>[A$85]
+
+  @final
+  @inlineOnce
+  @derived(law_associativity$0)
+  def law_associativity$2(x$120: A$85, y$30: A$85, z$14: A$85): Boolean = {
+    this.append$3(x$120, this.append$3(y$30, z$14)) ==
+    this.append$3(this.append$3(x$120, y$30), z$14)
+  }
+
+  @abstract
+  def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = {
+    <empty tree>[Boolean]
+  } ensuring {
+    (res$82: Boolean) => res$82 && this.law_associativity$2(x$109, y$25, z$11)
+  }
+}
+
+abstract class Monoid$0[A$86] extends Semigroup$0[A$86] {
+
+  @abstract
+  def empty$6: A$86 = <empty tree>[A$86]
+
+  @final
+  @inlineOnce
+  @derived(law_leftIdentity$0)
+  def law_leftIdentity$1(x$116: A$86): Boolean =
+    this.append$3(this.empty$6, x$116) == x$116
+
+  @abstract
+  def law_leftIdentity$0(x$110: A$86): Boolean = {
+    <empty tree>[Boolean]
+  } ensuring {
+    (res$77: Boolean) => res$77 && this.law_leftIdentity$1(x$110)
+  }
+
+  @final
+  @inlineOnce
+  @derived(law_rightIdentity$0)
+  def law_rightIdentity$2(x$117: A$86): Boolean =
+    this.append$3(x$117, this.empty$6) == x$117
+
+  @abstract
+  def law_rightIdentity$0(x$111: A$86): Boolean = {
+    <empty tree>[Boolean]
+  } ensuring {
+    (res$80: Boolean) => res$80 && this.law_rightIdentity$2(x$111)
+  }
+
+  @law
+  def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean = {
+    this.law_associativity$2(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12)
+  } ensuring {
+    (res$84: Boolean) => res$84 && this.law_associativity$2(x$112, y$26, z$12)
+  }
+}
+
+@derived(bigIntAdditiveMonoid$0)
+case class $anon$0() extends Monoid$0[BigInt] {
+
+  def empty$7: BigInt = 0
+  def append$4(x$114: BigInt, y$27: BigInt): BigInt = x$114 + y$27
+
+  @law
+  @derived(law_leftIdentity$0)
+  def law_leftIdentity$2(x$119: BigInt): Boolean = {
+    true
+  } ensuring {
+    (res$84: Boolean) => this.law_leftIdentity$1(x$119)
+  }
+
+  @law
+  def law_rightIdentity$1(x$115: BigInt): Boolean = {
+    someProof$0
+  } ensuring {
+    (res$79: Boolean) => res$79 && this.law_rightIdentity$2(x$115)
+  }
+
+  @law
+  @derived(law_associativity$0)
+  def law_associativity$2(x$120: BigInt, y$29: BigInt, z$13: BigInt): Boolean = {
+    true
+  } ensuring {
+    (res$85: Boolean) => this.law_associativity$1(x$120, y$29, z$13)
+  }
+}
+
+def bigIntAdditiveMonoid$0: Monoid$0[BigInt] = $anon$0()
+
+def someProof$0: Boolean = true
+
          +
          +

          There are a few things going on here:

          +
            +

          1. First of all, each method marked @law introduces a new method which +holds the original body of the law. The law’s body is then rewritten to +be empty, and is provided with a postcondition which refers to the newly +introduced method. This desugaring step basically turns the laws +into abstract methods which must be overridden at some point with +methods whose body can be proven to be true, while also satisfying the law +itself.

            +

            The helper method will be used in subsequent steps to refer to the +law’s body, without having to inline it or call the law itself, +which is disallowed since it is conceptually an abstract method, as +evidenced by its newly added @abstract flag.

            +
            // In class `Semigroup`...
+
+// This is the helper method.
+@final
+@inlineOnce
+@derived(law_associativity$0)
+def law_associativity$2(x$120: A$85, y$30: A$85, z$14: A$85): Boolean = {
+  this.append$3(x$120, this.append$3(y$30, z$14)) ==
+  this.append$3(this.append$3(x$120, y$30), z$14)
+}
+
+// This is the original law definition, which now became an abstract method.
+@abstract
+def law_associativity$0(x$109: A$85, y$25: A$85, z$11: A$85): Boolean = {
+  <empty tree>[Boolean]
+} ensuring {
+  (res$82: Boolean) => res$82 && this.law_associativity$2(x$109, y$25, z$11)
+}
+
            +
            +
            2. +

          2. Laws which are overridden into abstract subclasses, are provided with a +postcondition that ensures that their body can be proven true, +while still satisfying the original law via a call to the helper +method introduced in the previous step. This step ensures that laws +cannot be fully redefined, and thus potentially weakened, in subclasses.

            +
            // In class `Monoid`...
+
+@law
+def law_associativity$1(x$112: A$86, y$26: A$86, z$12: A$86): Boolean = {
+  this.law_associativity$2(x$112, y$26, z$12) && refineLaw$0[A$86](x$112, y$26, z$12)
+} ensuring {
+  (res$84: Boolean) => res$84 && this.law_associativity$2(x$112, y$26, z$12)
+}
+
            +
            +
            3. +

          3. In the typeclass implementations (eg. class $anon$0), methods which override laws +are provided with a postcondition which again ensures that their body holds, +while still satisfying the law they override, again via a call to the helper +method introduced in step 1.

            +
            // In class `$anon$0`...
+
+@law
+def law_rightIdentity$1(x$115: BigInt): Boolean = {
+  someProof$0
+} ensuring {
+  (res$79: Boolean) => res$79 && this.law_rightIdentity$2(x$115)
+}
+
            +
            +
            4. +

          4. If a law is not overridden in a typeclass implementation, a stub override is +automatically defined by Stainless, to ensure that a verification condition +will be generated. Those stubs just have true as a body, and a postcondition +which calls to the appropriate law helper introduced in step 1. +This expresses the fact that the law holds on its own, without any additional proof steps.

            +
            // In class `$anon$0`
+
+@law
+@derived(law_leftIdentity$0)
+def law_leftIdentity$2(x$119: BigInt): Boolean = {
+  true
+} ensuring {
+  (res$84: Boolean) => this.law_leftIdentity$1(x$119)
+}
+
            +
            +
            5. +
          +
          +

          Note

          +

          As can be seen above, calling the super method when refining (such as in law_associativity) +or proving (such as in law_rightIdentity) a law is superfluous, since it is done anyway +during the encoding as to ensure that laws cannot be weakened. Doing so can nonetheless help +readability, since it makes the code match more closely to the semantics of Scala.

          +
          +
          +
          WB89
          +
            +

          1. Wadler and S. Blott. 1989. How to make ad-hoc polymorphism less ad hoc.

            2. +
          +
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/library.html b/library.html new file mode 100644 index 0000000000..547db83ed9 --- /dev/null +++ b/library.html @@ -0,0 +1,645 @@ + + + + + + + Stainless Library — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Stainless Library

          +

          Stainless defines its own library with some core data types and +operations on them, which work with the fragment supported +by Stainless, available in frontends/library/stainless, which +we encourage the reader to consult as it is always up to date.

          +

          One of the reasons for a separate library is to +ensure that these operations can be correctly mapped to +mathematical functions and relations inside of SMT solvers, +largely defined by the SMT-LIB standard (see +http://www.smt-lib.org/). Thus for some data types, such as +BigInt, Stainless provides a dedicated mapping to support reasoning. +(If you are a fan +of growing the language only through libraries, keep in mind that +growing operations together with the ability to reason about them +is what the development of mathematical theories is all about, and +is a process slower than putting together +libraries of unverified code–efficient automation of reasoning about a +single decidable theory generally results in multiple research papers.) +For other operations (e.g., List[T]), the library +is much like Stainless user-defined code, but specifies some +useful preconditions and postconditions of the operations, thus +providing reasoning abilities using mechanisms entirely available +to the user.

          +
          +

          Note

          +

          The ScalaDoc for the library is available online.

          +

          For the most up-to-date version of the source code of library, +please consult the library/ directory in your Stainless distribution.

          +
          +

          To use Stainless’ libraries, you need to use the appropriate +import directive at the top of Stainless’ compilation units. +Here is a quick summary of what to import.

          + ++++ + + + + + + + + + + + + + + + + +

          Package to import

          What it gives access to

          stainless.annotation._

          Stainless annotations, e.g. @induct

          stainless.lang._

          Map, Set, PartialFunction, holds, passes, invariant

          stainless.collection._

          List[T] and subclasses, Option[T] and subclasses

          +

          To learn more, we encourage you to look in the library/ subdirectory of Stainless distribution.

          +
          +

          Annotations

          +

          Stainless provides some special annotations in the package stainless.annotation, +which instruct Stainless to handle some functions or objects in a specialized way.

          + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

          Annotation

          Meaning

          @library

          Treat this object/function as library, don’t try +to verify its specification. Can be overridden by +including a function name in the --functions +command line option.

          @induct

          Use the inductive tactic when generating +verification conditions.

          @invariant

          Treat the annotated method as an invariant of the enclosing +class. Can be used instead of require within a value class +body. For soundness, invariants can only refer to fields of +their class, and thus cannot call methods on this.

          @ghost

          Drop the annotated field or method during compilation. +See the corresponding section for more +information.

          @extern

          Only extract the contracts of a function, replacing +its body by a choose expression.

          @opaque

          Used to hide a function f’s body when doing verification +of functions (f itself, or others) invoking f. Does +not hide pre and postconditions.

          @dropVCs

          Do not generate verification conditions for this function.

          @pure

          Specify that this function is pure, which will then +be checked. If the function is also annotated with +@extern, it will not be checked, but assumed pure.

          @ignore

          Ignore this definition when extracting Stainless trees. +This annotation is useful to define functions +that are not in Stainless’s language but will be +hard-coded into specialized trees, or to include +code written in full Scala which is not verifiable +by Stainless. Can also be used on class fields whose type +cannot be understood by Stainless, eg. because it comes from +an external library, the JDK, or some other code which +does not understand. +See the corresponding documentation page.

          @inline

          Inline this function. Stainless will refuse to inline +(mutually) recursive functions.

          @inlineOnce

          Inline this function but only once, which is allowed +even on (mutually) recursive functions. +Note: A recursive function will not be inlined within itself.

          @partialEval

          Partially evaluate calls to this function. +Note: stainless.lang.partialEval can also be used to +partially evaluate an expression.

          +

          Stainless also has some special keywords defined in stainless.lang that can be used around +function calls. Here is an example for unfold.

          + ++++ + + + + + + + + + + + + + +

          Annotation

          Meaning

          inline

          Call-site inlining

          unfold

          Inject an equality assumption between a function call and its +unfolded version. Can be useful to locally override an +@opaque annotation.

          +
          +
          +

          List[T]

          +

          As there is no special support for Lists in SMT solvers, Stainless Lists are encoded +as an ordinary algebraic data type:

          +
          sealed abstract class List[T]
+case class Cons[T](h: T, t: List[T]) extends List[T]
+case class Nil[T]() extends List[T]
+
          +
          +
          +

          List API

          +

          Stainless Lists support a rich and strongly specified API.

          + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

          Method signature for List[T]

          Short description

          size: BigInt

          Number of elements in this List.

          content: Set[T]

          The set of elements in this List.

          contains(v: T): Boolean

          Returns true if this List contains v.

          ++(that: List[T]): List[T]

          Append this List with that.

          head: T

          Returns the head of this List. Can only be called +on a nonempty List.

          tail: List[T]

          Returns the tail of this List. Can only be called +on a nonempty List.

          apply(index: BigInt): T

          Return the element in index index in this +List (0-indexed).

          ::(t:T): List[T]

          Prepend an element to this List.

          :+(t:T): List[T]

          Append an element to this List.

          reverse: List[T]

          The reverse of this List.

          take(i: BigInt): List[T]

          Take the first i elements of this List, or +the whole List if it has less than i elements.

          drop(i: BigInt): List[T]

          This List without the first i elements, +or the Nil() if this List has less than i +elements.

          slice(from: BigInt, to: BigInt): List[T]

          Take a sublist of this List, from index from +to index to.

          replace(from: T, to: T): List[T]

          Replace all occurrences of from in this List +with to.

          chunks(s: BigInt): List[List[T]]

          zip[B](that: List[B]): List[(T, B)]

          Zip this list with that. In case the Lists +do not have equal size, take a prefix of the +longer.

          -(e: T): List[T]

          Remove all occurrences of e from this List.

          --(that: List[T]): List[T]

          Remove all occurrences of any element in that +from this List.

          &(that: List[T]): List[T]

          A list of all elements that occur both in +that and this List.

          pad(s: BigInt, e: T): List[T]

          Add s instances of e at the end of this +List.

          find(e: T): Option[BigInt]

          Look for the element e in this List, and +optionally return its index if it is found.

          init: List[T]

          Return this List except for the last element. +Can only be called on nonempty Lists.

          last: T

          Return the last element of this List. +Can only be called on nonempty Lists.

          lastOption: Option[T]

          Optionally return the last element of this List.

          headOption: Option[T]

          Optionally return the first element of this List.

          unique: List[T]

          Return this List without duplicates.

          splitAt(e: T): List[List[T]]

          Split this List to chunks separated by an +occurrence of e.

          split(seps: List[T]): List[List[T]]

          Split this List in chunks separated by an +occurrence of any element in seps.

          count(e: T): BigInt

          Count the occurrences of e in this List.

          evenSplit: (List[T], List[T])

          Split this List in two halves.

          insertAt(pos: BigInt, l: List[T]): List[T]

          Insert an element after index pos in this +List.

          replaceAt(pos: BigInt, l: List[T]): List[T]

          Replace the l.size elements after index +pos, or all elements after index pos +if there are not enough elements, +with the elements in l.

          rotate(s: BigInt): List[T]

          Rotate this list by s positions.

          isEmpty: Boolean

          Returns whether this List is empty.

          map[R](f: T => R): List[R]

          Builds a new List by applying a predicate f +to all elements of this list.

          foldLeft[R](z: R)(f: (R,T) => R): R

          Applies the binary operator f to a start value +z and all elements of this List, going left +to right.

          foldRight[R](f: (T,R) => R)(z: R): R

          Applies a binary operator f to all elements of +this list and a start value z, going right to +left.

          scanLeft[R](z: R)(f: (R,T) => R): List[R]

          Produces a List containing cumulative results +of applying the operator f going left to +right.

          scanRight[R](f: (T,R) => R)(z: R): List[R]

          Produces a List containing cumulative results +of applying the operator f going right to +left.

          flatMap[R](f: T => List[R]): List[R]

          Builds a new List by applying a function f +to all elements of this list and using the +elements of the resulting Lists.

          filter(p: T => Boolean): List[T]

          Selects all elements of this List +which satisfy the predicate p

          forall(p: T => Boolean): Boolean

          Tests whether predicate p holds +for all elements of this List.

          exists(p: T => Boolean): Boolean

          Tests whether predicate p holds for some of +the elements of this List.

          find(p: T => Boolean): Option[T]

          Finds the first element of this List satisfying +predicate p, if any.

          takeWhile(p: T => Boolean): List[T]

          Takes longest prefix of elements that satisfy +predicate p

          +
          +
          +

          Additional operations on Lists

          +

          The object ListOps offers this additional operations:

          + ++++ + + + + + + + + + + + + + + + + + + + +

          Function signature

          Short description

          flatten[T](ls: List[List[T]]): List[T]

          Converts the List of Lists ls into a List +formed by the elements of these Lists.

          isSorted(ls: List[BigInt]): Boolean

          Returns whether this list of mathematical integers +is sorted in ascending order.

          sorted(ls: List[BigInt]): List[BigInt]

          Sorts this list of mathematical integers +is sorted in ascending order.

          insSort(ls: List[BigInt], v: BigInt): List[BigInt]

          Sorts this list of mathematical integers +is sorted in ascending order using insertion sort.

          +
          +
          +

          Theorems on Lists

          +

          The following theorems on Lists have been proven by Stainless and are included +in the object ListSpecs:

          + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

          Theorem signature

          Proven Claim

          snocIndex[T](l: List[T], t: T, i: BigInt)

          (l :+ t).apply(i) == (if (i < l.size) l(i) else t)

          reverseIndex[T](l: List[T], i: BigInt)

          l.reverse.apply(i) == l.apply(l.size - 1 - i)

          appendIndex[T](l1: List[T], l2: List[T], i: BigInt)

          (l1 ++ l2).apply(i) == +(if (i < l1.size) l1(i) else l2(i - l1.size))

          appendAssoc[T](l1: List[T], l2: List[T], l3: List[T])

          ((l1 ++ l2) ++ l3) == (l1 ++ (l2 ++ l3))

          snocIsAppend[T](l: List[T], t: T)

          (l :+ t) == l ++ Cons[T](t, Nil())

          snocAfterAppend[T](l1: List[T], l2: List[T], t: T)

          (l1 ++ l2) :+ t == (l1 ++ (l2 :+ t))

          snocReverse[T](l: List[T], t: T)

          (l :+ t).reverse == Cons(t, l.reverse)

          reverseReverse[T](l: List[T])

          l.reverse.reverse == l

          scanVsFoldRight[A,B](l: List[A], z: B, f: (A,B) => B)

          l.scanRight(f)(z).head == l.foldRight(f)(z)

          +
          +
          +
          +

          Set[T], Map[T]

          +

          Stainless uses its own Sets and Maps, which are defined in the stainless.lang package. +However, these classes are not implemented within Stainless. +Instead, they are parsed into specialized trees. +Methods of these classes are mapped to specialized trees within SMT solvers. +For code generation, we rely on Java Sets and Maps.

          +

          The API of these classes is a subset of the Scala API and can be found +in the Pure Scala section.

          +

          Additionally, the following functions for Sets are provided in the +stainless.collection package:

          + ++++ + + + + + + + + + + + + + + + + +

          Function signature

          Short description

          setToList[A](set: Set[A]): List[A]

          Transforms the Set set into a List.

          setForall[A](set: Set[A], p: A => Boolean): Boolean

          Tests whether predicate p holds +for all elements of Set set.

          setExists[A](set: Set[A], p: A => Boolean): Boolean

          Tests whether predicate p holds +for all elements of Set set.

          +
          +
          +

          PartialFunction[A, B]

          +

          To define anonymous functions with preconditions, Stainless has a PartialFunction[A, B] type +with the corresponding annotation A ~> B. To construct a partial function, you must use +PartialFunction.apply as in the unOpt function below. The precondition written in the +require becomes the pre field of the partial function (as in the call to f.pre in map1).

          +
          def map1[A, B](l: List[A], f: A ~> B): List[B] = {
+  require(l.forall(f.pre))
+  l match {
+    case Cons(x, xs) => Cons[B](f(x), map1(xs, f))
+    case Nil() => Nil[B]()
+  }
+}
+
+def unOpt[T](l: List[Option[T]]): List[T] = {
+  require(l.forall(_.nonEmpty))
+  map1(l, PartialFunction {(x:Option[T]) => require(x.nonEmpty); x.get})
+}
+
          +
          +

          Partial functions can also be written using pattern matching:

          +
          def unOptCase[T](l: List[Option[T]]): List[T] = {
+  require(l.forall { case Some(_) => true; case _ => false })
+  map1(l, PartialFunction[Option[T], T] { case Some(v) => v })
+}
+
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/limitations.html b/limitations.html new file mode 100644 index 0000000000..ae29c132f4 --- /dev/null +++ b/limitations.html @@ -0,0 +1,169 @@ + + + + + + + Limitations of Verification — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Limitations of Verification

          +

          A goal of Stainless is to ensure that proven properties hold in +all program executions so that, for example, verified programs +do not crash and all of the preconditions and postconditions +are true in all executions. +For this to be the case, there needs +to be a precise correspondence between runtime execution +semantics and the semantics used in verification, including +the SMT solvers invoked.

          +

          Below we document several cases where we are aware that the +discrepancy exists and provide suggested workarounds.

          +
          +

          Out of Memory Errors

          +

          By default, Stainless assumes that unbounded data types can +be arbitrarily large and that all well-founded recursive +functions have enough stack space to finish their computation. +Thus a verified program may crash at run-time due to:

          +
          +
            +

          • stack overflow

            • +

          • heap overflow

            • +
          +
          +

          The set of values for recursive algebraic data types is assumed to be infinite. +In any given execution, there will be actual bounds on the +total available memory. The program could thus crash +with an out-of-memory error when trying to allocate another +value of algebraic data type.

          +

          For a safety critical application you may wish to resort to +tail-recursive programs only, and also write preconditions +and postconditions that enforce a bound on the maximum size +of the data structures that your application +manipulates. For this purpose, you can define size functions +that return BigInt data types.

          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/neon.html b/neon.html new file mode 100644 index 0000000000..b73f223931 --- /dev/null +++ b/neon.html @@ -0,0 +1,1068 @@ + + + + + + + Proving Theorems — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Proving Theorems

          +

          Verifying the contract of a function is really proving a mathematical +theorem. Stainless can be seen as a (mostly) automated theorem prover. It is +automated in the sense that once the property stated, Stainless will proceed with searching +for a proof without any user interaction. In practice, however, many theorems will be fairly +difficult to prove, and it is possible for the user to provide hints to Stainless.

          +

          Hints typically take the form of simpler properties that combine in order to prove +more complicated ones. In the remaining subsections, we provide code patterns and introduce +simple domain-specific language operators that can help in constructing complex Stainless proofs.

          +
          +

          A practical introduction to proofs

          +

          When writing logical propositions such as preconditions or +postconditions in Stainless, one is basically writing Boolean +predicates. They can be as simple as testing whether a list is empty +or not, to more complex combinations of properties. Lemmas or +theorems are simply logical tautologies, that is, propositions that +always hold. They can be expressed using Boolean-valued methods that +return true for all their inputs.

          +

          To make this more concrete, let’s take a simple lemma as an +example 1. Here we want to prove that the append operation (++) on +lists preserves the content of the two lists being concatenated. This +proposition is relatively straightforward and Stainless is able to verify +that it always holds.

          +
          import stainless.collection._ // for List
+import stainless.lang._       // for holds
+
+object Example {
+  def appendContent[A](l1: List[A], l2: List[A]): Boolean = {
+    l1.content ++ l2.content == (l1 ++ l2).content
+  }.holds
+}
+
          +
          +

          Here we wrote .holds which is a method implicitly available on Boolean +that ensure the returned value is true. It is equivalent to writing +ensuring { res => res }.

          +

          Now let’s look at another example that looks trivial but for which Stainless +needs some help with the proof: we want to prove that adding Nil +at the end of a list has no effect.

          +
          import stainless.collection._ // for List
+import stainless.lang._       // for holds
+
+object Example {
+  def rightUnitAppend[T](l1: List[T]): Boolean = {
+    l1 ++ Nil() == l1
+  }.holds
+}
+
          +
          +

          If you try to verify this last example you’ll face a delicate +situation: Stainless runs indeterminately until it is either killed or +times out. But why does this happen? The proposition doesn’t seem +more complicated than appendContent. Perhaps even more +surprisingly, Stainless is able to verify the following:

          +
          def leftUnitAppend[T](l1: List[T]): Boolean = {
+  Nil() ++ l1 == l1
+}.holds
+
          +
          +

          How is this possible? The two propositions are completely symmetric! +The problem is that Stainless doesn’t know anything about lists, a priori. +It can only reason about lists thanks to their definition in terms of +the case classes Cons and Nil and associated methods such as +++. In particular, Stainless doesn’t know that Nil represents the +empty list, and hence that appending it to some other list is a no-op. +What then, is the difference between the two examples above? To +answer this question, we need to have a look at the definition of the +++ method:

          +
          def ++(that: List[T]): List[T] = (this match {
+  case Nil()       => that
+  case Cons(x, xs) => Cons(x, xs ++ that)
+}) ensuring { res => /* ... */ }
+
          +
          +

          Note that the implementation of ++ is recursive in its first +argument this but not in its second argument that. This is +why Stainless was able to verify leftUnitAppend easily: it is true by +definition, i.e. Nil() ++ l1 is actually defined to be l1. +What about the symmetric case? How is l1 ++ Nil() defined? Well, +it depends on whether l1 is the empty list or not. So in order to +prove rightUnitAppend, we need to proceed with a case analysis. The +resulting proof has a recursive (i.e. inductive) structure reminiscent +of the definition of ++:

          +
          import stainless.collection._ // for List
+import stainless.lang._       // for holds
+import stainless.proof._      // for because
+
+object Example {
+  def rightUnitAppend[T](l1: List[T]): Boolean = {
+    (l1 ++ Nil() == l1) because {
+      l1 match {
+        case Nil()       => true
+        case Cons(x, xs) => rightUnitAppend(xs)
+      }
+    }
+  }.holds
+}
+
          +
          +

          With this new implementation of the rightUnitAppend lemma, Stainless is capable +of verifying that it holds. If you look closely at it, you can distinguish three +parts:

          +
            +

          1. the claim we want to prove l1 ++ Nil() == l1;

            2. +

          2. because, which is just some syntactic sugar for conjunction – remember, +every proposition is a Boolean formula;

            3. +

          3. and a recursion on l1 that serves as a hint for Stainless to perform +induction.

            4. +
          +

          The recursion is based here on pattern matching, which Stainless will also check for +exhaustiveness. It has essentially the same structure as +the implementation of ++: the base case is when l1 is the empty list +and the inductive case is performed on Cons objects.

          +
          +
          +

          Techniques for proving non-trivial propositions

          +

          In the previous section, we saw that “proof hints” can improve the odds +of Stainless successfully verifying a given proposition. In this section, +we will have a closer look at what constitutes such a proof and +discuss a few techniques for writing them.

          +

          As mentioned earlier, propositions are represented by Boolean +expressions in Stainless. But how are proofs represented? They are just +Boolean expressions as well 2. The difference +between propositions and proofs is not their representation, but how +they are used by Stainless. Intuitively, a proof p: Boolean for a +proposition x: Boolean is an expression such that

          +
          +
            +

          1. Stainless is able to verify p, and

            2. +

          2. Stainless is able to verify that p implies x.

            3. +
          +
          +

          This is what we mean when we say that proofs are “hints”. Typically, +a proof p of a proposition x is a more complex-looking but +equivalent version of x, i.e. an expression such that p == x. +This might seem a bit counter-intuitive: why should it be easier for +Stainless to verify an equivalent but more complex expression? The answer +is that the more complex version may consist of sub-expressions that +more closely resemble the definitions of functions used in x. We +have already seen an example of this principle in the previous +section: let’s have another look at the proof of rightUnitAppend:

          +
          def rightUnitAppend[T](l1: List[T]): Boolean = {
+  val x = l1 ++ Nil() == l1
+  val p = l1 match {
+    case Nil()       => true
+    case Cons(x, xs) => rightUnitAppend(xs)
+  }
+  x because p
+}.holds
+
          +
          +

          Here, we have rewritten the example to make the distinction between +the proposition x and its proof p more explicit. It’s easy to +check that indeed x == p, and hence the overall result of +rightUnitAppend is equivalent to x (recall that because is +just an alias of &&, so (x because p) == (x && x) == x). +However, the proof term p closely resembles the definition of +++ and its sub-expressions are easier to verify for Stainless than +x itself. The only non-trivial expression is the recursive call +to rightUnitAppend(xs), which serves as the inductive hypothesis. +We will discuss induction in more detail in Section +“Induction”.

          +
          +

          Divide and Conquer

          +

          Before we delve into the details of particular proof techniques, it is +worth revisiting a guiding principle for writing proofs – whether it +be in Stainless, by hand, or using some other form of mechanized proof +checker – namely to modularize proofs, i.e. to split the proofs of +complex propositions into manageable sub-goals. This can be +achieved in various ways.

          +
          +
            +

          • Use helper lemmas – these are propositions that are lemmas on +their own, i.e. they state and prove simple but self-contained +propositions that can be reused elsewhere. As such, they play a +role akin to helper methods in normal programming, and indeed, are +implemented in the same way, except that they carry a .holds +suffix.

            • +

          • Use case analysis to split complex propositions into simpler +sub-cases. This is especially helpful in the presence of +recursion, where it leads to inductive proofs (see Section +“Induction”).

            • +

          • Use relational reasoning to split complex relationships into +conjunctions of elementary ones. This often requires one to make +use of relational properties such as transitivity (e.g. to break a +single equation a == b into a chain of equations a == x1 && +x1 == x2 && ... && xN == b), symmetry (e.g. to use a previously +proven inequality a <= b where b >= a is expected), +anti-symmetry (to unify variables), and so on (see Section +“Relational reasoning”).

            • +

          • Separate specification form implementation. It is sometimes easier +to prove the fact that a given function fulfills its specification +as a separate lemma (although the proof techniques are roughly the +same, see Section “Techniques for proving non-trivial postconditions”).

            • +

          • Generalize (or specialize) propositions. Sometimes, propositions +are more easily proved in a stronger (or weaker) form and +subsequently instantiated (or combined with other propositions) to +yield a proof of the original proposition.

            • +
          +
          +

          While it is good practice to factor common propositions into helper +lemmas, one sometimes wants to verify simple, specific sub-goals in a +proof without going through the trouble of introducing an additional +method. This is especially true while one is exploring the branches +of a case analysis or wants to quickly check whether Stainless is able to +prove a seemingly trivial statement automatically (we will see +examples of such situations in the coming sections). For such cases, +one can use the check function from stainless.proof. The check +function behaves as the identity function on Booleans but additionally +assumes its argument in its precondition. As a result, Stainless will +check that x holds while verifying the call to check(x). +For example, when verifying the following function:

          +
          import stainless.proof.check
+
+def foo(x: BigInt): Boolean = {
+  check(x >= 0 || x < 0) && check(x + 0 == 0)
+}
+
          +
          +

          Stainless will check (separately) that x >= 0 || x < 0 and x + 0 == +0 hold for all x, even though the function foo does not +specify any pre or postconditions, and report a counter example for +the second case:

          +
          [  Info  ]  - Now considering 'precond. (call check(x >= 0 || x < 0))' VC for foo @40:5...
+[  Info  ]  => VALID
+[  Info  ]  - Now considering 'precond. (call check(x + 0 == 0))' VC for foo @40:31...
+[ Error  ]  => INVALID
+[ Error  ] Found counter-example:
+[ Error  ]   x -> 1
+
          +
          +

          This is especially helpful when “debugging” proofs.

          +
          +
          +

          Proof control using assert and check

          +

          Both the assert and check keywords generate a verification condition for +the corresponding formula in the current context. The difference in these +keywords is in how they affect the context of other verification conditions. As +a rule of thumb, assertions do not affect the context of verification conditions +outside the block of the assertion, while check does. Thus you can use +assertions to prove local properties, and use check to have the property +(checked and) visible outside the block.

          +
          def foo(): Unit = {
+  val x = {
+    assert(b1) // verification condition: b1
+    check(b2)  // verification condition: b1 ==> b2
+  }
+  assert(b3)   // verification condition: b2 ==> b3 (b1 not visible to the solver)
+}
+
          +
          +

          Similarly, assert’s are not guaranteed to be visible when generating +verification conditions for postconditions, while check’s are.

          +
          def foo(): Unit = {
+  assert(b1) // verification condition: b1
+  check(b2)  // verification condition: b1 ==> b2
+}.ensuring(_ => b3) // verification condition b2 ==> b3 (b1 might not be visible to the solver)
+
          +
          +
          +
          +

          Induction

          +

          The vast majority of functional programs are written as functions over +ADTs, and consequently, Stainless comes with some special +support for verifying properties of ADTs. Among other things, Stainless +provides an annotation @induct, which can be used to automatically +prove postconditions of recursive functions defined on ADTs by way of +structural induction. We have already seen an example of such an +inductive property, namely rightUnitAppend. In fact, using +@induct, Stainless is able to prove rightUnitAppend directly:

          +
          import stainless.annotation._  // for @induct
+
+@induct
+def rightUnitAppend[T](l1: List[T]): Boolean = {
+  l1 ++ Nil() == l1
+}.holds
+
          +
          +

          This is possible because the inductive step follows (more or less) +directly from the inductive hypothesis and Stainless can verify the base +case automatically. However, Stainless may fail to verify more complex +functions with non-trivial base cases or inductive steps. In such +cases, one may still try to provide proof hints by performing manual +case analysis. Consider the following lemma about list reversal:

          +
          import stainless.collection._ // for List
+import stainless.lang._       // for holds
+
+object Example {
+  def reverseReverse[T](l: List[T]): Boolean = {
+    l.reverse.reverse == l
+  }.holds
+}
+
          +
          +

          Stainless is unable to verify reverseReverse even using @induct. +So let’s try and prove the lemma using manual case analysis. We start +by adding an “unrolled” version of the proposition and inserting calls +to check in each branch of the resulting pattern match:

          +
          def reverseReverse[T](l: List[T]): Boolean = {
+  l.reverse.reverse == l because {
+    l match {
+      case Nil()       => check {  Nil[T]().reverse.reverse == Nil[T]()  }
+      case Cons(x, xs) => check { (x :: xs).reverse.reverse == (x :: xs) }
+    }
+  }
+}.holds
+
          +
          +

          Clearly, the two versions of the lemma are equivalent: all we did was +expand the proposition using a pattern match and add some calls to +check (remember check acts as the identity function on its +argument). Let’s see what output Stainless produces for the expanded +version:

          +
          [  Info  ]  - Now considering 'postcondition' VC for reverseReverse @615:5...
+[Warning ]  => UNKNOWN
+[  Info  ]  - Now considering 'precond. (call check(List[T]().reverse().reverse() ...)' VC for reverseReverse @617:28...
+[  Info  ]  => VALID
+[  Info  ]  - Now considering 'precond. (call check({val x$27 = l.h; ...)' VC for reverseReverse @618:28...
+[Warning ]  => UNKNOWN
+[  Info  ]  - Now considering 'match exhaustiveness' VC for reverseReverse @616:7...
+[  Info  ]  => VALID
+
          +
          +

          As expected, Stainless failed to verify the expanded version. However, we +get some additional information due to the extra pattern match and the +calls to check. In particular, Stainless tells us that the match is +exhaustive, which means we covered all the cases in our case analysis +– that’s certainly a good start. Stainless was also able to automatically +verify the base case, so we can either leave the call to check as +is, or replace it by trivial. Unfortunately, Stainless wasn’t able to +verify the inductive step, something is missing. Let’s try to +manually reduce the inductive case and see where we get.

          +
          def reverseReverse[T](l: List[T]): Boolean = {
+  l.reverse.reverse == l because {
+    l match {
+      case Nil()       => trivial
+      case Cons(x, xs) => check { (xs.reverse :+ x).reverse == (x :: xs) }
+    }
+  }
+}.holds
+
          +
          +

          And now we’re stuck. We can’t apply the inductive hypothesis here, +nor can we reduce the inductive case further, unless we perform +case analysis on xs, which would grow the term further without +changing its shape. To make any headway, we need to use an additional +property of reverse, given by the following lemma (which Stainless is +able to prove using @induct):

          +
          @induct
+def snocReverse[T](l: List[T], t: T): Boolean = {
+  (l :+ t).reverse == t :: l.reverse
+}.holds
+
          +
          +

          The lemma states that appending an element t to a list l and +reversing it is equivalent to first reversing l and then +prepending t. Using this lemma, we can write the proof of +reverseReverse as

          +
          def reverseReverse[T](l: List[T]): Boolean = {
+  l.reverse.reverse == l because {
+    l match {
+      case Nil()       => trivial
+      case Cons(x, xs) => check {
+        (xs.reverse :+ x).reverse == x :: xs.reverse.reverse &&
+        x :: xs.reverse.reverse   == (x :: xs)               because
+          snocReverse(xs.reverse, x) && reverseReverse(xs)
+      }
+    }
+  }
+}.holds
+
          +
          +

          Stainless is able to verify this version of the lemma. Note that Stainless +doesn’t actually require us to include the two equations as they are +equivalent to the applications snocReverse(xs.reverse, x) and +reverseReverse(xs). Similarly, the call to check is somewhat +redundant now that Stainless is able to verify the entire proof. We could +thus “simplify” the above to

          +
          def reverseReverse[T](l: List[T]): Boolean = {
+  l.reverse.reverse == l because {
+    l match {
+      case Nil()       => trivial
+      case Cons(x, xs) => snocReverse(xs.reverse, x) && reverseReverse(xs)
+    }
+  }
+}.holds
+
          +
          +

          However, the previous version is arguably more readable for a human +being, and therefore preferable. In Section “Relational reasoning” we +will see how readability can be improved even further through the use +of a DSL for equational reasoning.

          +

          So far, we have only considered structurally inductive proofs. +However, Stainless is also able to verify proofs using natural induction +– the form of induction that is perhaps more familiar to most +readers. Consider the following definition of the exponential +function \(exp(x, y) = x^y\) over integers:

          +
          def exp(x: BigInt, y: BigInt): BigInt = {
+  require(y >= 0)
+  if      (x == 0) 0
+  else if (y == 0) 1
+  else             x * exp(x, y - 1)
+}
+
          +
          +

          The function exp is again defined recursively, but this time using +if statements rather than pattern matching. Let’s try and prove +some properties of this function using natural induction. One such +property is that for any pair of positive numbers \(x, y \geq 0\), +the exponential \(x^y\) is again a positive number.

          +
          def positive(x: BigInt, y: BigInt): Boolean = {
+  require(y >= 0 && x >= 0)
+  exp(x, y) >= 0
+}
+
          +
          +

          Since Stainless doesn’t know anything about exponentials, it isn’t able to +verify the lemma without hints. As with the previous example, we +start writing our inductive proof by expanding the top-level if +statement in the definition of exp.

          +
          def positive(x: BigInt, y: BigInt): Boolean = {
+  require(y >= 0 && x >= 0)
+  exp(x, y) >= 0 because {
+    if      (x == 0) check { exp(x, y) >= 0 }  // <-- valid
+    else if (y == 0) check { exp(x, y) >= 0 }  // <-- valid
+    else             check { exp(x, y) >= 0 }  // <-- unknown
+  }
+}.holds
+
          +
          +

          Stainless was able to verify the first two (base) cases, but not the +inductive step, so let’s continue unfolding exp for that case.

          +
          def positive(x: BigInt, y: BigInt): Boolean = {
+  require(y >= 0 && x >= 0)
+  exp(x, y) >= 0 because {
+    if      (x == 0) trivial
+    else if (y == 0) trivial
+    else             check { x * exp(x, y - 1) >= 0 }
+  }
+}.holds
+
          +
          +

          Although Stainless still isn’t able to verify the lemma, we now see a way +to prove the inductive step: x is positive (by the second +precondition) and so is exp(x, y - 1) (by the inductive +hypothesis). Hence the product x * exp(x, y - 1) is again +positive.

          +
          def positive(x: BigInt, y: BigInt): Boolean = {
+  require(y >= 0 && x >= 0)
+  exp(x, y) >= 0 because {
+    if      (x == 0) trivial
+    else if (y == 0) trivial
+    else             check {
+      x >= 0 && exp(x, y - 1) >= 0 because positive(x, y - 1)
+    }
+  }
+}.holds
+
          +
          +

          With these hints, Stainless is able to verify the proof. Again, we could +shorten the proof by omitting inequalities that Stainless can infer +directly, albeit at the expense of readability.

          +
          def positiveShort(x: BigInt, y: BigInt): Boolean = {
+  require(y >= 0 && x > 0)
+  exp(x, y) >= 0 because {
+    if      (x == 0) trivial
+    else if (y == 0) trivial
+    else             positiveShort(x, y - 1)
+  }
+}.holds
+
          +
          +

          We conclude the section with the inductive proof of another, somewhat +more interesting property of the exponential function, namely that +\((x y)^z = x^z y^z\).

          +
          def expMultCommute(x: BigInt, y: BigInt, z: BigInt): Boolean = {
+  require(z >= 0)
+  exp(x * y, z) == exp(x, z) * exp(y, z) because {
+    if      (x == 0) trivial
+    else if (y == 0) trivial
+    else if (z == 0) trivial
+    else             check {
+      x * y * exp(x * y, z - 1) ==
+        x * exp(x, z - 1) * y * exp(y, z - 1) because
+        expMultCommute(x, y, z - 1)
+    }
+  }
+}.holds
+
          +
          +
          +
          +

          Relational reasoning

          +

          The majority of the example propositions we have seen so far related +some expression (e.g. l.reverse ++ Nil() or exp(x, y)) to some +other expression (e.g. ... == l1 or ... >= 0). This is +certainly a common case among the sorts of propositions about +functions and data structures one might wish to prove. The proofs of +such propositions typically involve some form of relational +reasoning, i.e. reasoning involving properties (such as transitivity, +reflexivity or symmetry) of the relations in question. Stainless knows +about these properties for built-in relations such as == or orders +on numbers. For user-defined relations, they first need to be +established as lemmas. In this section, we discuss how to make +effective use of built-in relations, but the general principles extend +to their user-defined counterparts.

          +

          When working with simple structural equality, we can rely on the default == +operator and Stainless will happily understand when the reflexivity, symmetry and +transitivity properties apply and use them to conclude bigger proofs. Similarly, +when working on BigInt, Stainless knows about reflexivity, antisymmetry and +transitivity over >= or <=, and also antireflexivity, antisymmetry +and transitivity of > and <.

          +

          However, even for relatively simple proofs about ADTs, Stainless needs +hints when combining, say equality, with user-defined operations, such +as ++ or reverse on lists. For example, Stainless is not able to +verify that the following holds for arbitrary pairs of lists l1 +and l2:

          +
          (l1 ++ l2).reverse == l2.reverse ++ l1.reverse
+
          +
          +

          The hard part of giving hints to Stainless is often to find them in the +first place. Here we can apply a general principle on top of +structural induction (as discussed in the previous section): we start +from the left-hand side of an equation and build a chain of +intermediate equations to the right-hand side. Using check +statements we can identify where Stainless times out and hence potentially +needs hints.

          +
          def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = {
+  ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because {
+    l1 match {
+      case Nil() =>
+        /* 1 */ check { (Nil() ++ l2).reverse == l2.reverse                  } &&
+        /* 2 */ check { l2.reverse            == l2.reverse ++ Nil()         } &&
+        /* 3 */ check { l2.reverse ++ Nil()   == l2.reverse ++ Nil().reverse }
+      case Cons(x, xs) =>
+        /* 4 */ check { ((x :: xs) ++ l2).reverse       == (x :: (xs ++ l2)).reverse       } &&
+        /* 5 */ check { (x :: (xs ++ l2)).reverse       == (xs ++ l2).reverse :+ x         } &&
+        /* 6 */ check { (xs ++ l2).reverse :+ x         == (l2.reverse ++ xs.reverse) :+ x } &&
+        /* 7 */ check { (l2.reverse ++ xs.reverse) :+ x == l2.reverse ++ (xs.reverse :+ x) } &&
+        /* 8 */ check { l2.reverse ++ (xs.reverse :+ x) == l2.reverse ++ (x :: xs).reverse }
+    }
+  }
+}.holds
+
          +
          +

          If we run the above code with a decent timeout, Stainless reports four +UNKNOWN cases: the postcondition of the reverseAppend function itself and +checks number 2, 6 and 7.

          +
          +
            +

          • Check #2 fails because, as we saw earlier, Stainless is not capable of +guessing the rightUnitAppend lemma by itself. We fix this case +by simply instantiating the lemma, i.e. by appending && +rightUnitAppend(l2.reverse) to the base case.

            • +

          • Check #6 fails because, at this point, we need to inject the +induction hypothesis on xs and l2 by adding && +reverseAppend(xs, l2).

            • +

          • Finally, check #7 fails for a similar reason as check #2: we need +an additional “associativity” lemma to prove that (l1 ++ l2) :+ t +== l1 ++ (l2 :+ t) holds for any l1, l2 and t. We +call this lemma snocAfterAppend and leave it as an exercise for +the reader.

            • +
          +
          +

          Once we have a valid proof, we can try to optimize it for readability. +As it stands, the resulting code is rather verbose because both sides +of most equations are duplicated. One option is to completely remove +the equations (they are implied by the instantiations of the lemmas) +and simply write

          +
          def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = {
+  ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because {
+    l1 match {
+      case Nil() =>
+        rightUnitAppend(l2.reverse)
+      case Cons(x, xs) =>
+        reverseAppend(xs, l2) && snocAfterAppend(l2.reverse, xs.reverse, x)
+    }
+  }
+}.holds
+
          +
          +

          Or we can employ the equational reasoning DSL provided by the +stainless.proofs package to remove the duplicate expressions and +interleave the equations with their associated proofs. This has the +advantage of not losing information that is still useful for a human +being reading the proof later on:

          +
          def reverseAppend[T](l1: List[T], l2: List[T]): Boolean = {
+  ( (l1 ++ l2).reverse == l2.reverse ++ l1.reverse ) because {
+    l1 match {
+      case Nil() => {
+        (Nil() ++ l2).reverse         ==| trivial                     |
+        l2.reverse                    ==| rightUnitAppend(l2.reverse) |
+        l2.reverse ++ Nil()           ==| trivial                     |
+        l2.reverse ++ Nil().reverse
+      }.qed
+      case Cons(x, xs) => {
+        ((x :: xs) ++ l2).reverse         ==| trivial               |
+        (x :: (xs ++ l2)).reverse         ==| trivial               |
+        (xs ++ l2).reverse :+ x           ==| reverseAppend(xs, l2) |
+        (l2.reverse ++ xs.reverse) :+ x   ==|
+          snocAfterAppend(l2.reverse, xs.reverse, x)                |
+        l2.reverse ++ (xs.reverse :+ x)   ==| trivial               |
+        l2.reverse ++ (x :: xs).reverse
+      }.qed
+    }
+  }
+}.holds
+
          +
          +

          The idea is to group statements in a block +({ }) and call qed on it. Then, instead of writing a == b && b == c +&& hint1 && hint2 we write a ==| hint1 | b ==| hint2 | c. And when no +additional hint is required, we can use trivial which simply stands for +true.

          +

          Additionally, by using this DSL, we get the same feedback granularity from Stainless +as if we had used check statements. This way we can construct proofs based +on equality more easily and directly identify where hints are vital.

          +

          One shortcoming of the relational reasoning DSL is that it relies on +Stainless’ knowledge of the relational properties of the built-in +relations, and in particular those of equality. Consequently it works +badly (if at all) with user-defined relations. However, since the DSL +is defined as a library (in library/proof/package.scala), it can +in principle be extended and modified to include specific user-defined +relations on a case-by-case basis.

          +
          +
          +

          Limits of the approach: HOFs, quantifiers and termination

          +

          While the techniques discussed in this section are useful in general, +their applicability has, of course, its limitations in practice. These +limitations are mostly due to Stainless’ limited support for certain +language constructs, such as higher-order functions (HOFs) or +quantifiers (which in turn is due, mostly, to the limited support of +the corresponding theories in the underlying SMT solvers).

          +

          Still, even using these “experimental” features, one manages to prove +some interesting propositions. Here is another list example, which +relates the foldLeft, foldRight and reverse operations +defined on lists and makes crucial use of HOFs:

          +
          import stainless.collection._
+import stainless.lang._
+import stainless.proof._
+
+def folds[A, B](xs: List[A], z: B, f: (B, A) => B): Boolean = {
+  val f2 = (x: A, z: B) => f(z, x)
+  xs.foldLeft(z)(f) == xs.reverse.foldRight(z)(f2) because {
+    xs match {
+      case Nil() => true
+      case Cons(x, xs) => {
+        (x :: xs).foldLeft(z)(f)              ==| trivial               |
+        xs.foldLeft(f(z, x))(f)               ==| folds(xs, f(z, x), f) |
+        xs.reverse.foldRight(f(z, x))(f2)     ==| trivial               |
+        xs.reverse.foldRight(f2(x, z))(f2)    ==|
+          snocFoldRight(xs.reverse, x, z, f2)                           |
+        (xs.reverse :+ x).foldRight(z)(f2)    ==| trivial               |
+        (x :: xs).reverse.foldRight(z)(f2)
+      }.qed
+    }
+  }
+}.holds
+
          +
          +

          A rather different, more general issue that arises when proving +propositions using Stainless is related to termination checking. When +verifying inductive proofs (and more generally the postconditions of +recursive methods), Stainless assumes that the corresponding proofs are +well-founded, or equivalently, that the corresponding recursive +methods terminate on all inputs. It is thus possible – and indeed rather +easy – to write bogus proofs (intentionally or accidentally) which +Stainless recognizes as valid, but which are not well-founded. Consider +the following lemma, which apparently establishes that all lists are +empty:

          +
          import stainless.collection._
+import stainless.lang._
+import stainless.proof._
+
+object NotWellFounded {
+
+  // This proof is not well-founded.  Since Stainless doesn't run the
+  // termination checker by default, it will accept the proof as
+  // valid.
+  def allListsAreEmpty[T](xs: List[T]): Boolean = {
+    xs.isEmpty because {
+      xs match {
+        case Nil()       => trivial
+        case Cons(x, xs) => allListsAreEmpty(x :: xs)
+      }
+    }
+  }.holds
+}
+
          +
          +

          Stainless hences performs termination checking by default to minimize +the risk of accidentally writing bogus proofs such as the one above. +It will thus emit a warning if it cannot prove that a function terminates, or +if it can show that its measure (inferred or user-defined) does not decreases between +recursive calls.

          +
          +
          +
          +

          Techniques for proving non-trivial postconditions

          +

          When proving a mathematical lemma, the return type of the +corresponding function is most of +the time, if not always, Boolean. For those proofs it is rather easy to +write a postcondition: using holds is generally enough.

          +

          But when it comes to writing postconditions for more general functions, such as +the addition of rational numbers, we are no longer dealing with Boolean so +we need a strategy to properly write ensuring statements.

          +
          +

          Rationals: a simple example

          +

          Let’s take rational numbers as an example: we define them as a case class with +two attributes, n for the numerator and d for the denominator. We also +define three simple properties on them: isRational, isNonZero and +isPositive.

          +
          case class Rational(n: BigInt, d: BigInt) {
+  def isRational = d != 0
+  def isPositive = isRational && (n * d >= 0)
+  def isNonZero  = isRational && (n != 0)
+
+  // ...
+}
+
          +
          +

          And on top of that, we want to support addition on Rational in a way that +the rationality and positiveness properties are correctly preserved:

          +
          def +(that: Rational): Rational = {
+  require(isRational && that.isRational)
+  Rational(n * that.d + that.n * d, d * that.d)
+} ensuring { res =>
+  res.isRational &&
+  (this.isPositive == that.isPositive ==> res.isPositive == this.isPositive)
+}
+
          +
          +

          In this simple case, things work nicely and we can write the +multiplication in a similar fashion:

          +
          def *(that: Rational): Rational = {
+  require(isRational && that.isRational)
+  Rational(n * that.n, d * that.d)
+} ensuring { res =>
+  res.isRational &&
+  (res.isNonZero  == (this.isNonZero && that.isNonZero)) &&
+  (res.isPositive == (!res.isNonZero || this.isPositive == that.isPositive))
+}
+
          +
          +
          +
          +

          Measures: a slightly more complex example

          +

          Now let’s look at a slightly more complex example: measures on +discrete probability spaces. We represent such measures using a +List-like recursive data structure: a generic abstract class +Meas[A] that has two subclasses, Empty[A] and Cons[A]. +The constructor of the class Empty[A] takes no arguments; it +represents an “empty” measure that evaluates to 0 when applied to any +set of values of type A. The constructor of Cons[A], on the +other hand, takes three parameters: a value x, its associated +weight w expressed as a Rational (since Stainless doesn’t quite yet +support real numbers out of the box), and another measure m on +A. The value Cons(x, w, m) represents the measure obtained by +adding to m the “single-point” measure that evaluates to w at +x and to 0 everywhere else. We also define an isMeasure +property – similar to the isRational property presented above – +which recursively checks that all the weights in a measure are +positive rationals (note that all our measures have finite support).

          +
          /** Measures on discrete probability spaces. */
+sealed abstract class Meas[A] {
+
+  /** All weights must be positive. */
+  def isMeasure: Boolean = this match {
+    case Empty()       => true
+    case Cons(x, w, m) => w.isPositive && m.isMeasure
+  }
+
+  // ...
+}
+
+/** The empty measure maps every subset of the space A to 0. */
+case class Empty[A]() extends Meas[A]
+
+/**
+ * The 'Cons' measure adjoins an additional element 'x' of type 'A'
+ * to an existing measure 'm' over 'A'.  Note that 'x' might already
+ * be present in 'm'.
+ */
+case class Cons[A](x: A, w: Rational, m: Meas[A]) extends Meas[A]
+
          +
          +

          The defining operation on a measure m is its evaluation m(xs) +(or equivalently m.apply(xs)) on some set xs: Set[A], i.e. on a +subset of the “space” A. The value of m should be a positive +rational for any such set xs, provided m.isMeasure holds. +This suggests _.isPositive as the postcondition for apply, +but simply claiming that the result is positive is not enough for Stainless +to verify this postcondition.

          +

          We can provide the necessary hint to Stainless by performing structural +induction on this inside the postcondition as follows:

          +
          /** Compute the value of this measure on a subset of the space 'A'. */
+def apply(xs: Set[A]): Rational = {
+  require (isMeasure)
+  this match {
+    case Empty()       => Rational(0, 1)
+    case Cons(x, w, m) => if (xs contains x) w + m(xs) else m(xs)
+  }
+} ensuring { res =>
+  res.isPositive because {
+    this match {
+      case Empty()       => trivial
+      case Cons(x, w, m) => m(xs).isPositive
+    }
+  }
+}
+
          +
          +

          Notice the similarity between the pattern match in the body of the +apply function and that in the postcondition. With this hint, +Stainless is able to verify the postcondition.

          +
          +
          +
          +

          A complex example: additivity of measures

          +

          Using the principles and techniques discussed so far, one can prove +quite advanced propositions using Stainless. Returning to the +measure-theoretic example from the previous section, we would like to +prove that our implementation of measures is properly additive. +Formally, a measure \(\mu \colon A \to \mathbb{R}\) on a countable +set \(A\) must fulfill the following additivity property +3:

          +
          +\[\forall A_1, A_2 \subseteq A . A_1 \cap A_2 = \emptyset \Rightarrow +\mu(A_1 \cup A_2) = \mu(A_1) + \mu(A_2)\]
          +

          which we can express in Stainless as

          +
          def additivity[A](m: Meas[A], xs: Set[A], ys: Set[A]): Boolean = {
+  require(m.isMeasure && (xs & ys).isEmpty)
+  m(xs ++ ys) == m(xs) + m(ys)
+}.holds
+
          +
          +

          We can prove this property using structural induction on the parameter +m, case analysis on the parameters xs and ys, equational +reasoning, and properties of rational numbers (in the form of +user-defined lemmas) as well as sets (using Stainless’s built-in support).

          +
          def additivity[A](m: Meas[A], xs: Set[A], ys: Set[A]): Boolean = {
+  require(m.isMeasure && (xs & ys).isEmpty)
+  m(xs ++ ys) == m(xs) + m(ys) because {
+    m match {
+      case Empty()       => trivial
+      case Cons(x, w, n) => if (xs contains x) {
+        w + n(xs ++ ys)     ==| additivity(n, xs, ys)        |
+        w + (n(xs) + n(ys)) ==| plusAssoc(w, n(xs), n(ys))   |
+        (w + n(xs)) + n(ys) ==| !(ys contains x)             |
+        m(xs)       + m(ys)
+      }.qed else if (ys contains x) {
+        w + n(xs ++ ys)     ==| additivity(n, xs, ys)        |
+        w + (n(xs) + n(ys)) ==| plusComm(w, (n(xs) + n(ys))) |
+        (n(xs) + n(ys)) + w ==| plusAssoc(n(xs), n(ys), w)   |
+        n(xs) + (n(ys) + w) ==| plusComm(n(ys), w)           |
+        n(xs) + (w + n(ys)) ==| !(xs contains x)             |
+        m(xs) + m(ys)
+      }.qed else {
+        n(xs ++ ys)         ==| additivity(n, xs, ys)        |
+        n(xs) + n(ys)
+      }.qed
+    }
+  }
+}.holds
+
          +
          +

          The full proof (including the proofs of all helper lemmas) as well as +its generalization to sub-additivity can be found in the +testcases/verification/proof/measure/ directory of the Stainless +distribution 1.

          +
          +
          +

          Quick Recap

          +

          Let’s summarize what we’ve learned here. To write proofs efficiently, +it’s good to keep the following in mind:

          +
            +

          1. Always use a proper timeout and ask Stainless for more information about +what he tries to verify, e.g. --timeout=5 --debug=verification.

            2. +

          2. Use @induct when working on structurally inductive proofs to +get a more precise feedback from Stainless: this will decompose the +proof into a base case and an inductive case for the first argument +of the function under consideration.

            +

            If Stainless isn’t able to verify the proof using @induct, try +performing manual case analysis.

            +
            3. +

          3. Modularize your proofs and verify sub-goals!

            +
              +

            • use plenty of helper lemmas;

              • +

            • use check abundantly;

              • +

            • if possible use the relational reasoning DSL presented above.

              • +
            +

            This is especially handy when you can connect the two sides of a relational +claim with sub-statements.

            +
            4. +
          +

          Footnotes

          +
          +
          1(1,2)
          +

          The source code of this example and all others in +this chapter is included in the Stainless distribution. Examples about +lists can be found in library/collection/List.scala, other +examples are located in the testcases/verification/proof/ +directory.

          +
          +
          2
          +

          Propositions and proofs +live in the same universe in Stainless. This is contrary to +e.g. type-theoretic proof assistants where propositions are +represented by types and proofs are terms inhabiting such types.

          +
          +
          3
          +

          To be precise, we are assuming here the underlying +measurable space \((A, \mathcal{P}(A))\), where \(A\) is +countable and \(\mathcal{P}(A)\) denotes its discrete σ-algebra +(i.e. the power set of \(A\)).

          +
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/objects.inv b/objects.inv new file mode 100644 index 0000000000..7d69f592b3 Binary files /dev/null and b/objects.inv differ diff --git a/options.html b/options.html new file mode 100644 index 0000000000..943e372500 --- /dev/null +++ b/options.html @@ -0,0 +1,471 @@ + + + + + + + Specifying Options — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          Specifying Options

          +

          Stainless’s command line options have the form --option or --option=value. +To enable a flag option, use --option=true or on or yes, +or just --option. To disable a flag option, use --option=false.

          +

          Additionally, if you need to pass options to the scalac frontend of Stainless, +you can do it by using a single dash -. For example, try -Ybrowse:typer.

          +

          The rest of this section presents some of the command-line options that Stainless recognizes. +For a short (but always up-to-date) summary, you can also invoke stainless --help.

          +
          +

          Choosing which Stainless feature to use

          +

          The first group of options determines which feature of Stainless will be used. +By default, --verification is chosen.

          +
            +

          • --verification

            +

            Proves or disproves function contracts, as explained in the Verification conditions section.

            +
            • +

          • --eval

            +

            Evaluate parameterless functions and report their body’s value and whether +or not their postcondition holds.

            +
            • +

          • --genc

            +

            Convert stainless code to C (implies –batched, default: false). +See documentation section for generating C code.

            +
            • +

          • --coq

            +

            Transform the program into a Coq program, and let Coq generate subgoals automatically

            +
            • +

          • --type-checker

            +

            Use type checker inspired by System FR to generate verification conditions. +Default is true and is strongly recommended; using false reverts to +an old verification-condition generator.

            +
            • +

          • --infer-measures=[yes|no|only] (default: yes)

            +

            Infers measures for recursive functions which do not already have one.

            +
            • +

          • --check-measures=[true|false] (default: true)

            +

            Check termination of functions with measures, ie. whether measures decrease between recursive calls.

            +
            • +

          • --testgen

            +

            Proves or disproves function contracts (like --verification) and attempts to create Scala test cases from reported counter-examples.

            +
            • +

          • --genc-testgen

            +

            Like --testgen, but generates C test cases using GenC.

            +
            • +

          • --help

            +

            Prints a helpful message, then exits.

            +
            • +
          +
          +
          +

          Additional top-level options

          +

          These options are available to all Stainless components:

          +
            +

          • --watch

            +

            Re-run the selected analysis components upon file changes, making the program analysis +interactive and significantly more efficient than restarting stainless manually.

            +
            • +

          • --no-colors

            +

            Disable colored output and non-ascii characters (consider this option for better support in IDEs)

            +
            • +

          • --compact

            +

            Reduces the components’ summaries to only the invalid elements (e.g. invalid VC).

            +
            • +

          • --debug=d1,d2,...

            +

            Enables printing detailed messages for the components d1,d2,… . +Available components include:

            +
              +

            • solver (SMT solvers and their wrappers)

              • +

            • termination (Termination analysis)

              • +

            • timers (Timers, timer pools)

              • +

            • trees (Manipulation of trees)

              • +

            • verification (Verification)

              • +

            • full-vc (Display VCs before and after simplification)

              • +

            • type-checker (Type checking of the final program for VC generation)

              • +

            • type-checker-vcs (Generation of VCs by the type-checker)

              • +

            • derivation (Dump typing derivations)

              • +
            +
            • +

          • --functions=f1,f2,...

            +

            Only consider functions f1, f2, … . This applies to all functionalities +where Stainless manipulates the input in a per-function basis.

            +

            Stainless will match against suffixes of qualified names. For instance: +--functions=List.size will match the method stainless.collection.List.size, +while --functions=size will match all methods and functions named size. +This option supports _ as wildcard: --functions=List._ will +match all List methods.

            +
            • +

          • --solvers=s1,s2,...

            +

            Use solvers s1, s2,… . If more than one solver is chosen, all chosen +solvers will be used in parallel, and the best result will be presented. +By default, the nativez3 solver is picked.

            +

            Some solvers are specialized in proving verification conditions +and will have a hard time finding a counterexample in the case of an invalid +verification condition, whereas some are specialized in finding +counterexamples, and some provide a compromise between the two. +Also, some solvers do not as of now support higher-order functions.

            +

            Available solvers include:

            +
              +

            • nativez3

              +

              Native Z3 with z3-templates for unfolding recursive functions (default).

              +
              • +

            • smt-cvc5

              +

              cvc5 through SMT-LIB. An algorithm within Stainless takes up the unfolding +of recursive functions, handling of lambdas etc. To use this or any +of the following cvc5-based solvers, you need to have the cvc5 +executable in your system path (the latest unstable version is recommended).

              +
              • +

            • smt-z3

              +

              Z3 through SMT-LIB. To use this or the next solver, you need to +have the z3 executable in your program path (the latest stable version +is recommended). Inductive reasoning happens on the Stainless side +(similarly to smt-cvc5).

              +
              • +

            • unrollz3

              +

              Native Z3, but inductive reasoning happens within Stainless (similarly to smt-z3).

              +
              • +

            • princess

              +

              Princess solver through its native interface (uses princess-templates) during +unfolding. This is a full-stack JVM solver and enables Stainless to run without +external solver dependencies.

              +
              • +
            +
            • +

          • --timeout=t

            +

            Set a timeout for each attempt to prove one verification condition/ +repair one function (in sec.) When using the --eval component, one +should use --max-calls instead.

            +
            • +

          • --cache

            +

            Use persistent cache on disk to save the state of the verification and/or +termination analyses.

            +
            • +

          • --cache-dir=<directory>

            +

            Specify in which directory the cache files generated by --cache and other +options should be stored. Defaults to .stainless-cache/.

            +
            • +

          • --json=<file>

            +

            Export the verification and/or termination analyses to the given file.

            +
            • +

          • --extra-deps=org:name_scalaVersion:version,...

            +

            Fetch the specified dependencies, and add their sources to the set of files +processed by Stainless. Each dependency must be available as a source JAR +from MavenCentral, the EPFL-LARA bintray organization, your local Ivy database, +or through another resolver specified via --extra-resolvers.

            +

            Note: Stainless will not pull transitive dependencies, so one has to specify +all transitive dependencies explicitely via this option.

            +

            Example: --extra-deps=ch.epfl.lara:stainless-algebra_2.12:0.1.2

            +
            • +

          • --extra-resolvers=URL,...

            +

            Specify additional resolvers to be used to fetch the dependencies specified via +the --extra-deps option.

            +

            Note: The full URL of the resolver must be used.

            +

            Example: --extra-resolvers=https://oss.sonatype.org/content/repositories/snapshots/

            +

            See the Coursier source code for the list of most common repositories URLs.

            +
            • +
          +
          +
          +

          Additional Options (by component)

          +

          The following options relate to specific components in Stainless.

          +
          +

          Verification

          +
            +

          • --strict-aritmetic

            +

            Check arithmetic operations for unintended behaviour and +overflows. Note that reasoning about bitvectors is sound +even if this option is false, but in that case no warnings +are generated for overflows and underflows because these +have well-defined semantics in Scala.

            +
            • +

          • --vc-cache

            +

            Use a persistent cache mechanism to speed up verification; on by default.

            +
            • +

          • --fail-early

            +

            Aborts verification as soon as a VC cannot be proven to be correct.

            +
            • +

          • --fail-invalid

            +

            Aborts verification as soon as an invalid VC is found.

            +
            • +
          +
          +
          +

          Termination

          +
            +

          • --ignore-posts

            +

            Ignore postconditions during termination verification.

            +
            • +
          +
          +
          +

          Unrolling Solver

          +
            +

          • --check-models

            +

            Double-check counterexamples with the evaluator.

            +
            • +

          • --feeling-lucky

            +

            Use evaluator to find counterexamples early.

            +
            • +

          • --unroll-assumptions

            +

            Use unsat-assumptions to drive unrolling while remaining fair.

            +
            • +

          • --silent-errors

            +

            Don’t crash on errors, simply return Unknown.

            +
            • +

          • --unroll-factor=n

            +

            Speeds up unrolling by a factor n.

            +
            • +

          • --model-finding=n

            +

            Boosts model-finding capabilities by a factor n. This may come at +the cost of proof construction.

            +
            • +

          • --no-simplifications

            +

            Disables program simplification heuristics.

            +
            • +
          +
          +
          +

          cvc5 Solver

          +
            +

          • --solver:cvc5=<cvc5-opt>

            +

            Pass extra command-line arguments to cvc5.

            +
            • +
          +
          +
          +

          Evaluators

          +
            +

          • --codegen

            +

            Use compiled evaluator instead of an interpreter.

            +
            • +

          • --small-arrays

            +

            Assume all arrays can fit into memory during compiled evaluation.

            +
            • +

          • --instrument

            +

            Instrument ADT field access during code generation.

            +
            • +

          • --max-calls=n

            +

            Bounds the total number of function call evaluations (before crashing).

            +
            • +

          • --ignore-contracts

            +

            Ignores function contracts during evaluation.

            +
            • +
          +
          +
          +

          Tests generation

          +
            +

          • testgen-file=<file>

            +

            Specifies the output file for the generated tests.

            +
            • +

          • genc-testgen-includes=header1.h,header2,...

            +

            Only applies for --genc-testgen. Indicates the headers to #include in the generated test file.

            +
            • +
          +
          +
          +
          +

          Configuration File

          +

          Stainless supports setting default values for command line options configuration files. +To specify configuration file you can use the option `--config-file=FILE. The default is +stainless.conf or .stainless.conf. The file should be a valid HOCON file.

          +

          For example, consider the config file containin the following lines:

          +
          vc-cache = false
+debug = [verification, trees]
+timeout = 5
+check-models = true
+print-ids = true
+
          +
          +

          The file will translate to the following command line options:

          +

          --vc-cache=false --debug=verification,trees --timeout=5 --print-ids

          +

          Stainless searches for a configuration file recursively +starting from the current directory and walking up the +directory hierarchy. For example, if one runs stainless +from /a/b/c and there is a config file in any of c, +b or a, the first of those is going to be loaded.

          +
          +
          +

          Library Files

          +
          +

          Purpose of library files

          +

          Stainless contains library source Scala files that define types and functions that are meant to be always available +via import statements such as import stainless.lang._, import stainless.annotation._, +import stainless.collection._, and so on. Many of these types have special treatment inside the extraction +pipeline and will map directly to mathematical data types of the underlying SMT solvers. +At build time, the build.sbt script computes the list of these files by traversing the frontends/library/ directory.

          +
          +
          +

          Changing the list of library files

          +

          To support further customization, if at run time stainless finds +a file libfiles.txt in the current directory, it replaces the list of library files files with the list contained +in this file, one file per line, with paths relative to the directory frontends/library/. For example, libfiles.txt +may contain:

          +
          stainless/util/Random.scala
+stainless/lang/Option.scala
+stainless/lang/StaticChecks.scala
+stainless/lang/Real.scala
+stainless/lang/Either.scala
+stainless/lang/Set.scala
+stainless/lang/MutableMap.scala
+stainless/lang/package.scala
+stainless/lang/Bag.scala
+stainless/lang/Map.scala
+stainless/collection/List.scala
+stainless/math/BitVectors.scala
+stainless/math/Nat.scala
+stainless/math/package.scala
+stainless/io/StdIn.scala
+stainless/io/package.scala
+stainless/annotation/annotations.scala
+stainless/annotation/isabelle.scala
+stainless/annotation/cCode.scala
+stainless/proof/Internal.scala
+stainless/proof/package.scala
+
          +
          +

          Shortening this list may reduce the startup time, but also cause Stainless to not work propertly, so +using the --watch and --functions options is the first option to try.

          +

          For further customization by advanced users, please examine the build.sbt file.

          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/purescala.html b/purescala.html new file mode 100644 index 0000000000..653b832a37 --- /dev/null +++ b/purescala.html @@ -0,0 +1,934 @@ + + + + + + + Pure Scala — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +
          +
          +

          Pure Scala

          +

          The input to Stainless is a purely functional subset of Scala, which we call +Pure Scala. Constructs specific for Stainless are defined inside +Stainless’s libraries in package stainless and its subpackages. +Stainless invokes standard scalac compiler on the input file, then +performs additional checks to ensure that the given program +belongs to Pure Scala.

          +

          Pure Scala supports two kinds of top-level declarations:

          +
            +

          1. Algebraic Data Type (ADT) definitions in the form of an +abstract class and case classes/objects

            2. +
          +
          abstract class MyList
+case object MyEmpty extends MyList
+case class MyCons(elem: BigInt, rest: MyList) extends MyList
+
          +
          +
            +

          1. Objects/modules, for grouping classes and functions

            2. +
          +
          object Specs {
+   def increment(a: BigInt): BigInt = {
+      a + 1
+   }
+
+   case class Identifier(id: BigInt)
+}
+
          +
          +
          +

          Booleans

          +

          Booleans are used to express truth conditions in Stainless. +Unlike some proof assistants, there is no separation +at the type level between +Boolean values and the truth conditions of conjectures +and theorems.

          +

          Typical propositional operations are available using Scala +notation, along +with a new shorthand for implication. The if expression +is also present.

          +
          a && b
+a || b
+a == b
+!a
+a ==> b // Stainless syntax for boolean implication
+
          +
          +

          Stainless uses short-circuit interpretation of &&, ||, and ==>, +which evaluates the second argument only when needed:

          +
          a && b  === if (a) b else false
+
+a || b  === if (a) true else b
+
+a ==> b === if (a) b else true
+
          +
          +

          This aspect is important because of:

          +
            +

          1. evaluation of expressions, which is kept compatible with Scala

            2. +
          +

          2. verification condition generation for safety: arguments of Boolean operations +may be operations with preconditions; these preconditions apply only in case +that the corresponding argument is evaluated.

          +
            +

          1. termination checking, which takes into account that only one of the paths in an if expression is evaluated for a given truth value of the condition.

            2. +
          +
          +
          +

          Algebraic Data Types

          +
          +

          Abstract Classes

          +

          ADT roots need to be defined as abstract, unless the ADT is defined with only one case class/object. Unlike in Scala, abstract classes cannot define fields or constructor arguments.

          +
          abstract class MyType
+
          +
          +

          An abstract class can be extended by other abstract classes.

          +
          +
          +

          Case Classes

          +

          The abstract root can also be extended by a case-class, defining several fields:

          +
          case class MyCase1(f: Type, f2: MyType) extends MyType
+case class MyCase2(f: Int) extends MyType
+
          +
          +
          +

          Note

          +

          You can also define single case-class, for Tuple-like structures.

          +
          +

          You can add invariants to case classes using a require clause, as follows:

          +
          case class Positive(value: BigInt = 0) {
+  require(value >= 0)
+}
+
          +
          +

          For classes without type parameters, when all fields have a default value, Stainless generates a +verification condition to check that the default instance respects the invariant. In this example, +the verification condition will be seen as coming from an internal function called +PositiveRequireForDefault.

          +
          +

          Note

          +

          Invariants are only allowed to refer to fields of their class, and +cannot call any methods on this (but calls to methods on their +fields are allowed).

          +
          +
          +
          +

          Case Objects

          +

          It is also possible to defined case objects, without fields:

          +
          case object BaseCase extends MyType
+
          +
          +
          +
          +

          Value Classes

          +

          One can define a value class just like in standard Scala, +by extending the AnyVal class.

          +
          case class Positive(value: BigInt) extends AnyVal {
+  @invariant
+  def isPositive: Boolean = value >= 0
+}
+
          +
          +

          In the code block above, we also specify an invariant of the value +class, using the @invariant annotation. Such invariants are +subsequently lifted into a refinement type of the underlying type.

          +
          +

          Note

          +

          Same remark as above: invariants are only allowed to refer to fields of their class.

          +
          +
          +
          +
          +

          Generics

          +

          Stainless supports type parameters for classes and functions.

          +
          object Test {
+  abstract class List[T]
+  case class Cons[T](hd: T, tl: List[T]) extends List[T]
+  case class Nil[T]() extends List[T]
+
+  def contains[T](l: List[T], el: T) = { ... }
+}
+
          +
          +
          +

          Note

          +

          Type parameters can also be marked as co- or contra-variant, eg.

          +
          abstract class List[+T]
+case class Cons[T](hd: T, tl: List[T]) extends List[T]
+case object Nil extends List[Nothing]
+
          +
          +
          +
          +
          +

          Methods

          +

          You can define methods in classes.

          +
          abstract class List[T] {
+  def contains(e: T) = { .. }
+}
+
+case class Cons[T](hd: T, tl: List[T]) extends List[T]
+case object Nil extends List[Nothing]
+
+def test(a: List[Int]) = a.contains(42)
+
          +
          +

          It is possible to define abstract methods in abstract classes and implement them in case classes. +Multiple layers of inheritance are allowed, as is the ability to override concrete methods.

          +
          abstract class A {
+  def x(a: Int): Int
+}
+
+abstract class B extends A {
+  def x(a: Int) = {
+    require(a > 0)
+    42
+  } ensuring { _ >= 0 }
+}
+
+case class C(c: Int) extends B {
+  override def x(i: Int) = {
+    require(i >= 0)
+    if (i == 0) 0
+    else c + x(i-1)
+  } ensuring ( _ == c * i )
+}
+
+case class D() extends B
+
          +
          +

          It is also possible to call methods of a superclass with the super keyword.

          +
          sealed abstract class Base {
+  def double(x: BigInt): BigInt = x * 2
+}
+
+case class Override() extends Base {
+  override def double(x: BigInt): BigInt = {
+    super.double(x + 1) + 42
+  }
+}
+
          +
          +

          Abstract methods may have contracts in terms of pre- and postconditions. The +syntax uses ??? and is as follows:

          +
          abstract class Set[T] {
+  def contains[T](t: T): Boolean
+
+  def add[T](t: T): Set[T] = {
+    require(!this.contains(t))
+    (??? : Set[T])
+  }.ensuring(res => res.contains(t))
+}
+
          +
          +

          You can then extend such abstract classes by concrete implementations, and +Stainless will generate verification conditions to make sure that the +implementation respects the specification.

          +

          You can also add implementations and assume that they are correct with respect +to the specification of the abstract class, without having Stainless check the +specification (e.g. if you want to use existing Scala data-structures inside). +In that case, mark the concrete class with @extern (see Section Working With Existing Code +for more info on @extern) or place the concrete implementation in files +which are not inspected by Stainless (see e.g. +https://github.com/epfl-lara/stainless-project.g8 for an example of how to setup +such a hybrid project).

          +
          +

          Copy Method

          +

          The copy method of classes with immutable fields is extracted as well, +and ensures that the class invariant (if any) is maintained by requiring it +to be satisfied as a precondition.

          +
          case class Foo(x: BigInt) {
+  require(x > 0)
+}
+
+def prop(foo: Foo, y: BigInt) = {
+  require(y > 1)
+  foo.copy(x = y)
+}
+
          +
          +
          +

          Note

          +

          The example above would not verify without the precondition in function prop, +as Foo require its field x to be positive.

          +
          +
          +
          +

          Initialization

          +

          In Pure Scala, initialization of val’s may not have future or self-references:

          +
          object Initialization {
+  case class C(x: BigInt) {
+    val y = x       // ok
+    val z = y + x   // ok
+    val a = b       // Error: "because field `a` can only refer to previous fields, not to `b`"
+    val b = z + y   // ok
+  }
+}
+
          +
          +
          +
          +

          Overriding

          +

          Stainless supports overriding methods with some constraints: +* A val in an abstract class can only be overridden by a concrete class parameter. +* Methods and lazy val``s in abstract classes can be overridden by concrete methods or +``lazy val’s (interchangably), or by a concrete class parameter, but not by +a val.

          +

          Here are a few examples that are rejected by Stainless:

          +
          object BadOverride1 {
+  sealed abstract class Abs {
+    require(x != 0)
+    val x: Int
+  }
+
+  // Error: "Abstract values `x` must be overridden with fields in concrete subclass"
+  case class AbsInvalid() extends Abs {
+    def x: Int = 1
+  }
+}
+
          +
          +
          object BadOverride2 {
+  sealed abstract class Abs {
+    val y: Int
+  }
+
+  // Error: "Abstract values `y` must be overridden with fields in concrete subclass"
+  case class AbsInvalid() extends Abs {
+    val y: Int = 2
+  }
+}
+
          +
          +
          object BadOverride3 {
+  sealed abstract class AAA {
+    def f: BigInt
+  }
+
+  // Error: "because abstract methods BadOverride3.AAA.f were not overridden by
+  //         a method, a lazy val, or a constructor parameter"
+  case class BBB() extends AAA {
+    val f: BigInt = 0
+  }
+}
+
          +
          +
          +
          +

          Default Parameters

          +

          Functions and methods can have default values for their parameters.

          +
          def test(x: Int = 21): Int = x * 2
+
+assert(test() == 42) // valid
+
          +
          +
          +
          +
          +

          Type Definitions

          +
          +

          Type Aliases

          +

          Type aliases can be defined the usual way:

          +
          object testcase {
+  type Identifier = String
+
+  def newIdentifier: Identifier = /* returns a String */
+}
+
          +
          +

          Type aliases can also have one or more type parameters:

          +
          type Collection[A] = List[A]
+
+def singleton[A](x: A): Collection[A] = List(x)
+
          +
          +
          +
          +

          Type Members

          +

          Much like classes can have field members and method members, they can also +define type members. Much like other members, those can also be declared +abstract within an abstract class and overridden in implementations:

          +
          case class Grass()
+
+abstract class Animal {
+  type Food
+  val happy: Boolean
+  def eat(food: Food): Animal
+}
+
+case class Cow(happy: Boolean) extends Animal {
+  type Food = Grass
+  def eat(g: Grass): Cow = Cow(happy = true)
+}
+
          +
          +

          Note: Like regular type aliases, type members can also have one or more type parameters.

          +

          Type members then give rise to path-dependent types, where the type of a variable +can depend on another variable, by selecting a type member on the latter:

          +
          //                             Path-dependent type
+//                                 vvvvvvvvvvv
+def giveFood(animal: Animal)(food: animal.Food): Animal = {
+  animal.eat(food)
+}
+
+def test = {
+  val cow1 = Cow(false)
+  val cow2 = giveFood(cow1)(Grass())
+  assert(cow2.happy) // VALID
+}
+
          +
          +
          +
          +
          +

          Specifications

          +

          Stainless supports three kinds of specifications to functions and methods:

          +
          +

          Preconditions

          +

          Preconditions constraint the argument and is expressed using require. It should hold for all calls to the function.

          +
          def foo(a: Int, b: Int) = {
+  require(a > b)
+  ...
+}
+
          +
          +
          +
          +

          Postconditions

          +

          Postconditions constraint the resulting value, and is expressed using ensuring:

          +
          def foo(a: Int): Int = {
+  a + 1
+} ensuring { res => res > a }
+
          +
          +
          +
          +

          Body Assertions

          +

          Assertions constrain intermediate expressions within the body of a function.

          +
          def foo(a: Int): Int = {
+  val b = -a
+  assert(a >= 0 || b >= 0, "This will fail for -2^31")
+  a + 1
+}
+
          +
          +

          The error description (last argument of assert) is optional.

          +
          +
          +
          +

          Expressions

          +

          Stainless supports most purely-functional Scala expressions:

          +
          +

          Pattern matching

          +
          expr match {
+  // Simple (nested) patterns:
+  case CaseClass( .. , .. , ..) => ...
+  case v @ CaseClass( .. , .. , ..) => ...
+  case v : CaseClass => ...
+  case (t1, t2) => ...
+  case 42 => ...
+  case _ => ...
+
+  // can also be guarded, e.g.
+  case CaseClass(a, b, c) if a > b => ...
+}
+
          +
          +

          Custom pattern matching with unapply methods are also supported:

          +
          object :: {
+  def unapply[A](l: List[A]): Option[(A, List[A])] = l match {
+    case Nil() => None()
+    case Cons(x, xs) => Some((x, xs))
+  }
+}
+
+def empty[A](l: List[A]) = l match {
+  case x :: xs => false
+  case Nil() => true
+}
+
          +
          +
          +
          +

          Values

          +
          val x = ...
+
+val (x, y) = ...
+
+val Cons(h, _) = ...
+
          +
          +
          +

          Note

          +

          The latter two cases are actually syntactic sugar for pattern matching with one case.

          +
          +
          +
          +

          Inner Functions

          +
          def foo(x: Int) = {
+  val y = x + 1
+  def bar(z: Int) = {
+     z + y
+  }
+  bar(42)
+}
+
          +
          +
          +
          +

          Local and Anonymous Classes

          +

          Functions and methods can declare local classes, which can close over +the fields of the enclosing class, as well as the parameters of the enclosing +function or method.

          +
          abstract class Foo {
+  def bar: Int
+}
+
+def makeFoo(x: Int): Foo = {
+  case class Local() extends Foo {
+    def bar: Int = x
+  }
+  Local()
+}
+
          +
          +
          +

          Note

          +

          Functions and methods which return an instance of a local class +must have an explicit return type, which will typically be that of the parent class. +Otherwise, a structural type will be inferred by the Scala compiler, and those are +currently unsupported.

          +
          +

          Anonymous classes with an explicit parent are supported as well:

          +
          abstract class Foo {
+  def bar: Int
+}
+
+def makeFoo(x: Int): Foo = new Foo {
+  def bar: Int = x
+}
+
          +
          +
          +

          Note

          +

          Anonymous classes cannot declare more public members than their parent class, +ie. the following is not supported:

          +
          +
          abstract class Foo {
+  def bar: Int
+}
+
+def makeFoo(x: Int): Foo = new Foo {
+  def bar: Int = x
+  def hi: String = "Hello, world"
+}
+
          +
          +
          +
          +
          +

          Predefined Types

          +
          +

          TupleX

          +
          val x = (1,2,3)
+val y = 1 -> 2 // alternative Scala syntax for Tuple2
+x._1 // == 1
+
          +
          +
          +
          +

          Int

          +
          a + b
+a - b
+-a
+a * b
+a / b
+a % b // a modulo b
+a < b
+a <= b
+a > b
+a >= b
+a == b
+
          +
          +
          +

          Note

          +

          Integers are treated as 32bits integers and are subject to overflows.

          +
          +
          +
          +

          BigInt

          +
          val a = BigInt(2)
+val b = BigInt(3)
+
+-a
+a + b
+a - b
+a * b
+a / b
+a % b // a modulo b
+a < b
+a > b
+a <= b
+a >= b
+a == b
+
          +
          +
          +

          Note

          +

          BigInt are mathematical integers (arbitrary size, no overflows).

          +
          +
          +
          +

          Real

          +

          Real represents the mathematical real numbers (different from floating points). It is an +extension to Scala which is meant to write programs closer to their true semantics.

          +
          val a: Real = Real(2)
+val b: Real = Real(3, 5) // 3/5
+
+-a
+a + b
+a - b
+a * b
+a / b
+a < b
+a > b
+a <= b
+a >= b
+a == b
+
          +
          +
          +

          Note

          +

          Real have infinite precision, which means their properties differ from Double. +For example, the following holds:

          +
          def associativity(x: Real, y: Real, z: Real): Boolean = {
+  (x + y) + z == x + (y + z)
+} holds
+
          +
          +

          While it does not hold with floating point arithmetic.

          +
          +
          +
          +

          Set

          +
          import stainless.lang.Set // Required to have support for Sets
+
+val s1 = Set(1,2,3,1)
+val s2 = Set[Int]()
+
+s1 ++ s2 // Set union
+s1 & s2  // Set intersection
+s1 -- s2 // Set difference
+s1 subsetOf s2
+s1 contains 42
+
          +
          +
          +
          +

          Functional Array

          +
          val a = Array(1,2,3)
+
+a(index)
+a.updated(index, value)
+a.length
+
          +
          +
          +
          +

          Map

          +
          import stainless.lang.Map // Required to have support for Maps
+
+val  m = Map[Int, Boolean](42 -> false)
+
+m(index)
+m isDefinedAt index
+m contains index
+m.updated(index, value)
+m + (index -> value)
+m + (value, index)
+m.get(index)
+m.getOrElse(index, value2)
+
          +
          +
          +
          +

          Function

          +
          val f1 = (x: Int) => x + 1                 // simple anonymous function
+
+val y  = 2
+val f2 = (x: Int) => f1(x) + y             // closes over `f1` and `y`
+val f3 = (x: Int) => if (x < 0) f1 else f2 // anonymous function returning another function
+
+list.map(f1)      // functions can be passed around ...
+list.map(f3(1) _) // ... and partially applied
+
          +
          +
          +

          Note

          +

          No operators are defined on function-typed expressions, so specification is +currently quite limited.

          +
          +
          +
          +

          Bitvectors

          +

          Bitvectors are currently only supported in GenC and for verification, but +not for compilation.

          +

          These examples are taken from BitVectors3.scala.

          +
          import stainless.math.BitVectors._
+
+val x1: UInt8 = 145
+val x2: Int8 = x1.toSigned[Int8] // conversion from unsigned to signed ints
+
+// Bitvectors can be compared to literal constants, which are encoded as a bitvector of the same
+// type as the left-hand-side bitvector.
+// In the line below, `-111` get encoded internally as an `Int8`.
+assert(x2 == -111)
+
+// In Stainless internals, `Int8` and `Byte` are the same type, but not for the surface language,
+// so `toByte` allows to go from `Int8` to `Byte`.
+// Similarly, we support `toShort`, `toInt`, `toLong` for conversions
+// respectively from `Int16` to `Short`, `Int32` to `Int`, `Int64` to `Long`,
+// and `fromByte`, `fromShort`, `fromInt`, `fromLong` for the other direction
+val x3: Byte = x2.toByte
+assert(x3 == -111)
+
+// Unsigned ints can be cast to larger unsigned types
+val x4: UInt12 = x1.widen[UInt12]
+assert(x4 == 145)
+
+// or truncated to smaller unsigned types.
+val x5: UInt4 = x1.narrow[UInt4]
+assert(x5 == 1) // 145 % 2^4 == 1
+
+// Signed ints can also be cast to larger signed types (using sign extension)
+val x6: Int8 = 120
+val x7: Int12 = x6.widen[Int12]
+assert(x7 == 120)
+
+// and cast to smaller signed types.
+// This corresponds to extracting the least significant bits of the representation
+// (see `extract` here http://smtlib.cs.uiowa.edu/logics-all.shtml).
+val x8: Int4 = x6.narrow[Int4]
+assert(x8 == -8)
+
+// the `toByte`, `toShort`, `toInt`, and `toLong` methods described above
+// can be used on any bitvector type. For signed integers, this corresponds
+// to a narrowing or a widening operation depending on the bitvector size.
+// For unsigned integers, this corresponds to first doing a widening/narrowing
+// operation, and then applying `toSigned`
+val x9: UInt2 = 3
+assert(x9.toInt == x9.widen[UInt32].toSigned[Int32].toInt)
+
+// The library also provide constants for maximum and minimum values.
+assert(max[Int8] == 127)
+assert(min[Int8] == -128)
+
          +
          +

          Arrays, which are usually indexed using Int, may also be indexed using the bitvector types. +This is similar to first converting the bitvector index using toInt.

          +

          Bitvector types can be understood as finite intervals of integers +(two’s complement representation). For X an integer larger than 1 +(and at most 256 in Stainless):

          +
            +

          • UIntX is the interval \([0, 2^X - 1]\),

            • +

          • IntX is the interval \([-2^{X-1}, 2^{X-1} - 1]\).

            • +
          +

          Conversions between these types can be interpreted as operations on the +arrays of bits of the bitvectors, or as operations on the integers they +represent.

          +
            +

          • widen from UIntX to UIntY with \(Y > X\) adds \(Y-X\) (most significant) 0-bits, and corresponds to the identity transformation on integers.

            • +

          • widen from IntX to IntY with \(Y > X\) copies \(Y-X\) times the sign bit (sign-extension), and corresponds to the identity transformation on integers.

            • +

          • narrow from UIntX to UIntY with \(Y < X\) removes the \(X-Y\) most significant bits, +and corresponds to taking the number modulo \(2^Y\). +When the strict-arithmetic option is enabled, narrowing a number n to UIntY generates +a check n < 2^Y.

            • +

          • narrow from IntX to IntY with \(Y < X\) removes the \(X-Y\) most significant bits (including the sign bit), +and corresponds to the identity for integers in the interval \([-2^{Y-1}, 2^{Y-1} - 1]\). Outside this range, +the narrowing operation on a number n can be described as: 1) (unsigning) adding 2^X if n is negative, +2) (unsigned narrowing) taking the result modulo 2^Y, 3) (signing) removing 2^Y if the result of (2) is +greater or equal than 2^{Y-1}. +In strict-arithmetic mode, narrowing a number n to IntY generates two checks: -2^{Y-1} <= n and n <= 2^{Y-1} - 1.

            • +

          • toSigned from UIntX to IntX does not change the bitvector, and behaves as the identity for integers not larger than \(2^{X-1}-1\), +and subtracts \(2^{X}\) for integers in the interval \([2^{X-1}, 2^{X} - 1]\). +In strict-arithmetic mode, making a number n signed generates a check n <= 2^{X-1}-1.

            • +

          • toUnsigned from IntX to UIntX does not change the bitvector, and behaves as the identity +for non-negative integers, and adds \(2^{X}\) for negative integers (in the interval \([-2^{X-1}, 0[\)). +In strict-arithmetic mode, making a number n unsigned generates a check n >= 0.

            • +
          +
          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

          +
          + + + +
          +
          +
          +
          +
          + + + + \ No newline at end of file diff --git a/references.html b/references.html new file mode 100644 index 0000000000..081251ddad --- /dev/null +++ b/references.html @@ -0,0 +1,182 @@ + + + + + + + References — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
          + + +
          + + +
          +
          + + +
          + +
          +
          +
          +
          + +
          +

          References

          +

          The Stainless/Inox stack has emerged as a cleaner and leaner version of the Leon +synthesis and verification framework. Leon is documented in several +papers and talks, which provide additional information on the algorithms +and techniques we used in Leon (and now Stainless/Inox).

          +
          +

          Videos

          +
          +
          +
          +
          +

          Papers

          +
          +
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          +
          +
          +

          Books

          +
          +
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          +
          +
          + + +
          +
          +
          + + +
          + +
          +

          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

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          © Copyright 2009-2021 EPFL, Lausanne. + Last updated on May 09, 2024. +

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          +
          + + + + + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 0000000000..7689d1a503 --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ 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Studies","Translation from Stainless to Coq","Equivalence Checking","FAQ: (Frequently) Asked Questions","Generating C Code","Verifying and Compiling Examples","Ghost Context","Imperative","Stainless documentation","Installing Stainless","Stainless\u2019 Internals","Introduction","Specifying Algebraic Properties","Stainless Library","Limitations of Verification","Proving Theorems","Specifying Options","Pure Scala","References","Tutorial: Sorting","Verification conditions","Working With Existing 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\ No newline at end of file diff --git a/static/images/pipeline.svg b/static/images/pipeline.svg new file mode 100644 index 0000000000..b9be3c3556 --- /dev/null +++ b/static/images/pipeline.svg @@ -0,0 +1 @@ +Stainless PipelineUserFrontendCompilerCallBackRegistryComponentUse ICG: Incremental Computational GraphVerification and/orTermination;Run in threadsVerification and/orTerminationdotc, scalac, ...Update Code;Run FrontendRun CompilerTypecheckCompilation Unit(xlang.Trees)Register newFunDef & ClassDefUse ICG to identifywhat is ready orneed to be recomputed.Option[self-containedprogram]transform trees, generate VCs, send to the solvers, ...The "loop" is executed once more to trigger the verification ofnon-sealed classes now that all the overridden functions are known.wait for Component's ReportsReports...Reports...Reports...All ReportsDisplay reportsunder --watch modethe process restart.The Registry's ICG is the center piece thatenables stainless to verify modified functionswhen the code is updated.loop[for each compilation unit]opt[solve] \ No newline at end of file diff --git a/static/images/pipeline.txt b/static/images/pipeline.txt new file mode 100644 index 0000000000..95d10166ae --- /dev/null +++ b/static/images/pipeline.txt @@ -0,0 +1,73 @@ +# http://sequencediagram.org/ + +title Stainless Pipeline + +actor User +entity Frontend +entity Compiler +control CallBack +database Registry +actor Component + +parallel + + note over Registry: Use ICG:\n Incremental\n Computational\n Graph + + note over Component: Verification and/or\nTermination;\nRun in threads + + note over CallBack: Verification and/or\nTermination + + note over Compiler: dotc, scalac, ... + +parallel off + +activate User + +User -> Frontend: Update Code;\nRun Frontend +activate Frontend + +Frontend -> Compiler: Run Compiler +activate Compiler + +Compiler --> Compiler: Typecheck + +loop for each compilation unit + +Compiler -> CallBack: Compilation Unit\n(xlang.Trees) +activate CallBack + +CallBack ->> Registry: Register new\nFunDef & ClassDef +activate Registry +Registry ->> Registry: Use ICG to identify\nwhat is ready or\nneed to be recomputed. +Registry --> CallBack: Option[self-contained\nprogram] +deactivate Registry + +opt solve + CallBack -> Component: transform trees, generate VCs, ... +end opt + +deactivate CallBack + +end + +deactivate Compiler + +note over Frontend,Component: The "loop" is executed once more to trigger the verification of\nnon-sealed classes now that all the overridden functions are known. + +Frontend -> CallBack: wait for Component's Reports +Component -> CallBack: Reports... +Component -> CallBack: Reports... +Component -> CallBack: Reports... +CallBack -> Frontend: All Reports + +Frontend -> User: Display reports +deactivate Frontend + +parallel + + note over User: under \--watch mode\nthe process restart. + + note over Registry: The Registry's ICG is the center piece that\nenables stainless to verify modified functions\nwhen the code is updated. + +parallel off + diff --git a/static/invalid/AbstractRefinementMap.html b/static/invalid/AbstractRefinementMap.html new file mode 100644 index 0000000000..7330c3e48b --- /dev/null +++ b/static/invalid/AbstractRefinementMap.html @@ -0,0 +1,50 @@ + + + +invalid/AbstractRefinementMap.scala + + +

          AbstractRefinementMap.scala [raw]


          +
          import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+
+object AbstractRefinementMap {
+
+  case class ~>[A,B](private val f: A => B, ens: B => Boolean) {
+    require(forall((b: B) => ens.pre(b)))
+
+    lazy val pre = f.pre
+
+    def apply(x: A): B = {
+      require(f.pre(x))
+      f(x)
+    } ensuring(ens)
+// Counterexample for postcondition violation in `apply`:
+//   when x is:
+//     A#0
+//   when thiss is:
+//     ~>[A, B]((x$304: A) => if (x$304 == A#0) {
+//       B#0
+//     } else {
+//       B#0
+//     }, (x$308: B) => if (x$308 == B#0) {
+//       false
+//     } else if (true) {
+//       false
+//     } else {
+//       false
+//     })
+  }
+
+  def map[A, B](l: List[A], f: A ~> B): List[B] = {
+    require(forall((x:A) => l.contains(x) ==> f.pre(x)))
+    l match {
+      case Cons(x, xs) => Cons[B](f(x), map(xs, f))
+      case Nil() => Nil[B]()
+    }
+  } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) }
+}
+
+
          +

          back

          diff --git a/static/invalid/AbstractRefinementMap.scala b/static/invalid/AbstractRefinementMap.scala new file mode 100644 index 0000000000..d11db628b1 --- /dev/null +++ b/static/invalid/AbstractRefinementMap.scala @@ -0,0 +1,26 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ + +object AbstractRefinementMap { + + case class ~>[A,B](private val f: A => B, ens: B => Boolean) { + require(forall((b: B) => ens.pre(b))) + + lazy val pre = f.pre + + def apply(x: A): B = { + require(f.pre(x)) + f(x) + } ensuring(ens) + } + + def map[A, B](l: List[A], f: A ~> B): List[B] = { + require(forall((x:A) => l.contains(x) ==> f.pre(x))) + l match { + case Cons(x, xs) => Cons[B](f(x), map(xs, f)) + case Nil() => Nil[B]() + } + } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) } +} + diff --git a/static/invalid/AssociativityProperties.html b/static/invalid/AssociativityProperties.html new file mode 100644 index 0000000000..dec46b7d76 --- /dev/null +++ b/static/invalid/AssociativityProperties.html @@ -0,0 +1,81 @@ + + + +invalid/AssociativityProperties.scala + + +

          AssociativityProperties.scala [raw]


          +
          import stainless.lang._
+
+object AssociativityProperties {
+
+  def isAssociative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z)))
+  }
+
+  def isCommutative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A) => f(x, y) == f(y, x))
+  }
+
+  def isRotate[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x))
+  }
+
+  def assocNotCommutative[A](f: (A,A) => A): Boolean = {
+    require(isAssociative(f))
+    isCommutative(f)
+  }.holds
+// Counterexample for postcondition violation in `assocNotCommutative`:
+//   when f is:
+//     (x$412: A, x$413: A) => if (x$412 == A#3 && x$413 == A#3) {
+//       A#3
+//     } else if (x$412 == A#3 && x$413 == A#2) {
+//       A#3
+//     } else if (x$412 == A#2 && x$413 == A#3) {
+//       A#2
+//     } else if (x$412 == A#2 && x$413 == A#2) {
+//       A#2
+//     } else if (x$412 == A#3) {
+//       A#3
+//     } else if (x$413 == A#2) {
+//       A#2
+//     } else if (x$412 == A#2) {
+//       A#2
+//     } else if (x$413 == A#3) {
+//       A#2
+//     } else if (true) {
+//       A#2
+//     } else {
+//       A#2
+//     }
+
+  def commNotAssociative[A](f: (A,A) => A): Boolean = {
+    require(isCommutative(f))
+    isAssociative(f)
+  }.holds
+// Counterexample for postcondition violation in `commNotAssociative`:
+//   when f is:
+//     (x$330: A, x$331: A) => if (x$330 == A#2 && x$331 == A#0) {
+//       A#2
+//     } else if (x$330 == A#0 && x$331 == A#0) {
+//       A#1
+//     } else if (x$330 == A#2 && x$331 == A#2) {
+//       A#0
+//     } else if (x$330 == A#0 && x$331 == A#2) {
+//       A#2
+//     } else if (x$331 == A#0) {
+//       A#2
+//     } else if (x$331 == A#2) {
+//       A#0
+//     } else if (x$330 == A#2) {
+//       A#0
+//     } else if (x$330 == A#0) {
+//       A#2
+//     } else if (true) {
+//       A#0
+//     } else {
+//       A#0
+//     }
+}
+
          +

          back

          diff --git a/static/invalid/AssociativityProperties.scala b/static/invalid/AssociativityProperties.scala new file mode 100644 index 0000000000..1dd552c76a --- /dev/null +++ b/static/invalid/AssociativityProperties.scala @@ -0,0 +1,26 @@ +import stainless.lang._ + +object AssociativityProperties { + + def isAssociative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z))) + } + + def isCommutative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A) => f(x, y) == f(y, x)) + } + + def isRotate[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x)) + } + + def assocNotCommutative[A](f: (A,A) => A): Boolean = { + require(isAssociative(f)) + isCommutative(f) + }.holds + + def commNotAssociative[A](f: (A,A) => A): Boolean = { + require(isCommutative(f)) + isAssociative(f) + }.holds +} diff --git a/static/invalid/BadConcRope.html b/static/invalid/BadConcRope.html new file mode 100644 index 0000000000..794ff71fde --- /dev/null +++ b/static/invalid/BadConcRope.html @@ -0,0 +1,472 @@ +

          BadConcRope.scala [raw]


          +
          package conc
+// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL
+
+import stainless.collection._
+import stainless.lang._
+import ListSpecs._
+import stainless.annotation._
+
+object BadConcRope {
+
+  def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y
+  def abs(x: BigInt): BigInt = if (x < 0) -x else x
+
+  sealed abstract class Conc[T] {
+
+    def isEmpty: Boolean = {
+      this == Empty[T]()
+    }
+
+    def isLeaf: Boolean = {
+      this match {
+        case Empty() => true
+        case Single(_) => true
+        case _ => false
+      }
+    }
+
+    def isNormalized: Boolean = this match {
+      case Append(_, _) => false
+      case _ => true
+    }
+
+    def valid: Boolean = {
+      concInv && balanced && appendInv
+    }
+
+    /**
+     * (a) left and right trees of conc node should be non-empty
+     * (b) they cannot be append nodes
+     */
+    def concInv: Boolean = this match {
+      case CC(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.isNormalized && r.isNormalized &&
+          l.concInv && r.concInv
+      case _ => true
+    }
+
+    def balanced: Boolean = {
+      this match {
+        case CC(l, r) =>
+          l.level - r.level >= -1 && l.level - r.level <= 1 &&
+            l.balanced && r.balanced
+        case _ => true
+      }
+    }
+
+    /**
+     * (a) Right subtree of an append node is not an append node
+     * (b) If the tree is of the form a@Append(b@Append(_,_),_) then
+     * 		a.right.level < b.right.level
+     * (c) left and right are not empty
+     */
+    def appendInv: Boolean = this match {
+      case Append(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.valid && r.valid &&
+          r.isNormalized &&
+          (l match {
+            case Append(_, lr) =>
+              lr.level > r.level
+            case _ =>
+              l.level > r.level
+          })
+      case _ => true
+    }
+
+    val level: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 0
+        case CC(l, r) =>
+          1 + max(l.level, r.level)
+        case Append(l, r) =>
+          1 + max(l.level, r.level)
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    val size: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 1
+        case CC(l, r) =>
+          l.size + r.size
+        case Append(l, r) =>
+          l.size + r.size
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    def toList: List[T] = {
+      this match {
+        case Empty() => Nil[T]()
+        case Single(x) => Cons(x, Nil[T]())
+        case CC(l, r) =>
+          l.toList ++ r.toList // note: left elements precede the right elements in the list
+        case Append(l, r) =>
+          l.toList ++ r.toList
+      }
+    } ensuring (res => res.size == this.size)
+  }
+
+  case class Empty[T]() extends Conc[T]
+  case class Single[T](x: T) extends Conc[T]
+  case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+  case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+
+  def lookup[T](xs: Conc[T], i: BigInt): T = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => x
+      case CC(l, r) =>
+        if (i < l.size) lookup(l, i)
+       else lookup(r, i - l.size)
+      case Append(l, r) =>
+        if (i < l.size) lookup(l, i)
+        else lookup(r, i - l.size)
+    }
+  } ensuring (res =>  instAppendIndexAxiom(xs, i) &&  // an auxiliary axiom instantiation that required for the proof
+    res == xs.toList(i)) // correctness
+
+
+  def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = {
+    require(0 <= i && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case Append(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case _ => true
+    }
+  }.holds
+
+  def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => Single(y)
+      case CC(l, r) =>
+        if (i < l.size) CC(update(l, i, y), r)
+        else CC(l, update(r, i - l.size, y))
+      case Append(l, r) =>
+        Append(update(l, i, y), r)
+// Counterexample for precond. (call update[T](l, i, y)) violation in `update`:
+//   when i is:
+//     2
+//   when xs is:
+//     Append[T](CC[T](Single[T](T#63), Single[T](T#62)), Single[T](T#64))
+    }
+  } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation
+    res.level == xs.level && // heights of the input and output trees are equal
+    res.valid && // tree invariants are preserved
+    res.toList == xs.toList.updated(i, y) && // correctness
+    numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function
+
+  def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case Append(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  /**
+   * A generic concat that applies to general concTrees
+   */
+  def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid)
+    concatNormalized(normalize(xs), normalize(ys))
+  }
+
+  /**
+   * This concat applies only to normalized trees.
+   * This prevents concat from being recursive
+   */
+  def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized)
+    (xs, ys) match {
+      case (xs, Empty()) => xs
+      case (Empty(), ys) => ys
+      case _ =>
+        concatNonEmpty(xs, ys)
+    }
+  } ensuring (res => res.valid && // tree invariants
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    (res.toList == xs.toList ++ ys.toList) && // correctness
+    res.isNormalized //auxiliary properties
+    )
+
+  def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized &&
+      !xs.isEmpty && !ys.isEmpty)
+
+    val diff = ys.level - xs.level
+    if (diff >= -1 && diff <= 1)
+      CC(xs, ys)
+    else if (diff < -1) {
+      // ys is smaller than xs
+      xs match {
+        case CC(l, r) =>
+          if (l.level >= r.level)
+            CC(l, concatNonEmpty(r, ys))
+          else {
+            r match {
+              case CC(rl, rr) =>
+                val nrr = concatNonEmpty(rr, ys)
+                if (nrr.level == xs.level - 3) {
+                  CC(l, CC(rl, nrr))
+                } else {
+                  CC(CC(l, rl), nrr)
+                }
+            }
+          }
+      }
+    } else {
+      ys match {
+        case CC(l, r) =>
+          if (r.level >= l.level) {
+            CC(concatNonEmpty(xs, l), r)
+          } else {
+            l match {
+              case CC(ll, lr) =>
+                val nll = concatNonEmpty(xs, ll)
+                if (nll.level == ys.level - 3) {
+                  CC(CC(nll, lr), r)
+                } else {
+                  CC(nll, CC(lr, r))
+                }
+            }
+          }
+      }
+    }
+  } ensuring (res =>
+    appendAssocInst(xs, ys) && // instantiation of an axiom
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    res.balanced && res.appendInv && res.concInv && //this is should not be needed
+    res.valid && // tree invariant is preserved
+    res.toList == xs.toList ++ ys.toList && // correctness
+    res.isNormalized // auxiliary properties
+    )
+
+
+  def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    (xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation
+          (r match {
+            case CC(rl, rr) =>
+              appendAssoc(rl.toList, rr.toList, ys.toList) &&
+                appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList)
+            case _ => true
+          })
+      case _ => true
+    }) &&
+      (ys match {
+        case CC(l, r) =>
+          appendAssoc(xs.toList, l.toList, r.toList) &&
+            (l match {
+              case CC(ll, lr) =>
+                appendAssoc(xs.toList, ll.toList, lr.toList) &&
+                  appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList)
+              case _ => true
+            })
+        case _ => true
+      })
+  }.holds
+
+
+  def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && i >= 0 && i <= xs.size &&
+      xs.isNormalized) //note the precondition
+    xs match {
+      case Empty() => Single(y)
+      case Single(x) =>
+        if (i == 0)
+          CC(Single(y), xs)
+        else
+          CC(xs, Single(y))
+      case CC(l, r) if i < l.size =>
+        concatNonEmpty(insert(l, i, y), r)
+      case CC(l, r) =>
+       concatNonEmpty(l, insert(r, i - l.size, y))
+    }
+  } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom
+    res.valid && res.isNormalized && // tree invariants
+    res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree
+    res.toList == insertAtIndex(xs.toList, i, y) // correctness
+    )
+
+  /**
+   * Using a different version of insert than of the library
+   * because the library implementation in unnecessarily complicated.
+   */
+  def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = {
+    require(0 <= i && i <= l.size)
+    l match {
+      case Nil() =>
+        Cons[T](y, Nil())
+      case _ if i == 0 =>
+        Cons[T](y, l)
+      case Cons(x, tail) =>
+        Cons[T](x, insertAtIndex(tail, i - 1, y))
+    }
+  }
+
+  // A lemma about `append` and `insertAtIndex`
+  def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = {
+    require(0 <= i && i <= l1.size + l2.size)
+    (l1 match {
+      case Nil() => true
+      case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y)
+    }) &&
+      // lemma
+      (insertAtIndex((l1 ++ l2), i, y) == (
+        if (i < l1.size) insertAtIndex(l1, i, y) ++ l2
+        else l1 ++ insertAtIndex(l2, (i - l1.size), y)))
+  }.holds
+
+  def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i <= xs.size)
+    xs match {
+      case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = {
+    require(xs.valid && xs.isNormalized)
+    xs match {
+      case Empty() =>
+        (Empty[T](), Empty[T]())
+      case s @ Single(x) =>
+        if (n <= 0) {
+          (Empty[T](), s)
+        } else {
+          (s, Empty[T]())
+        }
+      case CC(l, r) =>
+        if (n < l.size) {
+          val (ll, lr) = split(l, n)
+          (ll, concatNormalized(lr, r))
+        } else if (n > l.size) {
+          val (rl, rr) = split(r, n - l.size)
+          (concatNormalized(l, rl), rr)
+        } else {
+          (l, r)
+        }
+    }
+  } ensuring (res  => instSplitAxiom(xs, n) && // instantiation of an axiom
+    res._1.valid && res._2.valid && // tree invariants are preserved
+    res._1.isNormalized && res._2.isNormalized &&
+    xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree
+    res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness
+    )
+
+  def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendTakeDrop(l.toList, r.toList, n)
+      case _ => true
+    }
+  }.holds
+
+  def append[T](xs: Conc[T], x: T): Conc[T] = {
+    require(xs.valid)
+    val ys = Single[T](x)
+    xs match {
+      case xs @ Append(_, _) =>
+        appendPriv(xs, ys)
+      case CC(_, _) =>
+        Append(xs, ys) //creating an append node
+      case Empty() => ys
+      case Single(_) => CC(xs, ys)
+    }
+  } ensuring (res => res.valid && //conctree invariants
+    res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness
+    res.level <= xs.level + 1
+  )
+
+  /**
+   * This is a private method and is not exposed to the
+   * clients of conc trees
+   */
+  def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T]  = {
+    require(xs.valid && ys.valid &&
+      !ys.isEmpty && ys.isNormalized &&
+      xs.right.level >= ys.level)
+
+    if (xs.right.level > ys.level)
+      Append(xs, ys)
+    else {
+      val zs = CC(xs.right, ys)
+      xs.left match {
+        case l @ Append(_, _) => appendPriv(l, zs)
+        case l if l.level <= zs.level => //note: here < is not possible
+          CC(l, zs)
+        case l =>
+          Append(l, zs)
+      }
+    }
+  } ensuring (res => appendAssocInst2(xs, ys) &&
+    res.valid && //conc tree invariants
+    res.toList == xs.toList ++ ys.toList && //correctness invariants
+    res.level <= xs.level + 1 )
+
+  def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case Append(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case _ => true
+    }
+  }.holds
+
+  def numTrees[T](t: Conc[T]): BigInt = {
+    t match {
+      case Append(l, r) => numTrees(l) + 1
+      case _ => BigInt(1)
+    }
+  } ensuring (res => res >= 0)
+
+  def normalize[T](t: Conc[T]): Conc[T] = {
+    require(t.valid)
+    t match {
+      case Append(l @ Append(_, _), r) =>
+        wrap(l, r)
+      case Append(l, r) =>
+        concatNormalized(l, r)
+      case _ => t
+    }
+  } ensuring (res => res.valid &&
+    res.isNormalized &&
+    res.toList == t.toList && //correctness
+    res.size == t.size && res.level <= t.level //normalize preserves level and size
+    )
+
+  def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid && ys.isNormalized &&
+      xs.right.level >= ys.level)
+    val nr  = concatNormalized(xs.right, ys)
+    xs.left match {
+      case l @ Append(_, _) => wrap(l, nr)
+      case l =>
+        concatNormalized(l, nr)
+    }
+  } ensuring (res =>
+    appendAssocInst2(xs, ys) && //some lemma instantiations
+    res.valid &&
+    res.isNormalized &&
+    res.toList == xs.toList ++ ys.toList && //correctness
+    res.size == xs.size + ys.size && //other auxiliary properties
+    res.level <= xs.level
+    )
+}
+
          diff --git a/static/invalid/BadConcRope.scala b/static/invalid/BadConcRope.scala new file mode 100644 index 0000000000..dfff26ec5b --- /dev/null +++ b/static/invalid/BadConcRope.scala @@ -0,0 +1,465 @@ +package conc +// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL + +import stainless.collection._ +import stainless.lang._ +import ListSpecs._ +import stainless.annotation._ + +object BadConcRope { + + def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y + def abs(x: BigInt): BigInt = if (x < 0) -x else x + + sealed abstract class Conc[T] { + + def isEmpty: Boolean = { + this == Empty[T]() + } + + def isLeaf: Boolean = { + this match { + case Empty() => true + case Single(_) => true + case _ => false + } + } + + def isNormalized: Boolean = this match { + case Append(_, _) => false + case _ => true + } + + def valid: Boolean = { + concInv && balanced && appendInv + } + + /** + * (a) left and right trees of conc node should be non-empty + * (b) they cannot be append nodes + */ + def concInv: Boolean = this match { + case CC(l, r) => + !l.isEmpty && !r.isEmpty && + l.isNormalized && r.isNormalized && + l.concInv && r.concInv + case _ => true + } + + def balanced: Boolean = { + this match { + case CC(l, r) => + l.level - r.level >= -1 && l.level - r.level <= 1 && + l.balanced && r.balanced + case _ => true + } + } + + /** + * (a) Right subtree of an append node is not an append node + * (b) If the tree is of the form a@Append(b@Append(_,_),_) then + * a.right.level < b.right.level + * (c) left and right are not empty + */ + def appendInv: Boolean = this match { + case Append(l, r) => + !l.isEmpty && !r.isEmpty && + l.valid && r.valid && + r.isNormalized && + (l match { + case Append(_, lr) => + lr.level > r.level + case _ => + l.level > r.level + }) + case _ => true + } + + val level: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 0 + case CC(l, r) => + 1 + max(l.level, r.level) + case Append(l, r) => + 1 + max(l.level, r.level) + }): BigInt + } ensuring (_ >= 0) + + val size: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 1 + case CC(l, r) => + l.size + r.size + case Append(l, r) => + l.size + r.size + }): BigInt + } ensuring (_ >= 0) + + def toList: List[T] = { + this match { + case Empty() => Nil[T]() + case Single(x) => Cons(x, Nil[T]()) + case CC(l, r) => + l.toList ++ r.toList // note: left elements precede the right elements in the list + case Append(l, r) => + l.toList ++ r.toList + } + } ensuring (res => res.size == this.size) + } + + case class Empty[T]() extends Conc[T] + case class Single[T](x: T) extends Conc[T] + case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] + case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T] + + def lookup[T](xs: Conc[T], i: BigInt): T = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => x + case CC(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + case Append(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + } + } ensuring (res => instAppendIndexAxiom(xs, i) && // an auxiliary axiom instantiation that required for the proof + res == xs.toList(i)) // correctness + + + def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = { + require(0 <= i && i < xs.size) + xs match { + case CC(l, r) => + appendIndex(l.toList, r.toList, i) + case Append(l, r) => + appendIndex(l.toList, r.toList, i) + case _ => true + } + }.holds + + def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => Single(y) + case CC(l, r) => + if (i < l.size) CC(update(l, i, y), r) + else CC(l, update(r, i - l.size, y)) + case Append(l, r) => + Append(update(l, i, y), r) + } + } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation + res.level == xs.level && // heights of the input and output trees are equal + res.valid && // tree invariants are preserved + res.toList == xs.toList.updated(i, y) && // correctness + numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function + + def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i < xs.size) + xs match { + case CC(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case Append(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + /** + * A generic concat that applies to general concTrees + */ + def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid) + concatNormalized(normalize(xs), normalize(ys)) + } + + /** + * This concat applies only to normalized trees. + * This prevents concat from being recursive + */ + def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized) + (xs, ys) match { + case (xs, Empty()) => xs + case (Empty(), ys) => ys + case _ => + concatNonEmpty(xs, ys) + } + } ensuring (res => res.valid && // tree invariants + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + (res.toList == xs.toList ++ ys.toList) && // correctness + res.isNormalized //auxiliary properties + ) + + def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized && + !xs.isEmpty && !ys.isEmpty) + + val diff = ys.level - xs.level + if (diff >= -1 && diff <= 1) + CC(xs, ys) + else if (diff < -1) { + // ys is smaller than xs + xs match { + case CC(l, r) => + if (l.level >= r.level) + CC(l, concatNonEmpty(r, ys)) + else { + r match { + case CC(rl, rr) => + val nrr = concatNonEmpty(rr, ys) + if (nrr.level == xs.level - 3) { + CC(l, CC(rl, nrr)) + } else { + CC(CC(l, rl), nrr) + } + } + } + } + } else { + ys match { + case CC(l, r) => + if (r.level >= l.level) { + CC(concatNonEmpty(xs, l), r) + } else { + l match { + case CC(ll, lr) => + val nll = concatNonEmpty(xs, ll) + if (nll.level == ys.level - 3) { + CC(CC(nll, lr), r) + } else { + CC(nll, CC(lr, r)) + } + } + } + } + } + } ensuring (res => + appendAssocInst(xs, ys) && // instantiation of an axiom + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + res.balanced && res.appendInv && res.concInv && //this is should not be needed + res.valid && // tree invariant is preserved + res.toList == xs.toList ++ ys.toList && // correctness + res.isNormalized // auxiliary properties + ) + + + def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = { + (xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation + (r match { + case CC(rl, rr) => + appendAssoc(rl.toList, rr.toList, ys.toList) && + appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList) + case _ => true + }) + case _ => true + }) && + (ys match { + case CC(l, r) => + appendAssoc(xs.toList, l.toList, r.toList) && + (l match { + case CC(ll, lr) => + appendAssoc(xs.toList, ll.toList, lr.toList) && + appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList) + case _ => true + }) + case _ => true + }) + }.holds + + + def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && i >= 0 && i <= xs.size && + xs.isNormalized) //note the precondition + xs match { + case Empty() => Single(y) + case Single(x) => + if (i == 0) + CC(Single(y), xs) + else + CC(xs, Single(y)) + case CC(l, r) if i < l.size => + concatNonEmpty(insert(l, i, y), r) + case CC(l, r) => + concatNonEmpty(l, insert(r, i - l.size, y)) + } + } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom + res.valid && res.isNormalized && // tree invariants + res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree + res.toList == insertAtIndex(xs.toList, i, y) // correctness + ) + + /** + * Using a different version of insert than of the library + * because the library implementation in unnecessarily complicated. + */ + def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = { + require(0 <= i && i <= l.size) + l match { + case Nil() => + Cons[T](y, Nil()) + case _ if i == 0 => + Cons[T](y, l) + case Cons(x, tail) => + Cons[T](x, insertAtIndex(tail, i - 1, y)) + } + } + + // A lemma about `append` and `insertAtIndex` + def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = { + require(0 <= i && i <= l1.size + l2.size) + (l1 match { + case Nil() => true + case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y) + }) && + // lemma + (insertAtIndex((l1 ++ l2), i, y) == ( + if (i < l1.size) insertAtIndex(l1, i, y) ++ l2 + else l1 ++ insertAtIndex(l2, (i - l1.size), y))) + }.holds + + def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i <= xs.size) + xs match { + case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = { + require(xs.valid && xs.isNormalized) + xs match { + case Empty() => + (Empty[T](), Empty[T]()) + case s @ Single(x) => + if (n <= 0) { + (Empty[T](), s) + } else { + (s, Empty[T]()) + } + case CC(l, r) => + if (n < l.size) { + val (ll, lr) = split(l, n) + (ll, concatNormalized(lr, r)) + } else if (n > l.size) { + val (rl, rr) = split(r, n - l.size) + (concatNormalized(l, rl), rr) + } else { + (l, r) + } + } + } ensuring (res => instSplitAxiom(xs, n) && // instantiation of an axiom + res._1.valid && res._2.valid && // tree invariants are preserved + res._1.isNormalized && res._2.isNormalized && + xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree + res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness + ) + + def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = { + xs match { + case CC(l, r) => + appendTakeDrop(l.toList, r.toList, n) + case _ => true + } + }.holds + + def append[T](xs: Conc[T], x: T): Conc[T] = { + require(xs.valid) + val ys = Single[T](x) + xs match { + case xs @ Append(_, _) => + appendPriv(xs, ys) + case CC(_, _) => + Append(xs, ys) //creating an append node + case Empty() => ys + case Single(_) => CC(xs, ys) + } + } ensuring (res => res.valid && //conctree invariants + res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness + res.level <= xs.level + 1 + ) + + /** + * This is a private method and is not exposed to the + * clients of conc trees + */ + def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + !ys.isEmpty && ys.isNormalized && + xs.right.level >= ys.level) + + if (xs.right.level > ys.level) + Append(xs, ys) + else { + val zs = CC(xs.right, ys) + xs.left match { + case l @ Append(_, _) => appendPriv(l, zs) + case l if l.level <= zs.level => //note: here < is not possible + CC(l, zs) + case l => + Append(l, zs) + } + } + } ensuring (res => appendAssocInst2(xs, ys) && + res.valid && //conc tree invariants + res.toList == xs.toList ++ ys.toList && //correctness invariants + res.level <= xs.level + 1 ) + + def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = { + xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case Append(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case _ => true + } + }.holds + + def numTrees[T](t: Conc[T]): BigInt = { + t match { + case Append(l, r) => numTrees(l) + 1 + case _ => BigInt(1) + } + } ensuring (res => res >= 0) + + def normalize[T](t: Conc[T]): Conc[T] = { + require(t.valid) + t match { + case Append(l @ Append(_, _), r) => + wrap(l, r) + case Append(l, r) => + concatNormalized(l, r) + case _ => t + } + } ensuring (res => res.valid && + res.isNormalized && + res.toList == t.toList && //correctness + res.size == t.size && res.level <= t.level //normalize preserves level and size + ) + + def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && ys.isNormalized && + xs.right.level >= ys.level) + val nr = concatNormalized(xs.right, ys) + xs.left match { + case l @ Append(_, _) => wrap(l, nr) + case l => + concatNormalized(l, nr) + } + } ensuring (res => + appendAssocInst2(xs, ys) && //some lemma instantiations + res.valid && + res.isNormalized && + res.toList == xs.toList ++ ys.toList && //correctness + res.size == xs.size + ys.size && //other auxiliary properties + res.level <= xs.level + ) +} diff --git a/static/invalid/BraunTree.html b/static/invalid/BraunTree.html new file mode 100644 index 0000000000..67c7f43a4d --- /dev/null +++ b/static/invalid/BraunTree.html @@ -0,0 +1,55 @@ + + + +invalid/BraunTree.scala + + +

          BraunTree.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object BraunTree {
+  abstract class Tree
+  case class Node(value: Int, left: Tree, right: Tree) extends Tree
+  case class Leaf() extends Tree
+
+  def insert(tree: Tree, x: Int): Tree = {
+    require(isBraun(tree))
+    tree match {
+      case Node(value, left, right) =>
+        Node(value, insert(left, x), right)
+      case Leaf() => Node(x, Leaf(), Leaf())
+    }
+  } ensuring { res => isBraun(res) }
+// Counterexample for postcondition violation in `insert`:
+//   when x is:
+//     0
+//   when tree is:
+//     Node(0, Node(0, Leaf(), Leaf()), Leaf())
+
+  def height(tree: Tree): Int = {
+    tree match {
+      case Node(value, left, right) =>
+        val l = height(left)
+        val r = height(right)
+        val max = if (l > r) l else r
+        1 + max
+      case Leaf() => 0
+    }
+  }
+
+  def isBraun(tree: Tree): Boolean = {
+    tree match {
+      case Node(value, left, right) =>
+        isBraun(left) && isBraun(right) && {
+          val l = height(left)
+          val r = height(right)
+          l == r || l == r + 1
+        }
+      case Leaf() => true
+    }
+  }
+}
+
          +

          back

          diff --git a/static/invalid/BraunTree.scala b/static/invalid/BraunTree.scala new file mode 100644 index 0000000000..7733dcd0ec --- /dev/null +++ b/static/invalid/BraunTree.scala @@ -0,0 +1,41 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object BraunTree { + abstract class Tree + case class Node(value: Int, left: Tree, right: Tree) extends Tree + case class Leaf() extends Tree + + def insert(tree: Tree, x: Int): Tree = { + require(isBraun(tree)) + tree match { + case Node(value, left, right) => + Node(value, insert(left, x), right) + case Leaf() => Node(x, Leaf(), Leaf()) + } + } ensuring { res => isBraun(res) } + + def height(tree: Tree): Int = { + tree match { + case Node(value, left, right) => + val l = height(left) + val r = height(right) + val max = if (l > r) l else r + 1 + max + case Leaf() => 0 + } + } + + def isBraun(tree: Tree): Boolean = { + tree match { + case Node(value, left, right) => + isBraun(left) && isBraun(right) && { + val l = height(left) + val r = height(right) + l == r || l == r + 1 + } + case Leaf() => true + } + } +} diff --git a/static/invalid/Choose.html b/static/invalid/Choose.html new file mode 100644 index 0000000000..b1c6503787 --- /dev/null +++ b/static/invalid/Choose.html @@ -0,0 +1,53 @@ + + + +invalid/Choose.scala + + +

          Choose.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Choose1 {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def listOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        choose[List] { (res: List) => size(res) == i-1 }
+      }
+    } ensuring ( size(_) == i )
+// Counterexample for postcondition violation in `listOfSize`:
+//   when i is:
+//     1
+
+
+    def listOfSize2(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i > 0) {
+        Cons(0, listOfSize(i-1))
+      } else {
+        Nil()
+      }
+    } ensuring ( size(_) == i )
+}
+
          +

          back

          diff --git a/static/invalid/Choose.scala b/static/invalid/Choose.scala new file mode 100644 index 0000000000..7508725001 --- /dev/null +++ b/static/invalid/Choose.scala @@ -0,0 +1,41 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Choose1 { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def listOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + choose[List] { (res: List) => size(res) == i-1 } + } + } ensuring ( size(_) == i ) + + + def listOfSize2(i: BigInt): List = { + require(i >= 0) + + if (i > 0) { + Cons(0, listOfSize(i-1)) + } else { + Nil() + } + } ensuring ( size(_) == i ) +} diff --git a/static/invalid/FunctionCaching.html b/static/invalid/FunctionCaching.html new file mode 100644 index 0000000000..62e39fdf37 --- /dev/null +++ b/static/invalid/FunctionCaching.html @@ -0,0 +1,47 @@ + + + +invalid/FunctionCaching.scala + + +

          FunctionCaching.scala [raw]


          +
          import stainless.lang._
+import stainless.collection._
+
+object FunctionCaching {
+
+  case class FunCache(var cached: Map[BigInt, BigInt])
+
+  def fun(x: BigInt)(implicit funCache: FunCache): BigInt = {
+    funCache.cached.get(x) match {
+      case None() => 
+        val res = 2*x + 42
+        funCache.cached = funCache.cached.updated(x, res)
+        res
+      case Some(cached) =>
+        cached + 1
+    }
+  }
+
+  def funWronglyCached(x: BigInt, trash: List[BigInt]): Boolean = {
+    implicit val cache = FunCache(Map())
+    val res1 = fun(x)
+    multipleCalls(trash)
+    val res2 = fun(x)
+    res1 == res2
+  } holds
+// Counterexample for postcondition violation in `funWronglyCached`:
+//   when x is:
+//     -21
+//   when trash is:
+//     Nil[BigInt]()
+
+
+  def multipleCalls(args: List[BigInt])(implicit funCache: FunCache): Unit = args match {
+    case Nil() => ()
+    case x::xs => fun(x); multipleCalls(xs)
+  }
+
+}
+
          +

          back

          diff --git a/static/invalid/FunctionCaching.scala b/static/invalid/FunctionCaching.scala new file mode 100644 index 0000000000..dea5ff3a87 --- /dev/null +++ b/static/invalid/FunctionCaching.scala @@ -0,0 +1,33 @@ +import stainless.lang._ +import stainless.collection._ + +object FunctionCaching { + + case class FunCache(var cached: Map[BigInt, BigInt]) + + def fun(x: BigInt)(implicit funCache: FunCache): BigInt = { + funCache.cached.get(x) match { + case None() => + val res = 2*x + 42 + funCache.cached = funCache.cached.updated(x, res) + res + case Some(cached) => + cached + 1 + } + } + + def funWronglyCached(x: BigInt, trash: List[BigInt]): Boolean = { + implicit val cache = FunCache(Map()) + val res1 = fun(x) + multipleCalls(trash) + val res2 = fun(x) + res1 == res2 + } holds + + + def multipleCalls(args: List[BigInt])(implicit funCache: FunCache): Unit = args match { + case Nil() => () + case x::xs => fun(x); multipleCalls(xs) + } + +} diff --git a/static/invalid/InsertionSort.html b/static/invalid/InsertionSort.html new file mode 100644 index 0000000000..26c925d558 --- /dev/null +++ b/static/invalid/InsertionSort.html @@ -0,0 +1,57 @@ + + + +invalid/InsertionSort.scala + + +

          InsertionSort.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object InsertionSort {
+  sealed abstract class List
+  case class Cons(head:Int,tail:List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptInt
+  case class Some(value: Int) extends OptInt
+  case class None() extends OptInt
+
+  def size(l : List) : BigInt = (l match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def contents(l: List): Set[Int] = l match {
+    case Nil() => Set.empty
+    case Cons(x,xs) => contents(xs) ++ Set(x)
+  }
+
+  def isSorted(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(x, Nil()) => true
+    case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys))
+  }   
+
+  /* Inserting element 'e' into a sorted list 'l' produces a sorted list with
+   * the expected content and size */
+  def buggySortedIns(e: Int, l: List): List = {
+    // require(isSorted(l))
+    l match {
+      case Nil() => Cons(e,Nil())
+      case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l)
+    } 
+  } ensuring(res => contents(res) == contents(l) ++ Set(e) 
+                    && isSorted(res)
+                    && size(res) == size(l) + 1
+// Counterexample for postcondition violation in `buggySortedIns`:
+//   when e is:
+//     0
+//   when l is:
+//     Cons(-2147483643, Cons(-2147483644, Nil()))
+            )
+}
+
          +

          back

          diff --git a/static/invalid/InsertionSort.scala b/static/invalid/InsertionSort.scala new file mode 100644 index 0000000000..98aa2325d1 --- /dev/null +++ b/static/invalid/InsertionSort.scala @@ -0,0 +1,43 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object InsertionSort { + sealed abstract class List + case class Cons(head:Int,tail:List) extends List + case class Nil() extends List + + sealed abstract class OptInt + case class Some(value: Int) extends OptInt + case class None() extends OptInt + + def size(l : List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def contents(l: List): Set[Int] = l match { + case Nil() => Set.empty + case Cons(x,xs) => contents(xs) ++ Set(x) + } + + def isSorted(l: List): Boolean = l match { + case Nil() => true + case Cons(x, Nil()) => true + case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys)) + } + + /* Inserting element 'e' into a sorted list 'l' produces a sorted list with + * the expected content and size */ + def buggySortedIns(e: Int, l: List): List = { + // require(isSorted(l)) + l match { + case Nil() => Cons(e,Nil()) + case Cons(x,xs) => if (x <= e) Cons(x,buggySortedIns(e, xs)) else Cons(e, l) + } + } ensuring(res => contents(res) == contents(l) ++ Set(e) + && isSorted(res) + && size(res) == size(l) + 1 + ) +} diff --git a/static/invalid/ListOperations.html b/static/invalid/ListOperations.html new file mode 100644 index 0000000000..b9e8a0cc96 --- /dev/null +++ b/static/invalid/ListOperations.html @@ -0,0 +1,128 @@ + + + +invalid/ListOperations.scala + + +

          ListOperations.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ListOperations {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    sealed abstract class IntPairList
+    case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList
+    case class IPNil() extends IntPairList
+
+    sealed abstract class IntPair
+    case class IP(fst: Int, snd: Int) extends IntPair
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def iplSize(l: IntPairList) : BigInt = (l match {
+      case IPNil() => BigInt(0)
+      case IPCons(_, xs) => 1 + iplSize(xs)
+    }) ensuring(_ >= 0)
+
+    def zip(l1: List, l2: List) : IntPairList = {
+      // try to uncomment this and see how pattern-matching becomes exhaustive
+      // require(size(l1) == size(l2))
+
+      l1 match {
+        case Nil() => IPNil()
+        case Cons(x, xs) => l2 match {
+          case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys))
+        }
+// Counterexample for match exhaustiveness violation in `zip`:
+//   when l2 is:
+//     Nil()
+//   when l1 is:
+//     Cons(0, Nil())
+      }
+    } ensuring(iplSize(_) == size(l1))
+
+    def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0)
+    def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = {
+     require(acc >= 0)
+     l match {
+       case Nil() => acc
+       case Cons(_, xs) => sizeTailRecAcc(xs, acc+1)
+     }
+    } ensuring(res => res == size(l) + acc)
+
+    def sizesAreEquiv(l: List) : Boolean = {
+      size(l) == sizeTailRec(l)
+    }.holds
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def sizeAndContent(l: List) : Boolean = {
+      size(l) == BigInt(0) || content(l) != Set.empty[Int]
+    }.holds
+
+    def drunk(l : List) : List = (l match {
+      case Nil() => Nil()
+      case Cons(x,l1) => Cons(x,Cons(x,drunk(l1)))
+    }) ensuring (size(_) == 2 * size(l))
+
+    def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l))
+    def reverse0(l1: List, l2: List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => reverse0(xs, Cons(x, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    def append(l1 : List, l2 : List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x,xs) => Cons(x, append(xs, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds
+
+    @induct
+    def appendAssoc(xs : List, ys : List, zs : List) : Boolean =
+      (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds
+
+    def revAuxBroken(l1 : List, e : Int, l2 : List) : Boolean = {
+      (append(reverse(l1), Cons(e,l2)) == reverse0(l1, l2))
+    }.holds
+// Counterexample for postcondition violation in `revAuxBroken`:
+//   when e is:
+//     0
+//   when l1 is:
+//     Nil()
+//   when l2 is:
+//     Nil()
+
+    @induct
+    def sizeAppend(l1 : List, l2 : List) : Boolean =
+      (size(append(l1, l2)) == size(l1) + size(l2)).holds
+
+    @induct
+    def concat(l1: List, l2: List) : List =
+      concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def concat0(l1: List, l2: List, l3: List) : List = (l1 match {
+      case Nil() => l2 match {
+        case Nil() => reverse(l3)
+        case Cons(y, ys) => {
+          concat0(Nil(), ys, Cons(y, l3))
+        }
+      }
+      case Cons(x, xs) => concat0(xs, l2, Cons(x, l3))
+    }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3))
+}
+
          +

          back

          diff --git a/static/invalid/ListOperations.scala b/static/invalid/ListOperations.scala new file mode 100644 index 0000000000..7ba835b52d --- /dev/null +++ b/static/invalid/ListOperations.scala @@ -0,0 +1,107 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ListOperations { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class IntPairList + case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList + case class IPNil() extends IntPairList + + sealed abstract class IntPair + case class IP(fst: Int, snd: Int) extends IntPair + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def iplSize(l: IntPairList) : BigInt = (l match { + case IPNil() => BigInt(0) + case IPCons(_, xs) => 1 + iplSize(xs) + }) ensuring(_ >= 0) + + def zip(l1: List, l2: List) : IntPairList = { + // try to uncomment this and see how pattern-matching becomes exhaustive + // require(size(l1) == size(l2)) + + l1 match { + case Nil() => IPNil() + case Cons(x, xs) => l2 match { + case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys)) + } + } + } ensuring(iplSize(_) == size(l1)) + + def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0) + def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = { + require(acc >= 0) + l match { + case Nil() => acc + case Cons(_, xs) => sizeTailRecAcc(xs, acc+1) + } + } ensuring(res => res == size(l) + acc) + + def sizesAreEquiv(l: List) : Boolean = { + size(l) == sizeTailRec(l) + }.holds + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def sizeAndContent(l: List) : Boolean = { + size(l) == BigInt(0) || content(l) != Set.empty[Int] + }.holds + + def drunk(l : List) : List = (l match { + case Nil() => Nil() + case Cons(x,l1) => Cons(x,Cons(x,drunk(l1))) + }) ensuring (size(_) == 2 * size(l)) + + def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l)) + def reverse0(l1: List, l2: List) : List = (l1 match { + case Nil() => l2 + case Cons(x, xs) => reverse0(xs, Cons(x, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + def append(l1 : List, l2 : List) : List = (l1 match { + case Nil() => l2 + case Cons(x,xs) => Cons(x, append(xs, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds + + @induct + def appendAssoc(xs : List, ys : List, zs : List) : Boolean = + (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds + + def revAuxBroken(l1 : List, e : Int, l2 : List) : Boolean = { + (append(reverse(l1), Cons(e,l2)) == reverse0(l1, l2)) + }.holds + + @induct + def sizeAppend(l1 : List, l2 : List) : Boolean = + (size(append(l1, l2)) == size(l1) + size(l2)).holds + + @induct + def concat(l1: List, l2: List) : List = + concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def concat0(l1: List, l2: List, l3: List) : List = (l1 match { + case Nil() => l2 match { + case Nil() => reverse(l3) + case Cons(y, ys) => { + concat0(Nil(), ys, Cons(y, l3)) + } + } + case Cons(x, xs) => concat0(xs, l2, Cons(x, l3)) + }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3)) +} diff --git a/static/invalid/Lists.html b/static/invalid/Lists.html new file mode 100644 index 0000000000..c27cd96486 --- /dev/null +++ b/static/invalid/Lists.html @@ -0,0 +1,46 @@ + + + +invalid/Lists.scala + + +

          Lists.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object Lists {
+  abstract class List[T]
+  case class Cons[T](head: T, tail: List[T]) extends List[T]
+  case class Nil[T]() extends List[T]
+
+  def forall[T](list: List[T], f: T => Boolean): Boolean = list match {
+    case Cons(head, tail) => f(head) && forall(tail, f)
+    case Nil() => true
+  }
+
+  def positive(list: List[Int]): Boolean = list match {
+    case Cons(head, tail) => if (head < 0) false else positive(tail)
+    case Nil() => true
+  }
+
+  def gt(i: Int): Int => Boolean = x => x > i
+
+  def positive_lemma(list: List[Int]): Boolean = {
+    positive(list) == forall(list, gt(0))
+  }
+
+  def failling_1(list: List[Int]): Boolean = {
+    list match {
+      case Nil() => positive_lemma(list)
+      case Cons(head, tail) => positive_lemma(list) && failling_1(tail)
+    }
+  }.holds
+// Counterexample for postcondition violation in `failling_1`:
+//   when list is:
+//     Cons[Int](0, Nil[Int]())
+}
+
+// vim: set ts=4 sw=4 et:
+
          +

          back

          diff --git a/static/invalid/Lists.scala b/static/invalid/Lists.scala new file mode 100644 index 0000000000..7b3a056760 --- /dev/null +++ b/static/invalid/Lists.scala @@ -0,0 +1,34 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object Lists { + abstract class List[T] + case class Cons[T](head: T, tail: List[T]) extends List[T] + case class Nil[T]() extends List[T] + + def forall[T](list: List[T], f: T => Boolean): Boolean = list match { + case Cons(head, tail) => f(head) && forall(tail, f) + case Nil() => true + } + + def positive(list: List[Int]): Boolean = list match { + case Cons(head, tail) => if (head < 0) false else positive(tail) + case Nil() => true + } + + def gt(i: Int): Int => Boolean = x => x > i + + def positive_lemma(list: List[Int]): Boolean = { + positive(list) == forall(list, gt(0)) + } + + def failling_1(list: List[Int]): Boolean = { + list match { + case Nil() => positive_lemma(list) + case Cons(head, tail) => positive_lemma(list) && failling_1(tail) + } + }.holds +} + +// vim: set ts=4 sw=4 et: diff --git a/static/invalid/Mean.html b/static/invalid/Mean.html new file mode 100644 index 0000000000..ff317d449c --- /dev/null +++ b/static/invalid/Mean.html @@ -0,0 +1,27 @@ + + + +invalid/Mean.scala + + +

          Mean.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Mean {
+
+  def meanOverflow(x: Int, y: Int): Int = {
+    require(x <= y && x >= 0 && y >= 0)
+    (x + y)/2
+  } ensuring(m => m >= x && m <= y)
+// Counterexample for postcondition violation in `meanOverflow`:
+//   when y is:
+//     1865154560
+//   when x is:
+//     1277440000
+
+}
+
          +

          back

          diff --git a/static/invalid/Mean.scala b/static/invalid/Mean.scala new file mode 100644 index 0000000000..c79ad49794 --- /dev/null +++ b/static/invalid/Mean.scala @@ -0,0 +1,13 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Mean { + + def meanOverflow(x: Int, y: Int): Int = { + require(x <= y && x >= 0 && y >= 0) + (x + y)/2 + } ensuring(m => m >= x && m <= y) + +} diff --git a/static/invalid/PropositionalLogic.html b/static/invalid/PropositionalLogic.html new file mode 100644 index 0000000000..1ca8f024c8 --- /dev/null +++ b/static/invalid/PropositionalLogic.html @@ -0,0 +1,62 @@ + + + +invalid/PropositionalLogic.scala + + +

          PropositionalLogic.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object PropositionalLogic { 
+
+  sealed abstract class Formula
+  case class And(lhs: Formula, rhs: Formula) extends Formula
+  case class Or(lhs: Formula, rhs: Formula) extends Formula
+  case class Implies(lhs: Formula, rhs: Formula) extends Formula
+  case class Not(f: Formula) extends Formula
+  case class Literal(id: BigInt) extends Formula
+
+  def simplify(f: Formula): Formula = (f match {
+    case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs))
+    case _ => f
+  }) ensuring(isSimplified(_))
+// Counterexample for postcondition violation in `simplify`:
+//   when f is:
+//     And(Literal(8), Implies(Literal(7), Literal(6)))
+
+  def isSimplified(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Implies(_,_) => false
+    case Not(f) => isSimplified(f)
+    case Literal(_) => true
+  }
+
+  def isNNF(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Not(Literal(_)) => true
+    case Not(_) => false
+    case Literal(_) => true
+  }
+
+
+  // @induct
+  // def wrongCommutative(f: Formula) : Boolean = {
+  //   nnf(simplify(f)) == simplify(nnf(f))
+  // }.holds
+
+ def simplifyBreaksNNF(f: Formula) : Boolean = {
+    require(isNNF(f))
+    isNNF(simplify(f))
+  }.holds
+// Counterexample for postcondition violation in `simplifyBreaksNNF`:
+//   when f is:
+//     Implies(And(Literal(255), Literal(256)), Literal(267))
+}
+
          +

          back

          diff --git a/static/invalid/PropositionalLogic.scala b/static/invalid/PropositionalLogic.scala new file mode 100644 index 0000000000..654a28d303 --- /dev/null +++ b/static/invalid/PropositionalLogic.scala @@ -0,0 +1,47 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object PropositionalLogic { + + sealed abstract class Formula + case class And(lhs: Formula, rhs: Formula) extends Formula + case class Or(lhs: Formula, rhs: Formula) extends Formula + case class Implies(lhs: Formula, rhs: Formula) extends Formula + case class Not(f: Formula) extends Formula + case class Literal(id: BigInt) extends Formula + + def simplify(f: Formula): Formula = (f match { + case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs)) + case _ => f + }) ensuring(isSimplified(_)) + + def isSimplified(f: Formula): Boolean = f match { + case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Implies(_,_) => false + case Not(f) => isSimplified(f) + case Literal(_) => true + } + + def isNNF(f: Formula): Boolean = f match { + case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Not(Literal(_)) => true + case Not(_) => false + case Literal(_) => true + } + + + // @induct + // def wrongCommutative(f: Formula) : Boolean = { + // nnf(simplify(f)) == simplify(nnf(f)) + // }.holds + + def simplifyBreaksNNF(f: Formula) : Boolean = { + require(isNNF(f)) + isNNF(simplify(f)) + }.holds +} diff --git a/static/invalid/RedBlackTree2.html b/static/invalid/RedBlackTree2.html new file mode 100644 index 0000000000..aa2f672af0 --- /dev/null +++ b/static/invalid/RedBlackTree2.html @@ -0,0 +1,106 @@ + + + +invalid/RedBlackTree2.scala + + +

          RedBlackTree2.scala [raw]


          +
          /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object RedBlackTree2 { 
+  sealed abstract class Color
+  case class Red() extends Color
+  case class Black() extends Color
+ 
+  sealed abstract class Tree
+  case class Empty() extends Tree
+  case class Node(color: Color, left: Tree, value: Int, right: Tree) extends Tree
+
+  sealed abstract class OptionInt
+  case class Some(v : Int) extends OptionInt
+  case class None() extends OptionInt
+
+  def content(t: Tree) : Set[Int] = t match {
+    case Empty() => Set.empty
+    case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def size(t: Tree) : BigInt = (t match {
+    case Empty() => BigInt(0)
+    case Node(_, l, v, r) => size(l) + 1 + size(r)
+  }) ensuring(_ >= 0)
+
+  def isBlack(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(),_,_,_) => true
+    case _ => false
+  }
+
+  def redNodesHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+    case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def redDescHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def blackBalanced(t : Tree) : Boolean = t match {
+    case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r)
+    case Empty() => true
+  }
+
+  def blackHeight(t : Tree) : Int = t match {
+    case Empty() => 1
+    case Node(Black(), l, _, _) => blackHeight(l) + 1
+    case Node(Red(), l, _, _) => blackHeight(l)
+  }
+
+  def ins(x: Int, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    t match {
+      case Empty() => Node(Red(),Empty(),x,Empty())
+      case Node(c,a,y,b) =>
+        if      (x < y)  balance(c, ins(x, a), y, b)
+        else if (x == y) Node(c,a,y,b)
+        else             balance(c,a,y,ins(x, b))
+    }
+  } ensuring (res => content(res) == content(t) ++ Set(x) 
+                   && size(t) <= size(res) && size(res) <= size(t) + 1
+                   && redDescHaveBlackChildren(res)
+                   && blackBalanced(res))
+
+  def balance(c: Color, a: Tree, x: Int, b: Tree): Tree = {
+    Node(c,a,x,b) match {
+      case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(c,a,xV,b) => Node(c,a,xV,b)
+    }
+  } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res))
+
+  def buggyAdd(x: Int, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t))
+    ins(x, t)
+// Counterexample for precond. (call ins(x, t)) violation in `buggyAdd`:
+//   when t is:
+//     Node(Black(), Node(Black(), Empty(), 0, Empty()), 0, Empty())
+  } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res))
+// Counterexample for postcondition violation in `buggyAdd`:
+//   when x is:
+//     0
+//   when t is:
+//     Node(Red(), Empty(), 1048576, Empty())
+}
+
          +

          back

          diff --git a/static/invalid/RedBlackTree2.scala b/static/invalid/RedBlackTree2.scala new file mode 100644 index 0000000000..6fc4b6cf74 --- /dev/null +++ b/static/invalid/RedBlackTree2.scala @@ -0,0 +1,89 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object RedBlackTree2 { + sealed abstract class Color + case class Red() extends Color + case class Black() extends Color + + sealed abstract class Tree + case class Empty() extends Tree + case class Node(color: Color, left: Tree, value: Int, right: Tree) extends Tree + + sealed abstract class OptionInt + case class Some(v : Int) extends OptionInt + case class None() extends OptionInt + + def content(t: Tree) : Set[Int] = t match { + case Empty() => Set.empty + case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def size(t: Tree) : BigInt = (t match { + case Empty() => BigInt(0) + case Node(_, l, v, r) => size(l) + 1 + size(r) + }) ensuring(_ >= 0) + + def isBlack(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(),_,_,_) => true + case _ => false + } + + def redNodesHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def redDescHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def blackBalanced(t : Tree) : Boolean = t match { + case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r) + case Empty() => true + } + + def blackHeight(t : Tree) : Int = t match { + case Empty() => 1 + case Node(Black(), l, _, _) => blackHeight(l) + 1 + case Node(Red(), l, _, _) => blackHeight(l) + } + + def ins(x: Int, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + t match { + case Empty() => Node(Red(),Empty(),x,Empty()) + case Node(c,a,y,b) => + if (x < y) balance(c, ins(x, a), y, b) + else if (x == y) Node(c,a,y,b) + else balance(c,a,y,ins(x, b)) + } + } ensuring (res => content(res) == content(t) ++ Set(x) + && size(t) <= size(res) && size(res) <= size(t) + 1 + && redDescHaveBlackChildren(res) + && blackBalanced(res)) + + def balance(c: Color, a: Tree, x: Int, b: Tree): Tree = { + Node(c,a,x,b) match { + case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(c,a,xV,b) => Node(c,a,xV,b) + } + } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res)) + + def buggyAdd(x: Int, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t)) + ins(x, t) + } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res)) +} diff --git a/static/invalid/SpecWithExtern.html b/static/invalid/SpecWithExtern.html new file mode 100644 index 0000000000..064d0fb80b --- /dev/null +++ b/static/invalid/SpecWithExtern.html @@ -0,0 +1,33 @@ + + + +invalid/SpecWithExtern.scala + + +

          SpecWithExtern.scala [raw]


          +
          import stainless.annotation._
+
+object SpecWithExtern {
+
+
+  //random between returns any value between l and h.
+  //For execution via scalac, we pick one valid implementation, but
+  //we would like the program to be verified versus any possible
+  //implementation, which should happen thanks to @extern
+  @extern
+  def randomBetween(l: Int, h: Int): Int = {
+    require(l <= h)
+    l
+  } ensuring(res => (res >= l && res <= h))
+
+  //postcondition is wrong, but if stainless considers 
+  //actual body of randomBetween it would be correct
+  def wrongProp(): Int = {
+    randomBetween(0, 10)
+  } ensuring(res => res >= 0 && res < 10)
+// Counterexample for postcondition violation in `wrongProp`:
+// empty counter example
+
+}
+
          +

          back

          diff --git a/static/invalid/SpecWithExtern.scala b/static/invalid/SpecWithExtern.scala new file mode 100644 index 0000000000..4480b715f1 --- /dev/null +++ b/static/invalid/SpecWithExtern.scala @@ -0,0 +1,22 @@ +import stainless.annotation._ + +object SpecWithExtern { + + + //random between returns any value between l and h. + //For execution via scalac, we pick one valid implementation, but + //we would like the program to be verified versus any possible + //implementation, which should happen thanks to @extern + @extern + def randomBetween(l: Int, h: Int): Int = { + require(l <= h) + l + } ensuring(res => (res >= l && res <= h)) + + //postcondition is wrong, but if stainless considers + //actual body of randomBetween it would be correct + def wrongProp(): Int = { + randomBetween(0, 10) + } ensuring(res => res >= 0 && res < 10) + +} diff --git a/static/programs.html b/static/programs.html new file mode 100644 index 0000000000..7fb20bb2ed --- /dev/null +++ b/static/programs.html @@ -0,0 +1,59 @@ + + + +Sample of Verification Reports by Stainless Tool + + + +

          Below are some simple examples to get the idea of how Stainless works; +please contact LARA to learn about our larger case studies.

          + +

          Example Buggy Programs

          +

          + +

          Example Verified Programs

          +

          + +
          + +Back to Stainless page + + + diff --git a/static/stainless-library/index.html b/static/stainless-library/index.html new file mode 100644 index 0000000000..406f6f5acc --- /dev/null +++ b/static/stainless-library/index.html @@ -0,0 +1,158 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Packages

          + +
          +
          +
          + +
          +
          p
          + +

          root package + + + +

          + +
          + +

          + + + package + + + root + +

          + + +
          + + + + +
          +
          + + + + + + + + + + + +
          + +
          + + +
          + +
          +
          +

          Ungrouped

          + +
          +
          + +
          + +
          + + + +
          +
          +
          + + diff --git a/static/stainless-library/index.js b/static/stainless-library/index.js new file mode 100644 index 0000000000..c53b2200d8 --- /dev/null +++ b/static/stainless-library/index.js @@ -0,0 +1 @@ +Index.PACKAGES = {"stainless.io" : [{"name" : "stainless.io.FileInputStream", "shortDescription" : "", "object" : "stainless\/io\/FileInputStream$.html", "members_object" : [{"label" : "open", "tail" : "(filename: String)(state: State): FileInputStream", "member" : "stainless.io.FileInputStream.open", "link" : "stainless\/io\/FileInputStream$.html#open(filename:String)(implicitstate:stainless.io.State):stainless.io.FileInputStream", "kind" : "def"}, {"label" : "synchronized", "tail" : "(arg0: ⇒ T0): T0", "member" : "scala.AnyRef.synchronized", "link" : "stainless\/io\/FileInputStream$.html#synchronized[T0](x$1:=>T0):T0", "kind" : "final def"}, {"label" : "##", "tail" : "(): Int", "member" : "scala.AnyRef.##", "link" : "stainless\/io\/FileInputStream$.html###():Int", "kind" 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font-size: 1.5em; +} + +svg a { + cursor:pointer; +} + +svg text { + font-size: 8.5px; +} + +/* try to move the node text 1px in order to be vertically + * centered (does not work in all browsers) + */ +svg .node text { + transform: translate(0px,1px); + -ms-transform: translate(0px,1px); + -webkit-transform: translate(0px,1px); + -o-transform: translate(0px,1px); + -moz-transform: translate(0px,1px); +} + +/* hover effect for edges */ + +svg .edge.over text, +svg .edge.implicit-incoming.over polygon, +svg .edge.implicit-outgoing.over polygon { + fill: #103A51; +} + +svg .edge.over path, +svg .edge.over polygon { + stroke: #103A51; +} + +/* for hover effect on nodes in diagrams, edit the following */ +svg.class-diagram .node {} +svg.class-diagram .node.this {} +svg.class-diagram .node.over {} + +svg .node.over polygon { + stroke: #202020; +} + +/* hover effect for nodes in package diagrams */ + +svg.package-diagram .node.class.over polygon, +svg.class-diagram .node.this.class.over polygon { + fill: #098552; + fill: #04663e; +} + +svg.package-diagram .node.trait.over polygon, +svg.class-diagram .node.this.trait.over polygon { + fill: #3c7b9b; + fill: #235d7b; +} + +svg.package-diagram .node.type.over polygon, +svg.class-diagram .node.this.type.over polygon { + fill: #098552; + fill: #04663e; +} + + +svg.package-diagram .node.object.over polygon { + fill: #183377; +} + +svg.package-diagram .node.outside.over polygon { + fill: #d4d4d4; +} + +svg.package-diagram .node.default.over polygon { + fill: #d4d4d4; +} diff --git a/static/stainless-library/lib/diagrams.js b/static/stainless-library/lib/diagrams.js new file mode 100644 index 0000000000..b13732760a --- /dev/null +++ b/static/stainless-library/lib/diagrams.js @@ -0,0 +1,240 @@ +/** + * JavaScript functions enhancing the SVG diagrams. + * + * @author Damien Obrist + */ + +var diagrams = {}; + +/** + * Initializes the diagrams in the main window. + */ +$(document).ready(function() +{ + // hide diagrams in browsers not supporting SVG + if(Modernizr && !Modernizr.inlinesvg) + return; + + if($("#content-diagram").length) + $("#inheritance-diagram").css("padding-bottom", "20px"); + + $(".diagram-container").css("display", "block"); + + $(".diagram").each(function() { + // store initial dimensions + $(this).data("width", $("svg", $(this)).width()); + $(this).data("height", $("svg", $(this)).height()); + // store unscaled clone of SVG element + $(this).data("svg", $(this).get(0).childNodes[0].cloneNode(true)); + }); + + // make diagram visible, hide container + $(".diagram").css("display", "none"); + $(".diagram svg").css({ + "position": "static", + "visibility": "visible", + "z-index": "auto" + }); + + // enable linking to diagrams + if($(location).attr("hash") == "#inheritance-diagram") { + diagrams.toggle($("#inheritance-diagram-container"), true); + } else if($(location).attr("hash") == "#content-diagram") { + diagrams.toggle($("#content-diagram-container"), true); + } + + $(".diagram-link").click(function() { + diagrams.toggle($(this).parent()); + }); + + // register resize function + $(window).resize(diagrams.resize); + + // don't bubble event to parent div + // when clicking on a node of a resized + // diagram + $("svg a").click(function(e) { + e.stopPropagation(); + }); + + diagrams.initHighlighting(); + + $("button#diagram-fs").click(function() { + $(".diagram-container").toggleClass("full-screen"); + $(".diagram-container > div.diagram").css({ + height: $("svg").height() + "pt" + }); + + $panzoom.panzoom("reset", { animate: false, contain: false }); + }); +}); + +/** + * Initializes highlighting for nodes and edges. + */ +diagrams.initHighlighting = function() +{ + // helper function since $.hover doesn't work in IE + + function hover(elements, fn) + { + elements.mouseover(fn); + elements.mouseout(fn); + } + + // inheritance edges + + hover($("svg .edge.inheritance"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + var parts = $(this).attr("id").split("_"); + toggleClass($("#" + parts[0] + "_" + parts[1])); + toggleClass($("#" + parts[0] + "_" + parts[2])); + toggleClass($(this)); + }); + + // nodes + + hover($("svg .node"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + var parts = $(this).attr("id").split("_"); + var index = parts[1]; + $("svg#" + parts[0] + " .edge.inheritance").each(function(){ + var parts2 = $(this).attr("id").split("_"); + if(parts2[1] == index) + { + toggleClass($("#" + parts2[0] + "_" + parts2[2])); + toggleClass($(this)); + } else if(parts2[2] == index) + { + toggleClass($("#" + parts2[0] + "_" + parts2[1])); + toggleClass($(this)); + } + }); + }); + + // incoming implicits + + hover($("svg .node.implicit-incoming"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .edge.implicit-incoming")); + toggleClass($("svg .node.this")); + }); + + hover($("svg .edge.implicit-incoming"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .node.this")); + $("svg .node.implicit-incoming").each(function(){ + toggleClass($(this)); + }); + }); + + // implicit outgoing nodes + + hover($("svg .node.implicit-outgoing"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .edge.implicit-outgoing")); + toggleClass($("svg .node.this")); + }); + + hover($("svg .edge.implicit-outgoing"), function(evt){ + var toggleClass = evt.type == "mouseout" ? diagrams.removeClass : diagrams.addClass; + toggleClass($(this)); + toggleClass($("svg .node.this")); + $("svg .node.implicit-outgoing").each(function(){ + toggleClass($(this)); + }); + }); +}; + +/** + * Resizes the diagrams according to the available width. + */ +diagrams.resize = function() { + // available width + var availableWidth = $(".diagram-container").width(); + + $(".diagram-container").each(function() { + // unregister click event on whole div + $(".diagram", this).unbind("click"); + var diagramWidth = $(".diagram", this).data("width"); + var diagramHeight = $(".diagram", this).data("height"); + + if (diagramWidth > availableWidth) { + // resize diagram + var height = diagramHeight / diagramWidth * availableWidth; + $(".diagram svg", this).width(availableWidth); + $(".diagram svg", this).height(height); + } else { + // restore full size of diagram + $(".diagram svg", this).width(diagramWidth); + $(".diagram svg", this).height(diagramHeight); + // don't show custom cursor any more + $(".diagram", this).removeClass("magnifying"); + } + }); +}; + +/** + * Shows or hides a diagram depending on its current state. + */ +diagrams.toggle = function(container, dontAnimate) +{ + // change class of link + $(".diagram-link", container).toggleClass("open"); + // get element to show / hide + var div = $(".diagram", container); + if (div.is(':visible')) { + $(".diagram-help", container).hide(); + div.unbind("click"); + div.slideUp(100); + + $("#diagram-controls", container).hide(); + $("#inheritance-diagram-container").unbind('mousewheel.focal'); + } else { + diagrams.resize(); + if(dontAnimate) + div.show(); + else + div.slideDown(100); + $(".diagram-help", container).show(); + + $("#diagram-controls", container).show(); + + $(".diagram-container").on('mousewheel.focal', function(e) { + e.preventDefault(); + var delta = e.delta || e.originalEvent.wheelDelta; + var zoomOut = delta ? delta < 0 : e.originalEvent.deltaY > 0; + $panzoom.panzoom('zoom', zoomOut, { + increment: 0.1, + animate: true, + focal: e + }); + }); + } +}; + +/** + * Helper method that adds a class to a SVG element. + */ +diagrams.addClass = function(svgElem, newClass) { + newClass = newClass || "over"; + var classes = svgElem.attr("class"); + if ($.inArray(newClass, classes.split(/\s+/)) == -1) { + classes += (classes ? ' ' : '') + newClass; + svgElem.attr("class", classes); + } +}; + +/** + * Helper method that removes a class from a SVG element. + */ +diagrams.removeClass = function(svgElem, oldClass) { + oldClass = oldClass || "over"; + var classes = svgElem.attr("class"); + classes = $.grep(classes.split(/\s+/), function(n, i) { return n != oldClass; }).join(' '); + svgElem.attr("class", classes); +}; diff --git a/static/stainless-library/lib/index.css b/static/stainless-library/lib/index.css new file mode 100644 index 0000000000..488bf3b8b5 --- /dev/null +++ b/static/stainless-library/lib/index.css @@ -0,0 +1,928 @@ +/* Fonts */ +@font-face { + font-family: 'Lato'; + font-style: normal; + font-weight: 100; + src: url('lato-v11-latin-regular.eot'); + src: local('Lato'), local('Lato'), + url('lato-v11-latin-100.eot?#iefix') format('embedded-opentype'), + url('lato-v11-latin-100.woff') format('woff'), + url('lato-v11-latin-100.ttf') format('truetype'); +} + +@font-face { + font-family: 'Lato'; + font-style: normal; + font-weight: 400; + src: url('lato-v11-latin-regular.eot'); + src: local('Lato'), local('Lato'), + url('lato-v11-latin-regular.eot?#iefix') format('embedded-opentype'), + url('lato-v11-latin-regular.woff') format('woff'), + url('lato-v11-latin-regular.ttf') format('truetype'); +} + +@font-face { + font-family: 'Open Sans'; + font-style: normal; + font-weight: 400; + src: url('open-sans-v13-latin-regular.eot'); + src: local('Open Sans'), local('OpenSans'), + url('open-sans-v13-latin-regular.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-regular.woff') format('woff'), + url('open-sans-v13-latin-regular.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: italic; + font-weight: 400; + src: url('open-sans-v13-latin-400i.eot'); + src: local('Open Sans Italic'), local('OpenSans-Italic'), + url('open-sans-v13-latin-400i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-400i.woff') format('woff'), + url('open-sans-v13-latin-400i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: oblique; + font-weight: 400; + src: url('open-sans-v13-latin-400i.eot'); + src: local('Open Sans Italic'), local('OpenSans-Italic'), + url('open-sans-v13-latin-400i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-400i.woff') format('woff'), + url('open-sans-v13-latin-400i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: normal; + font-weight: 700; + src: url('open-sans-v13-latin-700.eot'); + src: local('Open Sans Bold'), local('OpenSans-Bold'), + url('open-sans-v13-latin-700.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700.woff') format('woff'), + url('open-sans-v13-latin-700.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: italic; + font-weight: 700; + src: url('open-sans-v13-latin-700i.eot'); + src: local('Open Sans Bold Italic'), local('OpenSans-BoldItalic'), + url('open-sans-v13-latin-700i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700i.woff') format('woff'), + url('open-sans-v13-latin-700i.ttf') format('truetype'); +} +@font-face { + font-family: 'Open Sans'; + font-style: oblique; + font-weight: 700; + src: url('open-sans-v13-latin-700i.eot'); + src: local('Open Sans Bold Italic'), local('OpenSans-BoldItalic'), + url('open-sans-v13-latin-700i.eot?#iefix') format('embedded-opentype'), + url('open-sans-v13-latin-700i.woff') format('woff'), + url('open-sans-v13-latin-700i.ttf') format('truetype'); +} + +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 400; + src: url('source-code-pro-v6-latin-regular.eot'); + src: local('Source Code Pro'), local('SourceCodePro-Regular'), + url('source-code-pro-v6-latin-regular.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-regular.woff') format('woff'), + url('source-code-pro-v6-latin-regular.ttf') format('truetype'); +} +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 700; + src: url('source-code-pro-v6-latin-700.eot'); + src: local('Source Code Pro Bold'), local('SourceCodePro-Bold'), + url('source-code-pro-v6-latin-700.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-700.woff') format('woff'), + url('source-code-pro-v6-latin-700.ttf') format('truetype'); +} + +* { + color: inherit; + text-decoration: none; + font-family: "Lato", Arial, sans-serif; + border-width: 0px; + margin: 0px; +} + +u { + text-decoration: underline; +} + +a { + cursor: pointer; + text-decoration: none; +} + +a:hover { + text-decoration: underline; +} + +span.entity > a { + padding: 0.1em 0.5em; + margin-left: 0.2em; +} + +span.entity > a.selected { + background-color: #C2D2DC; + border-radius: 0.2em; +} + +html { + background-color: #f0f3f6; + box-sizing: border-box; +} +*, *:before, *:after { + box-sizing: inherit; +} + +textarea, input { outline: none; } + +#library { + display: none; +} + +#browser { + width: 17.5em; + top: 0px; + left: 0; + bottom: 0px; + display: block; + position: fixed; + background-color: #f0f3f6; +} + +#browser.full-screen { + left: -17.5em; +} + +#search { + background-color: #103a51; /* typesafe blue */ + min-height: 5.5em; + position: fixed; + top: 0; + left: 0; + right: 0; + height: 3em; + min-height: initial; + z-index: 103; + box-shadow: 0 0 4px rgba(0, 0, 0, 0.18), 0 4px 8px rgba(0, 0, 0, 0.28); +} + +#search > h1 { + font-size: 2em; + position: absolute; + left: 0.25em; + top: 0.5em; +} + +#search > h2 { + position: absolute; + left: 3.8em; + top: 3em; +} + +#search > img.scala-logo { + width: 3em; + height: auto; + position: absolute; + left: 5.8em; + top: 0.43em; +} + +#search > span.toggle-sidebar { + position: absolute; + top: 0.8em; + left: 0.2em; + color: #fff; + z-index: 99; + width: 1.5em; + height: 1.5em; +} + +#search > span#doc-title { + color: #fff; + position: absolute; + top: 0.8em; + left: 0; + width: 18em; + text-align: center; + cursor: pointer; + z-index: 2; +} + +#search > span#doc-title > span#doc-version { + color: #c2c2c2; + font-weight: 100; + font-size: 0.72em; + display: inline-block; + width: 12ex; + overflow: hidden; + white-space: nowrap; + text-overflow: ellipsis; +} + +#search > span#doc-title > span#doc-version:hover { + overflow: visible; +} + +#search > span.toggle-sidebar:hover { + cursor: pointer; +} + +/* Pseudo element replacing UTF8-symbol "Trigram From Heaven" */ +#search > span.toggle-sidebar:before { + position: absolute; + top: -0.45em; + left: 0.45em; + content: ""; + display: block; + width: 0.7em; + -webkit-box-shadow: 0 0.8em 0 1px #fff, 0 1.1em 0 1px #fff, 0 1.4em 0 1px #fff; + box-shadow: 0 0.8em 0 1px #fff, 0 1.1em 0 1px #fff, 0 1.4em 0 1px #fff; +} + +#search > span.toggle-sidebar:hover:before { + -webkit-box-shadow: 0 0.8em 0 1px #c2c2c2, 0 1.1em 0 1px #c2c2c2, 0 1.4em 0 1px #c2c2c2; + box-shadow: 0 0.8em 0 1px #c2c2c2, 0 1.1em 0 1px #c2c2c2, 0 1.4em 0 1px #c2c2c2; +} + +#textfilter > .pre { + display: block; + position: absolute; + top: 0; + left: 0; + height: 23px; + width: 21px; +} + +#textfilter { + position: absolute; + top: 0.5em; + bottom: 0.8em; + left: 0; + right: 0; + display: block; + height: 2em; +} + +#textfilter > .input { + position: relative; + display: block; + padding: 0.2em; + max-width: 48.5em; + margin: 0 auto; +} + +#textfilter > .input > i#search-icon { + color: rgba(255,255,255, 0.4); + position: absolute; + left: 0.34em; + top: 0.3em; + font-size: 1.3rem; +} + +#textfilter > span.toggle { + cursor: pointer; + padding-left: 15px; + position: absolute; + left: -0.55em; + top: 3em; + z-index: 99; + color: #fff; + font-size: 0.8em; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#textfilter > span.toggle:hover { + color: #c2c2c2; +} + +#textfilter > span.toggle:hover { + cursor: pointer; +} + +#textfilter > .hide:hover { + cursor: pointer; + color: #a2a2a2; +} + +#textfilter > .input > input { + font-family: "Open Sans"; + font-size: 0.85em; + height: 2em; + padding: 0 0 0 2.1em; + color: #fff; + width: 100%; + border-radius: 0.2em; + background: rgba(255, 255, 255, 0.2); +} + + +#textfilter > .input > input::-webkit-input-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input::-moz-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input:-ms-input-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > input:-moz-placeholder { + color: rgba(255, 255, 255, 0.4); +} + +#focusfilter > .focusremove:hover { + text-decoration: none; +} + +#textfilter > .input > .clear { + display: none; + position: absolute; + font-size: 0.9em; + top: 0.7em; + right: 0.1em; + height: 23px; + width: 21px; + color: rgba(255, 255, 255, 0.4); +} + +#textfilter > .input > .clear:hover { + cursor: pointer; + color: #fff; +} + +#focusfilter { + font-size: 0.9em; + position: relative; + text-align: center; + display: none; + padding: 0.6em; + background-color: #f16665; + color: #fff; + margin: 3.9em 0.55em 0 0.35em; + border-radius: 0.2em; + z-index: 1; +} + +div#search-progress { + position: absolute; + top: 0; + left: 0; + width: 100%; + height: 0.25em; +} + +div#search-progress > div#progress-fill { + width: 0%; + background-color: #f16665; + transition: 0.1s; +} + +#focusfilter .focuscoll { + font-weight: bold; +} + +#focusfilter a.focusremove { + margin-left: 0.2em; + font-size: 0.9em; +} + +#kindfilter-container { + position: fixed; + display: block; + z-index: 99; + bottom: 0.5em; + left: 0; + width: 17.25em; +} + +#kindfilter { + float: right; + text-align: center; + padding: 0.3em 1em; + border-radius: 0.8em; + background: #f16665; + border-bottom: 2px solid #d64546; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; + color: #fff; + font-size: 0.8em; +} + +#kindfilter:hover { + cursor: pointer; + background-color: rgb(226, 87, 88); +} + +#letters { + position: relative; + text-align: center; + border: 0; + margin-top: 0em; + color: #fff; +} + +#letters > a, #letters > span { + color: #fff; + font-size: 0.67em; + padding-right: 2px; +} + +#letters > a:hover { + text-decoration: none; + color: #c2c2c2; +} + +#letters > span { + color: #bbb; +} + +div#content-scroll-container { + position: absolute; + top: 0; + right: 0; + bottom: 0; + left: 0; + z-index: 100; + overflow-x: hidden; + overflow-y: auto; +} + +div#content-container { + max-width: 1140px; + margin: 0 auto; +} + +div#content-container > div#content { + -webkit-overflow-scrolling: touch; + display: block; + overflow-y: hidden; + max-width: 1140px; + margin: 4em auto 0; +} + +div#content-container > div#subpackage-spacer { + float: right; + height: 100%; + margin: 1.1rem 0.5rem 0 0.5em; + font-size: 0.8em; + min-width: 8rem; + max-width: 16rem; +} + +div#packages > h1 { + color: #103a51; +} + +div#packages > ul { + list-style-type: none; +} + +div#packages > ul > li { + position: relative; + margin: 0.5rem 0; + width: 100%; + border-radius: 0.2em; + min-height: 1.5em; + padding-left: 2em; +} + +div#packages > ul > li.current-entities { + margin: 0.3rem 0; +} + +div#packages > ul > li.current:hover { + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + cursor: pointer; +} + +div#packages > ul > li.current-entities > *:nth-child(1), +div#packages > ul > li.current-entities > *:nth-child(2) { + float: left; + display: inline; + height: 1rem; + width: 1rem; + margin: 1px 0 0 0; + cursor: pointer; +} + +div#packages > ul > li > a.class { + background: url("class.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.trait { + background: url("trait.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.object { + background: url("object.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a.abstract.type { + background: url("abstract_type.svg") no-repeat center; + background-size: 0.9rem; +} + +div#packages > ul > li > a { + text-decoration: none !important; + margin-left: 1px; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.9em; +} + +/* Indentation levels for packages */ +div#packages > ul > li.indented0 { padding-left: 0em; } +div#packages > ul > li.indented1 { padding-left: 1em; } +div#packages > ul > li.indented2 { padding-left: 2em; } +div#packages > ul > li.indented3 { padding-left: 3em; } +div#packages > ul > li.indented4 { padding-left: 4em; } +div#packages > ul > li.indented5 { padding-left: 5em; } +div#packages > ul > li.indented6 { padding-left: 6em; } +div#packages > ul > li.indented7 { padding-left: 7em; } +div#packages > ul > li.indented8 { padding-left: 8em; } +div#packages > ul > li.indented9 { padding-left: 9em; } +div#packages > ul > li.indented10 { padding-left: 10em; } +div#packages > ul > li.current.indented0 { padding-left: -0.5em } +div#packages > ul > li.current.indented1 { padding-left: 0.5em } +div#packages > ul > li.current.indented2 { padding-left: 1.5em } +div#packages > ul > li.current.indented3 { padding-left: 2.5em } +div#packages > ul > li.current.indented4 { padding-left: 3.5em } +div#packages > ul > li.current.indented5 { padding-left: 4.5em } +div#packages > ul > li.current.indented6 { padding-left: 5.5em } +div#packages > ul > li.current.indented7 { padding-left: 6.5em } +div#packages > ul > li.current.indented8 { padding-left: 7.5em } +div#packages > ul > li.current.indented9 { padding-left: 8.5em } +div#packages > ul > li.current.indented10 { padding-left: 9.5em } + +div#packages > ul > li.current > span.symbol { + border-left: 0.25em solid #72D0EB; + padding-left: 0.25em; +} + +div#packages > ul > li > span.symbol > a { + text-decoration: none; +} + +div#packages > ul > li > span.symbol > span.name { + font-weight: normal; +} + +div#packages > ul > li .fullcomment, +div#packages > ul > li .modifier_kind, +div#packages > ul > li .permalink, +div#packages > ul > li .shortcomment { + display: none; +} + +div#search-results { + color: #103a51; + position: absolute; + left: 0; + top: 3em; + right: 0; + bottom: 0; + background-color: rgb(240, 243, 246); + z-index: 101; + overflow-x: hidden; + display: none; + padding: 1em; + -webkit-overflow-scrolling: touch; +} + +div#search > span.close-results { + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + position: fixed; + top: 0.8em; + left: 1em; + color: #fff; + display: none; + z-index: 1; +} + +div#search > span.close-results:hover { + cursor: pointer; +} + +div#results-content { + max-width: 1140px; + margin: 0 auto; +} + +div#results-content > span.search-text { + margin-left: 1em; + font-size: 1.2em; + float: left; + width: 100%; +} + +div#results-content > span.search-text > span.query-str { + font-weight: 900; +} + +div#results-content > div > h1.result-type { + font-size: 1.5em; + margin: 1em 0 0.3em; + font-family: "Open Sans"; + font-weight: 300; + border-bottom: 1px solid #103a51; +} + +div#results-content > div#entity-results { + float: left; + width: 50%; + padding: 1em; + display: inline; +} + +div#results-content > div#member-results { + float: left; + width: 50%; + padding: 1em; + display: inline; +} + +div#results-content > div#member-results > a.package, +div#results-content > div#entity-results > a.package { + font-size: 1em; + margin: 0 0 1em 0; + color: #f16665; + cursor: pointer; +} + +div#results-content > div#member-results > ul.entities, +div#results-content > div#entity-results > ul.entities { + list-style-type: none; + padding-left: 0; +} + +div#results-content > div#member-results > ul.entities > li, +div#results-content > div#entity-results > ul.entities > li { + margin: 0.5em 0; +} + +div#results-content > div#member-results > ul.entities > li > .icon, +div#results-content > div#entity-results > ul.entities > li > .icon { + float: left; + display: inline; + height: 1em; + width: 1em; + margin: 0.23em 0 0; + cursor: pointer; +} + +div#results-content > div#member-results > ul.entities > li > .icon.class, +div#results-content > div#entity-results > ul.entities > li > .icon.class { + background: url("class.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > .icon.trait, +div#results-content > div#entity-results > ul.entities > li > .icon.trait { + background: url("trait.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > .icon.object, +div#results-content > div#entity-results > ul.entities > li > .icon.object { + background: url("object.svg") no-repeat center; + background-size: 1em 1em; +} + +div#results-content > div#member-results > ul.entities > li > span.entity, +div#results-content > div#entity-results > ul.entities > li > span.entity { + font-size: 1.1em; + font-weight: 900; +} + +div#results-content > div#member-results > ul.entities > li > ul.members, +div#results-content > div#entity-results > ul.entities > li > ul.members { + margin-top: 0.5em; + list-style-type: none; + font-size: 0.85em; + margin-left: 0.2em; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li, +div#results-content > div#entity-results > ul.entities > li > ul.members > li { + margin: 0.5em 0; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.kind, +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.tail, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > span.kind, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > span.tail { + margin-right: 0.6em; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > span.kind { + font-weight: 600; +} + +div#results-content > div#member-results > ul.entities > li > ul.members > li > a.label, +div#results-content > div#entity-results > ul.entities > li > ul.members > li > a.label { + color: #2C3D9B; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +/** Scrollpane settings needed for jquery.scrollpane.min.js */ +.jspContainer { + overflow: hidden; + position: relative; +} + +.jspPane { + position: absolute; +} + +.jspVerticalBar { + position: absolute; + top: 0; + right: 0; + width: 0.6em; + height: 100%; + background: transparent; +} + +.jspHorizontalBar { + position: absolute; + bottom: 0; + left: 0; + width: 100%; + height: 16px; + background: red; +} + +.jspCap { + display: none; +} + +.jspHorizontalBar .jspCap { + float: left; +} + +.jspTrack { + background: #f0f3f6; + position: relative; +} + +.jspDrag { + display: none; + background: rgba(0, 0, 0, 0.35); + position: relative; + top: 0; + left: 0; + cursor: pointer; +} + +#tpl:hover .jspDrag { + display: block; +} + +.jspHorizontalBar .jspTrack, +.jspHorizontalBar .jspDrag { + float: left; + height: 100%; +} + +.jspArrow { + background: #50506d; + text-indent: -20000px; + display: block; + cursor: pointer; + padding: 0; + margin: 0; +} + +.jspArrow.jspDisabled { + cursor: default; + background: #80808d; +} + +.jspVerticalBar .jspArrow { + height: 16px; +} + +.jspHorizontalBar .jspArrow { + width: 16px; + float: left; + height: 100%; +} + +.jspVerticalBar .jspArrow:focus { + outline: none; +} + +.jspCorner { + background: #eeeef4; + float: left; + height: 100%; +} + +/* CSS Hack for IE6 3 pixel bug */ +* html .jspCorner { + margin: 0 -3px 0 0; +} + +/* Media query rules for smaller viewport */ +@media only screen /* Large screen with a small window */ +and (max-width: 1300px) +{ + #textfilter { + left: 17.8em; + right: 0.35em; + } + + #textfilter .input { + max-width: none; + margin: 0; + } +} + +@media only screen /* Large screen with a smaller window */ +and (max-width: 800px) +{ + div#results-content > div#entity-results { + width: 100%; + padding: 0em; + } + + div#results-content > div#member-results { + width: 100%; + padding: 0em; + } +} + +/* Media query rules specifically for mobile devices */ +@media +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + div#content-container > div#subpackage-spacer { + display: none; + } + + div#content-container > div#content { + margin: 3.3em auto 0; + } + + #search > span#doc-title { + width: 100%; + text-align: left; + padding-left: 0.7em; + top: 0.95em; + z-index: 1; + } + + #search > div#textfilter { + z-index: 2; + } + + #search > span#doc-title > span#doc-version { + display: none; + } + + #textfilter { + left: 12.2em; + } +} diff --git a/static/stainless-library/lib/index.js b/static/stainless-library/lib/index.js new file mode 100644 index 0000000000..12f6ed6889 --- /dev/null +++ b/static/stainless-library/lib/index.js @@ -0,0 +1,616 @@ +// © 2009–2010 EPFL/LAMP +// code by Gilles Dubochet with contributions by Johannes Rudolph, "spiros", Marcin Kubala and Felix Mulder + +var scheduler = undefined; + +var title = $(document).attr('title'); + +var lastFragment = ""; + +var Index = {}; +(function (ns) { + ns.keyLength = 0; + ns.keys = function (obj) { + var result = []; + var key; + for (key in obj) { + result.push(key); + ns.keyLength++; + } + return result; + } +})(Index); + +/** Find query string from URL */ +var QueryString = function(key) { + if (QueryString.map === undefined) { // only calc once + QueryString.map = {}; + var keyVals = window.location.search.split("?").pop().split("&"); + keyVals.forEach(function(elem) { + var pair = elem.split("="); + if (pair.length == 2) QueryString.map[pair[0]] = pair[1]; + }); + } + + return QueryString.map[key]; +}; + +$(document).ready(function() { + // Clicking #doc-title returns the user to the root package + $("#doc-title").on("click", function() { document.location = toRoot + "index.html" }); + + scheduler = new Scheduler(); + scheduler.addLabel("init", 1); + scheduler.addLabel("focus", 2); + scheduler.addLabel("filter", 4); + scheduler.addLabel("search", 5); + + configureTextFilter(); + + $("#index-input").on("input", function(e) { + if($(this).val().length > 0) + $("#textfilter > .input > .clear").show(); + else + $("#textfilter > .input > .clear").hide(); + }); + + if (QueryString("search") !== undefined) { + $("#index-input").val(QueryString("search")); + searchAll(); + } +}); + +/* Handles all key presses while scrolling around with keyboard shortcuts in search results */ +function handleKeyNavigation() { + /** Iterates both back and forth among selected elements */ + var EntityIterator = function (litems, ritems) { + var it = this; + this.index = -1; + + this.items = litems; + this.litems = litems; + this.ritems = ritems; + + if (litems.length == 0) + this.items = ritems; + + /** Returns the next entry - if trying to select past last element, it + * returns the last element + */ + it.next = function() { + it.index = Math.min(it.items.length - 1, it.index + 1); + return $(it.items[it.index]); + }; + + /** Returns the previous entry - will return `undefined` instead if + * selecting up from first element + */ + it.prev = function() { + it.index = Math.max(-1, it.index - 1); + return it.index == -1 ? undefined : $(it.items[it.index]); + }; + + it.right = function() { + if (it.ritems.length != 0) { + it.items = it.ritems; + it.index = Math.min(it.index, it.items.length - 1); + } + return $(it.items[it.index]); + }; + + it.left = function() { + if (it.litems.length != 0) { + it.items = it.litems; + it.index = Math.min(it.index, it.items.length - 1); + } + return $(it.items[it.index]); + }; + }; + + function safeOffset($elem) { + return $elem.length ? $elem.offset() : { top:0, left:0 }; // offset relative to viewport + } + + /** Scroll helper, ensures that the selected elem is inside the viewport */ + var Scroller = function ($container) { + scroller = this; + scroller.container = $container; + + scroller.scrollDown = function($elem) { + var offset = safeOffset($elem); + if (offset !== undefined) { + var yPos = offset.top; + if ($container.height() < yPos || (yPos - $("#search").height()) < 0) { + $container.animate({ + scrollTop: $container.scrollTop() + yPos - $("#search").height() - 10 + }, 200); + } + } + }; + + scroller.scrollUp = function ($elem) { + var offset = safeOffset($elem); + if (offset !== undefined) { + var yPos = offset.top; + if (yPos < $("#search").height()) { + $container.animate({ + scrollTop: $container.scrollTop() + yPos - $("#search").height() - 10 + }, 200); + } + } + }; + + scroller.scrollTop = function() { + $container.animate({ + scrollTop: 0 + }, 200); + } + }; + + scheduler.add("init", function() { + $("#textfilter input").trigger("blur"); + var items = new EntityIterator( + $("div#results-content > div#entity-results > ul.entities span.entity > a").toArray(), + $("div#results-content > div#member-results > ul.entities span.entity > a").toArray() + ); + + var scroller = new Scroller($("#search-results")); + + var $old = items.next(); + $old.addClass("selected"); + scroller.scrollDown($old); + + $(window).on("keydown", function(e) { + switch ( e.keyCode ) { + case 9: // tab + $old.removeClass("selected"); + break; + + case 13: // enter + var href = $old.attr("href"); + location.replace(href); + $old.trigger("click"); + $("#textfilter input").val(""); + break; + + case 27: // escape + $("#textfilter input").val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + break; + + case 37: // left + var oldTop = safeOffset($old).top; + $old.removeClass("selected"); + $old = items.left(); + $old.addClass("selected"); + + (oldTop - safeOffset($old).top < 0 ? scroller.scrollDown : scroller.scrollUp)($old); + break; + + case 38: // up + $old.removeClass('selected'); + $old = items.prev(); + + if ($old === undefined) { // scroll past top + $(window).off("keydown"); + $("#textfilter input").trigger("focus"); + scroller.scrollTop(); + return false; + } else { + $old.addClass("selected"); + scroller.scrollUp($old); + } + break; + + case 39: // right + var oldTop = safeOffset($old).top; + $old.removeClass("selected"); + $old = items.right(); + $old.addClass("selected"); + + (oldTop - safeOffset($old).top < 0 ? scroller.scrollDown : scroller.scrollUp)($old); + break; + + case 40: // down + $old.removeClass("selected"); + $old = items.next(); + $old.addClass("selected"); + scroller.scrollDown($old); + break; + } + }); + }); +} + +/* Configures the text filter */ +function configureTextFilter() { + scheduler.add("init", function() { + var input = $("#textfilter input"); + input.on('keyup', function(event) { + switch ( event.keyCode ) { + case 27: // escape + input.val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + break; + + case 38: // up arrow + return false; + + case 40: // down arrow + $(window).off("keydown"); + handleKeyNavigation(); + return false; + } + + searchAll(); + }); + }); + scheduler.add("init", function() { + $("#textfilter > .input > .clear").on("click", function() { + $("#textfilter input").val(""); + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + + $(this).hide(); + }); + }); + + scheduler.add("init", function() { + $("div#search > span.close-results").on("click", function() { + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + $("#textfilter input").val(""); + }); + }); +} + +function compilePattern(query) { + var escaped = query.replace(/([\.\*\+\?\|\(\)\[\]\\])/g, '\\$1'); + + if (query.toLowerCase() != query) { + // Regexp that matches CamelCase subbits: "BiSe" is + // "[a-z]*Bi[a-z]*Se" and matches "BitSet", "ABitSet", ... + return new RegExp(escaped.replace(/([A-Z])/g,"[a-z]*$1")); + } + else { // if query is all lower case make a normal case insensitive search + return new RegExp(escaped, "i"); + } +} + +/** Searches packages for entites matching the search query using a regex + * + * @param {[Object]} pack: package being searched + * @param {RegExp} regExp: a regular expression for finding matching entities + */ +function searchPackage(pack, regExp) { + scheduler.add("search", function() { + var entities = Index.PACKAGES[pack]; + var matched = []; + var notMatching = []; + + scheduler.add("search", function() { + searchMembers(entities, regExp, pack); + }); + + entities.forEach(function (elem) { + regExp.test(elem.name) ? matched.push(elem) : notMatching.push(elem); + }); + + var results = { + "matched": matched, + "package": pack + }; + + scheduler.add("search", function() { + handleSearchedPackage(results, regExp); + setProgress(); + }); + }); +} + +function searchMembers(entities, regExp, pack) { + var memDiv = document.getElementById("member-results"); + var packLink = document.createElement("a"); + packLink.className = "package"; + packLink.appendChild(document.createTextNode(pack)); + packLink.style.display = "none"; + packLink.title = pack; + packLink.href = toRoot + urlFriendlyEntity(pack).replace(new RegExp("\\.", "g"), "/") + "/index.html"; + memDiv.appendChild(packLink); + + var entityUl = document.createElement("ul"); + entityUl.className = "entities"; + memDiv.appendChild(entityUl); + + entities.forEach(function(entity) { + var entityLi = document.createElement("li"); + var name = entity.name.split('.').pop() + + var iconElem = document.createElement("a"); + iconElem.className = "icon " + entity.kind; + iconElem.title = name + " " + entity.kind; + iconElem.href = toRoot + entity[entity.kind]; + entityLi.appendChild(iconElem); + + if (entity.kind != "object" && entity.object) { + var companion = document.createElement("a"); + companion.className = "icon object"; + companion.title = name + " companion object"; + companion.href = toRoot + entity.object; + entityLi.insertBefore(companion, iconElem); + } else { + var spacer = document.createElement("div"); + spacer.className = "icon spacer"; + entityLi.insertBefore(spacer, iconElem); + } + + var nameElem = document.createElement("span"); + nameElem.className = "entity"; + + var entityUrl = document.createElement("a"); + entityUrl.title = entity.shortDescription ? entity.shortDescription : name; + entityUrl.href = toRoot + entity[entity.kind]; + entityUrl.appendChild(document.createTextNode(name)); + + nameElem.appendChild(entityUrl); + entityLi.appendChild(nameElem); + + var membersUl = document.createElement("ul"); + membersUl.className = "members"; + entityLi.appendChild(membersUl); + + + searchEntity(entity, membersUl, regExp) + .then(function(res) { + if (res.length > 0) { + packLink.style.display = "block"; + entityUl.appendChild(entityLi); + } + }); + }); +} + +/** This function inserts `li` into the `ul` ordered by the li's id + * + * @param {Node} ul: the list in which to insert `li` + * @param {Node} li: item to insert + */ +function insertSorted(ul, li) { + var lis = ul.childNodes; + var beforeLi = null; + + for (var i = 0; i < lis.length; i++) { + if (lis[i].id > li.id) + beforeLi = lis[i]; + } + + // if beforeLi == null, it will be inserted last + ul.insertBefore(li, beforeLi); +} + +/** Defines the callback when a package has been searched and searches its + * members + * + * It will search all entities which matched the regExp. + * + * @param {Object} res: this is the searched package. It will contain the map + * from the `searchPackage`function. + * @param {RegExp} regExp + */ +function handleSearchedPackage(res, regExp) { + $("div#search-results").show(); + $("#search > span.close-results").show(); + $("#search > span#doc-title").hide(); + + var searchRes = document.getElementById("results-content"); + var entityDiv = document.getElementById("entity-results"); + + var packLink = document.createElement("a"); + packLink.className = "package"; + packLink.title = res.package; + packLink.href = toRoot + urlFriendlyEntity(res.package).replace(new RegExp("\\.", "g"), "/") + "/index.html"; + packLink.appendChild(document.createTextNode(res.package)); + + if (res.matched.length == 0) + packLink.style.display = "none"; + + entityDiv.appendChild(packLink); + + var ul = document.createElement("ul") + ul.className = "entities"; + + // Generate html list items from results + res.matched + .map(function(entity) { return listItem(entity, regExp); }) + .forEach(function(li) { ul.appendChild(li); }); + + entityDiv.appendChild(ul); +} + +/** Searches an entity asynchronously for regExp matches in an entity's members + * + * @param {Object} entity: the entity to be searched + * @param {Node} ul: the list in which to insert the list item created + * @param {RegExp} regExp + */ +function searchEntity(entity, ul, regExp) { + return new Promise(function(resolve, reject) { + var allMembers = + (entity.members_trait || []) + .concat(entity.members_class || []) + .concat(entity.members_object || []) + + var matchingMembers = $.grep(allMembers, function(member, i) { + return regExp.test(member.label); + }); + + resolve(matchingMembers); + }) + .then(function(res) { + res.forEach(function(elem) { + var kind = document.createElement("span"); + kind.className = "kind"; + kind.appendChild(document.createTextNode(elem.kind)); + + var label = document.createElement("a"); + label.title = elem.label; + label.href = toRoot + elem.link; + label.className = "label"; + label.appendChild(document.createTextNode(elem.label)); + + var tail = document.createElement("span"); + tail.className = "tail"; + tail.appendChild(document.createTextNode(elem.tail)); + + var li = document.createElement("li"); + li.appendChild(kind); + li.appendChild(label); + li.appendChild(tail); + + ul.appendChild(li); + }); + return res; + }); +} + +/** Creates a list item representing an entity + * + * @param {Object} entity, the searched entity to be displayed + * @param {RegExp} regExp + * @return {Node} list item containing entity + */ +function listItem(entity, regExp) { + var name = entity.name.split('.').pop() + var nameElem = document.createElement("span"); + nameElem.className = "entity"; + + var entityUrl = document.createElement("a"); + entityUrl.title = entity.shortDescription ? entity.shortDescription : name; + entityUrl.href = toRoot + entity[entity.kind]; + + entityUrl.appendChild(document.createTextNode(name)); + nameElem.appendChild(entityUrl); + + var iconElem = document.createElement("a"); + iconElem.className = "icon " + entity.kind; + iconElem.title = name + " " + entity.kind; + iconElem.href = toRoot + entity[entity.kind]; + + var li = document.createElement("li"); + li.id = entity.name.replace(new RegExp("\\.", "g"),"-"); + li.appendChild(iconElem); + li.appendChild(nameElem); + + if (entity.kind != "object" && entity.object) { + var companion = document.createElement("a"); + companion.title = name + " companion object"; + companion.href = toRoot + entity.object; + companion.className = "icon object"; + li.insertBefore(companion, iconElem); + } else { + var spacer = document.createElement("div"); + spacer.className = "icon spacer"; + li.insertBefore(spacer, iconElem); + } + + var ul = document.createElement("ul"); + ul.className = "members"; + + li.appendChild(ul); + + return li; +} + +/** Searches all packages and entities for the current search string in + * the input field "#textfilter" + * + * Then shows the results in div#search-results + */ +function searchAll() { + scheduler.clear("search"); // clear previous search + maxJobs = 1; // clear previous max + var searchStr = ($("#textfilter input").val() || '').trim(); + + if (searchStr === '') { + $("div#search-results").hide(); + $("#search > span.close-results").hide(); + $("#search > span#doc-title").show(); + return; + } + + // Replace ?search=X with current search string if not hosted locally on Chrome + try { + window.history.replaceState({}, "", "?search=" + searchStr); + } catch(e) {} + + $("div#results-content > span.search-text").remove(); + + var memberResults = document.getElementById("member-results"); + memberResults.innerHTML = ""; + var memberH1 = document.createElement("h1"); + memberH1.className = "result-type"; + memberH1.innerHTML = "Member results"; + memberResults.appendChild(memberH1); + + var entityResults = document.getElementById("entity-results"); + entityResults.innerHTML = ""; + var entityH1 = document.createElement("h1"); 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + p + + + + + + + diff --git a/static/stainless-library/lib/ref-index.css b/static/stainless-library/lib/ref-index.css new file mode 100644 index 0000000000..7cdcd9de21 --- /dev/null +++ b/static/stainless-library/lib/ref-index.css @@ -0,0 +1,56 @@ +/* fonts */ +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 400; + src: url('source-code-pro-v6-latin-regular.eot'); + src: local('Source Code Pro'), local('SourceCodePro-Regular'), + url('source-code-pro-v6-latin-regular.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-regular.woff') format('woff'), + url('source-code-pro-v6-latin-regular.ttf') format('truetype'); +} +@font-face { + font-family: 'Source Code Pro'; + font-style: normal; + font-weight: 700; + src: url('source-code-pro-v6-latin-700.eot'); + src: local('Source Code Pro Bold'), local('SourceCodePro-Bold'), + url('source-code-pro-v6-latin-700.eot?#iefix') format('embedded-opentype'), + url('source-code-pro-v6-latin-700.woff') format('woff'), + url('source-code-pro-v6-latin-700.ttf') format('truetype'); +} + +body { + font-size: 10pt; + font-family: Arial, sans-serif; +} + +a { + color:#315479; +} + +.letters { + width:100%; + text-align:center; + margin:0.6em; + padding:0.1em; + border-bottom:1px solid gray; +} + +div.entry { + padding: 0.5em; + background-color: #e1e7ed; + border-radius: 0.2em; + color: #103a51; + margin: 0.5em 0; +} + +.name { + font-family: "Source Code Pro"; + font-size: 1.1em; +} + +.occurrences { + margin-left: 1em; + margin-top: 5px; +} diff --git a/static/stainless-library/lib/scheduler.js b/static/stainless-library/lib/scheduler.js new file mode 100644 index 0000000000..eb396bb5d3 --- /dev/null +++ b/static/stainless-library/lib/scheduler.js @@ -0,0 +1,108 @@ +// © 2010 EPFL/LAMP +// code by Gilles Dubochet, Felix Mulder + +function Scheduler() { + var scheduler = this; + var resolution = 0; + this.timeout = undefined; + this.queues = new Array(0); // an array of work packages indexed by index in the labels table. + this.labels = new Array(0); // an indexed array of labels indexed by priority. This should be short. + + this.label = function(name, priority) { + this.name = name; + this.priority = priority; + } + + this.work = function(fn, self, args) { + this.fn = fn; + this.self = self; + this.args = args; + } + + this.addLabel = function(name, priority) { + var idx = 0; + while (idx < scheduler.queues.length && scheduler.labels[idx].priority <= priority) { idx = idx + 1; } + scheduler.labels.splice(idx, 0, new scheduler.label(name, priority)); + scheduler.queues.splice(idx, 0, new Array(0)); + } + + this.clearLabel = function(name) { + var idx = scheduler.indexOf(name); + if (idx != -1) { + scheduler.labels.splice(idx, 1); + scheduler.queues.splice(idx, 1); + } + } + + this.nextWork = function() { + var fn = undefined; + var idx = 0; + while (idx < scheduler.queues.length && scheduler.queues[idx].length == 0) { idx = idx + 1; } + + if (idx < scheduler.queues.length && scheduler.queues[idx].length > 0) + var fn = scheduler.queues[idx].shift(); + + return fn; + } + + this.add = function(labelName, fn, self, args) { + var doWork = function() { + scheduler.timeout = setTimeout(function() { + var work = scheduler.nextWork(); + if (work != undefined) { + if (work.args == undefined) { work.args = new Array(0); } + work.fn.apply(work.self, work.args); + doWork(); + } + else { + scheduler.timeout = undefined; + } + }, resolution); + } + + var idx = scheduler.indexOf(labelName) + if (idx != -1) { + scheduler.queues[idx].push(new scheduler.work(fn, self, args)); + if (scheduler.timeout == undefined) doWork(); + } else { + throw("queue for add is non-existent"); + } + } + + this.clear = function(labelName) { + scheduler.queues[scheduler.indexOf(labelName)] = new Array(); + } + + this.indexOf = function(label) { + var idx = 0; + while (idx < scheduler.labels.length && scheduler.labels[idx].name != label) + idx++; + + return idx < scheduler.queues.length && scheduler.labels[idx].name == label ? idx : -1; + } + + this.queueEmpty = function(label) { + var idx = scheduler.indexOf(label); + if (idx != -1) + return scheduler.queues[idx].length == 0; + else + throw("queue for label '" + label + "' is non-existent"); + } + + this.scheduleLast = function(label, fn) { + if (scheduler.queueEmpty(label)) { + fn(); + } else { + scheduler.add(label, function() { + scheduler.scheduleLast(label, fn); + }); + } + } + + this.numberOfJobs = function(label) { + var index = scheduler.indexOf(label); + if (index == -1) throw("queue for label '" + label + "' non-existent"); + + return scheduler.queues[index].length; + } +}; diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-700.eot b/static/stainless-library/lib/source-code-pro-v6-latin-700.eot new file mode 100644 index 0000000000..094e578e59 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-700.eot differ diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-700.ttf b/static/stainless-library/lib/source-code-pro-v6-latin-700.ttf new file mode 100644 index 0000000000..04159884d6 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-700.ttf differ diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-700.woff b/static/stainless-library/lib/source-code-pro-v6-latin-700.woff new file mode 100644 index 0000000000..6ac8a3b295 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-700.woff differ diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-regular.eot b/static/stainless-library/lib/source-code-pro-v6-latin-regular.eot new file mode 100644 index 0000000000..60bd73b583 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-regular.eot differ diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf b/static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf new file mode 100644 index 0000000000..268a2e4322 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-regular.ttf differ diff --git a/static/stainless-library/lib/source-code-pro-v6-latin-regular.woff b/static/stainless-library/lib/source-code-pro-v6-latin-regular.woff new file mode 100644 index 0000000000..7daeecc8a6 Binary files /dev/null and b/static/stainless-library/lib/source-code-pro-v6-latin-regular.woff differ diff --git a/static/stainless-library/lib/template.css b/static/stainless-library/lib/template.css new file mode 100644 index 0000000000..ae285a7023 --- /dev/null +++ b/static/stainless-library/lib/template.css @@ -0,0 +1,1224 @@ +/* Reset */ + +html, body, div, span, object, iframe, +h1, h2, h3, h4, h5, h6, p, blockquote, pre, +a, abbr, acronym, address, code, pre, +del, dfn, em, img, q, dl, dt, dd, ol, ul, li, +fieldset, form, label, legend, input, +table, caption, tbody, tfoot, thead, tr, th, td { + margin: 0; + padding: 0; + border: 0; + font-weight: inherit; + font-style: inherit; + font-size: 100%; + font-family: inherit; + vertical-align: baseline; +} + +table { border-collapse: separate; border-spacing: 0; } +caption, th, td { text-align: left; font-weight: normal; } +table, td, th { vertical-align: middle; } + +textarea, input { outline: none; } + +blockquote:before, blockquote:after, q:before, q:after { content: ""; } +blockquote, q { quotes: none; } + +a img { border: none; } + +input { border-width: 0px; } + +/* Page */ +body { + overflow-x: hidden; + font-family: Arial, sans-serif; + background-color: #f0f3f6; +} + +#footer { + text-align: center; + color: #858484; + bottom: 0; + min-height: 20px; + margin: 0 1em 0.5em; +} + +#content-container a[href] { + text-decoration: underline; + color: #315479; +} + +#content-container a[href]:hover { + text-decoration: none; +} + +#types ol li > p { + margin-top: 5px; +} + +#types ol li:last-child { + margin-bottom: 5px; +} + +#definition { + position: relative; + display: block; + padding: 5px 0; + padding: 0; + margin: 0.5em; + min-height: 4.72em; +} + +#definition > a > img { + float: left; + padding-right: 6px; + padding-left: 5px; +} + +#definition p + h1 { + margin-top: 3px; +} + +#definition > h1 { + float: left; + color: #103a51; + display: inline-block; + overflow: hidden; + margin-top: 10px; + font-size: 2.0em; +} + +#definition h1 > a { + color: #103a51 !important; + text-decoration: none !important; +} + +#template ol > li > span.permalink > a > i { + transform: rotate(-45deg); +} + +#definition #owner { + color: #103a51; + padding-top: 1.3em; + font-size: 0.8em; + overflow: hidden; +} + +#definition > h3 { + margin-top: 0.85em; + padding: 0; +} + +#definition #owner > a { + color: #103a51; +} + +#definition #owner > a:hover { + text-decoration: none; +} + +#signature { + background-color: #c2d2dc; + min-height: 18px; + font-size: 0.9em; + padding: 8px; + color: #103a51; + border-radius: 0.2em; + margin: 0 0.5rem; +} + +#signature > span.modifier_kind { + display: inline; + float: left; + text-align: left; + width: auto; + position: static; + padding-left: 0; +} + +span.symbol > a { + display: inline-block; +} + +#signature > span.symbol { + text-align: left; + display: inline; + padding-left: 0.7em; +} + +/* Linear super types and known subclasses */ +.hiddenContent { + display: none; +} + +.toggleContainer .toggle { + position: relative; + color: #103a51; + margin-left: 0.3em; + cursor: pointer; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +.toggleContainer .toggle > i { + position: absolute; + left: -1.5em; + top: 0em; + font-size: 1.3em; + transition: 0.1s; +} + +.toggleContainer .toggle.open > i { + transform: rotate(90deg); +} + +.toggleContainer .hiddenContent { + margin-top: 1.5em; +} + +#memberfilter > i.arrow { + position: absolute; + top: 0.45em; + left: -0.9em; + color: #fff; + font-size: 1.3em; + opacity: 0; + transition: 0.1s; + cursor: pointer; +} + +#memberfilter > i.arrow.rotate { + transform: rotate(90deg); +} + +#memberfilter:hover > i.arrow { + opacity: 1; +} + +.big-circle { + box-sizing: content-box; + height: 5.7em; + width: 5.7em; + float: left; + color: transparent; +} + +.big-circle:hover { + background-size: 5.7em; +} + +.big-circle.class { + background: url("class.svg") no-repeat center; +} + +.big-circle.class-companion-object { + background: url("class_comp.svg") no-repeat center; +} + +.big-circle.object-companion-class { + background: url("object_comp.svg") no-repeat center; +} + +.big-circle.trait-companion-object { + background: url("trait_comp.svg") no-repeat center; +} + +.big-circle.object-companion-trait { + background: url("object_comp_trait.svg") no-repeat center; +} + +.big-circle.object { + background: url("object.svg") no-repeat center; +} + +.big-circle.trait { + background: url("trait.svg") no-repeat center; +} + +.big-circle.package { + background: url("package.svg") no-repeat center; +} + +body.abstract.type div.big-circle { + background: url("abstract_type.svg") no-repeat center; +} + +body.alias.type div.big-circle { + background: url("abstract_type.svg") no-repeat center; +} + +#template { + margin: 0.9em 0.75em 0.75em; + padding-bottom: 0.5em; +} + +#template h3 { + color: #103a51; + height: 2em; + padding: 1em 1em 2em; + font-size: 1.2em; +} + +#order { + margin-top: 1.5em; +} + +h3 { + color: #103a51; + padding: 5px 10px; + font-size: 1em; + font-weight: bold; +} + +dl.attributes > dt { + display: block; + float: left; + font-style: italic; + font-weight: bold; +} + +dl.attributes > dt.implicit { + font-weight: bold; + color: darkgreen; +} + +dl.attributes > dd { + display: block; + padding-left: 10em; + margin-bottom: 5px; + min-height: 15px; +} + +.values ol li:last-child { + margin-bottom: 5px; +} + +#constructors > h3 { + height: 2em; + padding: 1em 1em 2em; + color: #2C475C; +} + +#inheritedMembers > div.parent > h3 { + height: 17px; + font-style: italic; +} + +#inheritedMembers > div.parent > h3 * { + color: white; +} + +#inheritedMembers > div.conversion > h3 { + height: 2em; + padding: 1em; + font-style: italic; + color: #2C475C; +} + +#groupedMembers > div.group > h3 { + color: #2C475C; + height: 2em; + padding: 1em 1em 2em; +} + +/* Member cells */ +div.members > ol { + list-style: none; +} + +div.members > ol > li { + display: table; + width: 100%; + position: relative; + background-color: #fff; + border-radius: 0.2em; + color: #103a51; + padding: 5px 0 5px; + margin-bottom: 0.4em; + min-height: 3.7em; + border-left: 0.25em solid white; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.1); + box-shadow: 0 0 10px rgba(0,0,0,0.1); + transition: 0.1s; +} + +div.members > ol >li.selected, +div.members > ol > li:hover { + background-color: #dae7f0; + border-left-color: #dae7f0; +} + +div.members > ol >li[fullComment=yes].selected, +div.members > ol > li[fullComment=yes]:hover { + cursor: pointer; + border-left: 0.25em solid #72D0EB; +} + +div.members > ol > li:last-child { + padding: 5px 0 5px; +} + +/* Member signatures */ + +#tooltip { + background: #EFD5B5; + border: 1px solid gray; + color: black; + display: none; + padding: 5px; + position: absolute; +} + +.signature { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.8rem; + line-height: 18px; + clear: both; + display: block; +} + +.modifier_kind { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + font-size: 0.8rem; + padding-right: 0.5em; + text-align: right; + display: table-cell; + white-space: nowrap; + width: 16em; +} + +.symbol { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +a > .symbol > .name { + text-decoration: underline; +} + +a:hover > .symbol > .name { + text-decoration: none; +} + +.signature > a { + text-decoration: none; +} + +.signature > .symbol { + display: inline; +} + +.signature .name { + display: inline-block; + font-weight: bold; +} + +span.symbol > span.name { + font-weight: bold; +} + +#types > ol > li > span.symbol > span.result { + display: none; +} + +#types > ol > li > span.symbol > span.result.alias, +#types > ol > li:hover > span.symbol > span.result, +#types > ol > li.open > span.symbol > span.result { + display: inline; +} + +.symbol > .implicit { + display: inline-block; + font-weight: bold; + text-decoration: underline; + color: darkgreen; +} + +.symbol .shadowed { + color: darkseagreen; +} + +.symbol .params > .implicit { + font-style: italic; +} + +.symbol .deprecated { + text-decoration: line-through; +} + +.symbol .params .default { + font-style: italic; +} + +#template .closed { + cursor: pointer; +} + +#template .opened { + cursor: pointer; +} + +i.unfold-arrow { + font-size: 1em; + position: absolute; + top: 0.55em; + left: 0.7em; + transition: 0.1s; +} + +#template .modifier_kind.opened > i.unfold-arrow { + transform: rotate(90deg); +} + +#template .values .name { + font-weight: 600; + color: #315479; +} + +#template .types .name { + font-weight: 600; + color: darkgreen; +} + +.full-signature-usecase h4 span { + font-size: 0.8rem; +} + +.full-signature-usecase > #signature { + padding-top: 0px; + position: relative; + top: 0; +} + +/* Hide unfold arrow where appropriate */ +#template li[fullComment=no] .modifier_kind > i.unfold-arrow, +div#definition > h4#signature > span.modifier_kind > i.unfold-arrow, +.full-signature-usecase > .signature > .closed > i.unfold-arrow, +.full-signature-usecase > .signature > .opened > i.unfold-arrow { + display: none; +} + +#template .full-signature-usecase > .signature > .closed { + background: none; +} + +#template .full-signature-usecase > .signature > .opened { + background: none; +} + +.full-signature-block { + padding: 5px 0 0; + border-top: 1px solid #EBEBEB; + margin-top: 5px; + margin-bottom: 5px; +} + +#definition .morelinks { + text-align: right; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +#definition .morelinks a { + color: #103a51; +} + +#template .members li .permalink { + position: absolute; + left: 0.25em; + top: 0.95em; +} + +#definition .permalink { + display: none; + color: black; +} + +#definition .permalink a { + color: #103a51; + transform: rotate(-45deg); +} + +#definition > h1 > span > a > i { + font-size: 1.4rem; +} + +#template ol > li > span.permalink > a > i { + color: #fff; +} + +#template .members li .permalink, +#definition .permalink a { + display: none; +} + +#template .members li:hover .permalink, +#definition:hover .permalink a { + display: block; +} + +#template .members li .permalink a, +#definition .permalink a { + text-decoration: none; + font-weight: bold; +} + +/* Comments text formatting */ + +.cmt { + color: #103a51; +} + +.cmt p { + margin: 0.7em 0; +} + +.cmt p:first-child { + margin-top: 0; +} + +.cmt p:last-child { + margin-bottom: 0; +} + +.cmt h3, +.cmt h4, +.cmt h5, +.cmt h6 { + margin-bottom: 0.7em; + margin-top: 1.4em; + display: block; + text-align: left; + font-weight: bold; +} + +.cmt pre { + padding: 0.5em; + border: 0px solid #ddd; + background-color: #fff; + margin: 5px 0; + display: block; + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; + border-radius: 0.2em; + overflow-x: auto; +} + +.cmt pre span.ano { + color: blue; +} + +.cmt pre span.cmt { + color: green; +} + +.cmt pre span.kw { + font-weight: bold; +} + +.cmt pre span.lit { + color: #c71585; +} + +.cmt pre span.num { + color: #1e90ff; /* dodgerblue */ +} + +.cmt pre span.std { + color: #008080; /* teal */ +} + +.cmt ul { + display: block; + list-style: circle; + padding-left: 20px; +} + +.cmt ol { + display: block; + padding-left:20px; +} + +.cmt ol.decimal { + list-style: decimal; +} + +.cmt ol.lowerAlpha { + list-style: lower-alpha; +} + +.cmt ol.upperAlpha { + list-style: upper-alpha; +} + +.cmt ol.lowerRoman { + list-style: lower-roman; +} + +.cmt ol.upperRoman { + list-style: upper-roman; +} + +.cmt li { + display: list-item; +} + +.cmt code { + font-family: "Source Code Pro", "Monaco", "Ubuntu Mono Regular", "Lucida Console", monospace; +} + +.cmt a { + font-style: bold; +} + +.cmt em, .cmt i { + font-style: italic; +} + +.cmt strong, .cmt b { + font-weight: bold; +} + +/* Comments structured layout */ + +.group > div.comment { + display: block; + padding: 0 1.2em 1em; + font-family: "Open Sans"; +} + +p.comment { + display: block; + margin-left: 14.7em; + margin-top: 5px; +} + +.shortcomment { + display: block; + margin: 5px 10px; +} + +.shortcomment > span.badge { + display: block; + position: absolute; + right: 0; + top: 0.7em; +} + +div.fullcommenttop { + padding: 1em 0.8em; +} + +div.fullcomment { + margin: 5px 10px; +} + +#template div.fullcommenttop, +#template div.fullcomment { + display:none; + margin: 0.5em 1em 0 0; +} + +#template .shortcomment { + margin: 5px 0 0 0; + padding: 0; + font-family: "Open Sans"; +} + +div.fullcomment .block { + padding: 5px 0 0; + border-top: 2px solid #fff; + margin-top: 5px; + overflow: hidden; + font-family: "Open Sans"; +} + +div.fullcommenttop .block { + position: relative; + padding: 1em; + margin: 0.5em 0; + border-radius: 0.2em; + background-color: #fff; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.1); + box-shadow: 0 0 10px rgba(0,0,0,0.1); +} + +div.fullcommenttop .toggleContainer { + border-left: 0 solid #72D0EB; + transition: 0.1s; + cursor: pointer; +} + +div.fullcommenttop .toggleContainer:hover { + border-left: 0.25em solid #72D0EB; +} + +div#comment, +div#mbrsel, +div#template, +div#footer { + font-size: 0.8em; +} + +#comment { + font-family: "Open Sans"; +} + +#comment > dl { + background: transparent; + -webkit-box-shadow: none; + box-shadow: none; +} + +#comment > dl > div > ol { + list-style-type: none; +} + +div.fullcomment div.block ol li p, +div.fullcomment div.block ol li { + display:inline +} + +div.fullcomment .block > h5 { + font-style: italic; + font-weight: normal; + display: inline-block; +} + +div.fullcomment .comment { + font-family: "Open Sans"; + margin: 5px 0 10px; +} + +div.fullcommenttop .comment:last-child, +div.fullcomment .comment:last-child { + margin-bottom: 0; +} + +div.fullcommenttop dl.paramcmts { + margin-bottom: 0.8em; + padding-bottom: 0.8em; +} + +div.fullcommenttop dl.paramcmts > dt, +div.fullcomment dl.paramcmts > dt { + display: block; + float: left; + font-weight: bold; + min-width: 70px; +} + +div.fullcommenttop dl.paramcmts > dd, +div.fullcomment dl.paramcmts > dd { + display: block; + padding-left: 10px; + margin-bottom: 5px; + margin-left: 70px; + min-height: 15px; +} + +/* Author Content Table formatting */ + +.doctbl { + border-collapse: collapse; + margin: 1.0em 0em; +} + +.doctbl-left { + text-align: left; +} + +.doctbl-center { + text-align: center; +} + +.doctbl-right { + text-align: right; +} + +table.doctbl th { + border: 1px dotted #364550; + background-color: #c2d2dc; + padding: 5px; + color: #103a51; + font-weight: bold; +} + +table.doctbl td { + border: 1px dotted #364550; + padding: 5px; +} + +/* Members filter tool */ + +#memberfilter { + position: relative; + display: block; + height: 2.7em; + margin-bottom: 5px; + margin-left: 1.5em; +} + +#memberfilter > .input { + display: block; + position: absolute; + top: 0; + left: -1.65em; + right: -0.2em; + transition: 0.2s; +} + +#memberfilter > .input > input { + color: #fff; + width: 100%; + border-radius: 0.2em; + padding: 0.5em; + background: rgba(255, 255, 255, 0.2); + font-family: "Open Sans"; +} + +#memberfilter > .input > input::-webkit-input-placeholder { + color: #fff; + opacity: 0.6; +} +#memberfilter > .input > input:-ms-input-placeholder { + color: #fff; + opacity: 0.6; +} +#memberfilter > .input > input::placeholder { + color: #fff; + opacity: 0.6; +} + +#memberfilter > .clear { + display: none; + position: absolute; + top: 0.55em; + color: rgba(255, 255, 255, 0.4); + right: 0; + font-size: 1.2em; +} + +#memberfilter > .clear:hover { + color: #fff; + cursor: pointer; +} + +#mbrsel { + display: block; + padding: 1em 1em 0.5em; + margin: 0.8em; + border-radius: 0.2em; + background-color: #364550; + -webkit-box-shadow: 0 0 10px rgba(0,0,0,0.2); + box-shadow: 0 0 10px rgba(0,0,0,0.2); + position: relative; +} + +#mbrsel > div.toggle { + opacity: 0; + position: absolute; + left: 1.85em; + top: 1.75em; + width: 1em; + height: 1em; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; + transition: 0.2s; +} + +#mbrsel:hover > div.toggle { + opacity: 1; +} + +#mbrsel:hover #memberfilter > .input { + left: 0.7em; +} + +#mbrsel > div.toggle > i { + cursor: pointer; + position: absolute; + left: 0; + top: 0; + color: #fff; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#mbrsel > div.toggle.open > i { + transform: rotate(90deg); +} + +#mbrsel > div#filterby { + display: none; +} + +#mbrsel > div#filterby > div { + margin-bottom: 5px; +} + +#mbrsel > div#filterby > div:last-child { + margin-bottom: 0; +} + +#mbrsel > div#filterby > div > span.filtertype { + color: #fff; + padding: 4px; + margin-right: 1em; + float: left; + display: inline-block; + font-weight: bold; + width: 4.5em; +} + +#mbrsel > div#filterby > div > ol { + display: inline-block; +} + +#mbrsel > div#filterby > div > a { + position:relative; + top: -8px; + font-size: 11px; +} + +#mbrsel > div#filterby > div > ol#linearization { + display: table; + margin-left: 70px; +} + +#mbrsel > div#filterby > div > ol#linearization > li.in { + text-decoration: none; + float: left; + margin-right: 5px; + background-position: right 0px; +} + +#mbrsel > div#filterby > div > ol#linearization > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol#implicits { + display: table; + margin-left: 70px; +} + +#mbrsel > div#filterby > div > ol#implicits > li { + text-decoration: none; + float: left; + margin: 0.4em 0.4em 0.4em 0; +} + +#mbrsel > div#filterby > div > ol#implicits > li.in { + text-decoration: none; + float: left; +} + +#mbrsel > div#filterby > div > ol#implicits > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol > li { + line-height: 1.5em; + display: inline-block; + cursor: pointer; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +#mbrsel > div#filterby > div > ol > li.in { + text-decoration: none; + float: left; + margin-right: 5px; + + font-size: 0.8em; + -webkit-border-radius: 0.2em; + border-radius: 0.2em; + padding: 5px 15px; + cursor: pointer; + background: #f16665; + border-bottom: 2px solid #d64546; + color: #fff; + font-weight: 700; +} + +#mbrsel > div#filterby > div > ol > li.in > span{ + float: left; +} + +#mbrsel > div#filterby > div > ol > li.out { + text-decoration: none; + float: left; + padding-right: 10px; + margin-right: 5px; + font-size: 0.8em; + -webkit-border-radius: 0.2em; + border-radius: 0.2em; + padding: 5px 15px; + cursor: pointer; + background: #c2d2dc; + border-bottom: 2px solid rgba(0, 0, 0, 0.1); + color: #103a51; + font-weight: 700; +} + +#mbrsel > div#filterby > div > ol > li.out > span{ + float: left; +} + +.badge { + display: inline-block; + padding: 0.3em 1em; + font-size: 0.8em; + font-weight: bold; + color: #ffffff; + white-space: nowrap; + vertical-align: middle; + background-color: #999999; + -webkit-border-radius: 9px; + -moz-border-radius: 9px; + border-radius: 1em; + font-family: "Open Sans"; +} + +.badge-red { + background-color: #b94a48; + margin-right: 0.8em !important; +} + +/* Media query rules for smaller viewport */ +@media only screen /* Large screen with a small window */ +and (max-width: 650px) +, +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + body, + body > h4#signature { + min-width: 300px; + } + + #template .modifier_kind { + width: 1px; + padding-left: 2.5em; + } + + span.modifier_kind > span.modifier { + display: none; + } + + #definition { + height: 6em; + } + + #definition > h1 { + font-size: 1em; + margin-right: 0.3em; + } + + #definition > h3 { + float: left; + margin: 0.3em 0; + } + + #definition > #owner { + padding-top: 2.6em; + } + + #definition .morelinks { + text-align: left; + font-size: 0.8em; + } + + .big-circle { + margin-top: 0.6em; + } +} + +/* Media query rules specifically for mobile devices */ +@media +screen /* HiDPI device like Nexus 5 */ +and (max-device-width: 360px) +and (max-device-height: 640px) +and (-webkit-device-pixel-ratio: 3) +, +screen /* Most mobile devices */ +and (max-device-width: 480px) +and (orientation: portrait) +, +only screen /* iPhone 6 */ +and (max-device-width: 667px) +and (-webkit-device-pixel-ratio: 2) +{ + #signature { + font-size: 0.7em; + } + + #definition > h1 { + font-size: 1.3em; + } + + #definition .morelinks { + display: none; + } + + #definition #owner { + padding-top: 0.7em; + } + + #signature > span.modifier_kind { + width: auto; + } + + div.fullcomment dl.attributes > dt { + margin: 0.5em 0; + clear: both; + } + + div.fullcomment dl.attributes > dd { + padding-left: 0; + clear: both; + } + + .big-circle { + width: 3em; + height: 3em; + background-size: 3em !important; + margin: 0.5em; + } + + div#template { + margin-bottom: 0.5em; + } + + div#footer { + font-size: 0.5em; + } + + .shortcomment > span.badge { + display: none; + } +} diff --git a/static/stainless-library/lib/template.js b/static/stainless-library/lib/template.js new file mode 100644 index 0000000000..89112cb02e --- /dev/null +++ b/static/stainless-library/lib/template.js @@ -0,0 +1,548 @@ +// © 2009–2010 EPFL/LAMP +// code by Gilles Dubochet with contributions by Pedro Furlanetto, Marcin Kubala and Felix Mulder + +var $panzoom = undefined; +$(document).ready(function() { + // Add zoom functionality to type inheritance diagram + $panzoom = $(".diagram-container > .diagram").panzoom({ + increment: 0.1, + minScale: 1, + maxScale: 7, + transition: true, + duration: 200, + contain: 'invert', + easing: "ease-in-out", + $zoomIn: $('#diagram-zoom-in'), + $zoomOut: $('#diagram-zoom-out'), + }); + + var oldWidth = $("div#subpackage-spacer").width() + 1 + "px"; + $("div#packages > ul > li.current").on("click", function() { + $("div#subpackage-spacer").css({ "width": oldWidth }); + $("li.current-entities").toggle(); + }); + + var controls = { + visibility: { + publicOnly: $("#visbl").find("> ol > li.public"), + all: $("#visbl").find("> ol > li.all") + } + }; + + // Escapes special characters and returns a valid jQuery selector + function escapeJquery(str){ + return str.replace(/([;&,\.\+\*\~':"\!\^#$%@\[\]\(\)=<>\|])/g, '\\$1'); + } + + function toggleVisibilityFilter(ctrlToEnable, ctrToDisable) { + if (ctrlToEnable.hasClass("out")) { + ctrlToEnable.removeClass("out").addClass("in"); + ctrToDisable.removeClass("in").addClass("out"); + filter(); + } + } + + controls.visibility.publicOnly.on("click", function() { + toggleVisibilityFilter(controls.visibility.publicOnly, controls.visibility.all); + }); + + controls.visibility.all.on("click", function() { + toggleVisibilityFilter(controls.visibility.all, controls.visibility.publicOnly); + }); + + function exposeMember(jqElem) { + var jqElemParent = jqElem.parent(), + parentName = jqElemParent.attr("name"), + ancestorName = /^([^#]*)(#.*)?$/gi.exec(parentName)[1]; + + // switch visibility filter if necessary + if (jqElemParent.attr("visbl") == "prt") { + toggleVisibilityFilter(controls.visibility.all, controls.visibility.publicOnly); + } + + // toggle appropriate ancestor filter buttons + if (ancestorName) { + $("#filterby li.out[name='" + ancestorName + "']").removeClass("out").addClass("in"); + } + + filter(); + jqElemParent.addClass("selected"); + commentToggleFct(jqElemParent); + $("#content-scroll-container").animate({scrollTop: $("#content-scroll-container").scrollTop() + jqElemParent.offset().top - $("#search").height() - 23 }, 1000); + } + + var isHiddenClass = function (name) { + return name == 'scala.Any' || + name == 'scala.AnyRef'; + }; + + var isHidden = function (elem) { + return $(elem).attr("data-hidden") == 'true'; + }; + + $("#linearization li:gt(0)").filter(function(){ + return isHiddenClass($(this).attr("name")); + }).removeClass("in").addClass("out"); + + $("#implicits li").filter(function(){ + return isHidden(this); + }).removeClass("in").addClass("out"); + + $("#memberfilter > i.arrow").on("click", function() { + $(this).toggleClass("rotate"); + $("#filterby").toggle(); + }); + + // Pre-filter members + filter(); + + // Member filter box + var input = $("#memberfilter input"); + input.on("keyup", function(event) { + + switch ( event.keyCode ) { + + case 27: // escape key + input.val(""); + filter(true); + break; + + case 38: // up + input.val(""); + filter(false); + window.scrollTo(0, $("body").offset().top); + input.trigger("focus"); + break; + + case 33: //page up + input.val(""); + filter(false); + break; + + case 34: //page down + input.val(""); + filter(false); + break; + + default: + window.scrollTo(0, $("#mbrsel").offset().top - 130); + filter(true); + break; + + } + }); + input.on("focus", function(event) { + input.trigger("select"); + }); + $("#memberfilter > .clear").on("click", function() { + $("#memberfilter input").val(""); + $(this).hide(); + filter(); + }); + $(document).on("keydown", function(event) { + if (event.keyCode == 9) { // tab + $("#index-input", window.parent.document).trigger("focus"); + input.val( ""); + return false; + } + }); + + $("#linearization li").on("click", function(){ + if ($(this).hasClass("in")) { + $(this).removeClass("in"); + $(this).addClass("out"); + } else if ($(this).hasClass("out")) { + $(this).removeClass("out"); + $(this).addClass("in"); + } + filter(); + }); + + $("#implicits li").on("click", function(){ + if ($(this).hasClass("in")) { + $(this).removeClass("in"); + $(this).addClass("out"); + } else if ($(this).hasClass("out")) { + $(this).removeClass("out"); + $(this).addClass("in"); + } + filter(); + }); + + $("#mbrsel > div > div.ancestors > ol > li.hideall").on("click", function() { + $("#linearization li.in").removeClass("in").addClass("out"); + $("#linearization li:first").removeClass("out").addClass("in"); + $("#implicits li.in").removeClass("in").addClass("out"); + + if ($(this).hasClass("out") && $("#mbrsel > div > div.ancestors > ol > li.showall").hasClass("in")) { + $(this).removeClass("out").addClass("in"); + $("#mbrsel > div > div.ancestors > ol > li.showall").removeClass("in").addClass("out"); + } + + filter(); + }) + $("#mbrsel > div > div.ancestors > ol > li.showall").on("click", function() { + var filteredLinearization = + $("#linearization li.out").filter(function() { + return ! isHiddenClass($(this).attr("name")); + }); + filteredLinearization.removeClass("out").addClass("in"); + + var filteredImplicits = + $("#implicits li.out").filter(function() { + return ! isHidden(this); + }); + filteredImplicits.removeClass("out").addClass("in"); + + if ($(this).hasClass("out") && $("#mbrsel > div > div.ancestors > ol > li.hideall").hasClass("in")) { + $(this).removeClass("out").addClass("in"); + $("#mbrsel > div > div.ancestors > ol > li.hideall").removeClass("in").addClass("out"); + } + + filter(); + }); + $("#order > ol > li.alpha").on("click", function() { + if ($(this).hasClass("out")) + orderAlpha(); + }) + $("#order > ol > li.inherit").on("click", function() { + if ($(this).hasClass("out")) + orderInherit(); + }); + $("#order > ol > li.group").on("click", function() { + if ($(this).hasClass("out")) + orderGroup(); + }); + $("#groupedMembers").hide(); + + initInherit(); + + // Create tooltips + $(".extype").add(".defval").each(function(_,e) { + var $this = $(e); + $this.attr("title", $this.attr("name")); + }); + + /* Add toggle arrows */ + $("#template li[fullComment=yes] .modifier_kind").addClass("closed"); + + function commentToggleFct(element){ + $("#template li.selected").removeClass("selected"); + if (element.is("[fullcomment=no]")) { + return; + } + element.toggleClass("open"); + var signature = element.find(".modifier_kind") + var shortComment = element.find(".shortcomment"); + var fullComment = element.find(".fullcomment"); + var vis = $(":visible", fullComment); + signature.toggleClass("closed").toggleClass("opened"); + if (vis.length > 0) { + if (!isMobile()) { + shortComment.slideDown(100); + fullComment.slideUp(100); + } else { + fullComment.hide(); + shortComment.show(); + } + } + else { + if (!isMobile()) { + shortComment.slideUp(100); + fullComment.slideDown(100); + } else { + shortComment.hide(); + fullComment.show(); + } + } + }; + + $("#template li[fullComment=yes]").on("click", function() { + var sel = window.getSelection().toString(); + if (!sel) commentToggleFct($(this)); + }); + + /* Linear super types and known subclasses */ + function toggleShowContentFct(e){ + e.toggleClass("open"); + var content = $(".hiddenContent", e); + if(content.is(':visible')) { + if (!isMobile()) content.slideUp(100); + else content.hide(); + } else { + if (!isMobile()) content.slideDown(100); + else content.show(); + } + }; + + $(".toggleContainer:not(.diagram-container):not(.full-signature-block)").on("click", function() { + toggleShowContentFct($(this)); + }); + + $(".toggleContainer.full-signature-block").on("click", function() { + toggleShowContentFct($(this)); + return false; + }); + + if ($("#order > ol > li.group").length == 1) { orderGroup(); }; + + function findElementByHash(locationHash) { + var temp = locationHash.replace('#', ''); + var memberSelector = '#' + escapeJquery(temp); + return $(memberSelector); + } + + // highlight and jump to selected member if an anchor is provided + if (window.location.hash) { + var jqElem = findElementByHash(window.location.hash); + if (jqElem.length > 0) + exposeMember(jqElem); + } + + $("#template span.permalink").on("click", function(e) { + e.preventDefault(); + var href = $("a", this).attr("href"); + if (href.indexOf("#") != -1) { + var hash = href.split("#").pop() + try { + window.history.pushState({}, "", "#" + hash) + } catch (e) { + // fallback for file:// URLs, has worse scrolling behavior + location.hash = hash; + } + exposeMember(findElementByHash(hash)) + } + return false; + }); + + $("#mbrsel-input").on("input", function() { + if ($(this).val().length > 0) + $("#memberfilter > .clear").show(); + else + $("#memberfilter > .clear").hide(); + }); +}); + +function orderAlpha() { + $("#order > ol > li.alpha").removeClass("out").addClass("in"); + $("#order > ol > li.inherit").removeClass("in").addClass("out"); + $("#order > ol > li.group").removeClass("in").addClass("out"); + $("#template > div.parent").hide(); + $("#template > div.conversion").hide(); + $("#mbrsel > div.ancestors").show(); + filter(); +}; + +function orderInherit() { + $("#order > ol > li.inherit").removeClass("out").addClass("in"); + $("#order > ol > li.alpha").removeClass("in").addClass("out"); + $("#order > ol > li.group").removeClass("in").addClass("out"); + $("#template > div.parent").show(); + $("#template > div.conversion").show(); + $("#mbrsel > div.ancestors").hide(); + filter(); +}; + +function orderGroup() { + $("#order > ol > li.group").removeClass("out").addClass("in"); + $("#order > ol > li.alpha").removeClass("in").addClass("out"); + $("#order > ol > li.inherit").removeClass("in").addClass("out"); + $("#template > div.parent").hide(); + $("#template > div.conversion").hide(); + $("#mbrsel > div.ancestors").show(); + filter(); +}; + +/** Prepares the DOM for inheritance-based display. To do so it will: + * - hide all statically-generated parents headings; + * - copy all members from the value and type members lists (flat members) to corresponding lists nested below the + * parent headings (inheritance-grouped members); + * - initialises a control variable used by the filter method to control whether filtering happens on flat members + * or on inheritance-grouped members. */ +function initInherit() { + // inheritParents is a map from fully-qualified names to the DOM node of parent headings. + var inheritParents = new Object(); + var groupParents = new Object(); + $("#inheritedMembers > div.parent").each(function(){ + inheritParents[$(this).attr("name")] = $(this); + }); + $("#inheritedMembers > div.conversion").each(function(){ + inheritParents[$(this).attr("name")] = $(this); + }); + $("#groupedMembers > div.group").each(function(){ + groupParents[$(this).attr("name")] = $(this); + }); + + $("#types > ol > li").each(function(){ + var mbr = $(this); + this.mbrText = mbr.find("> .fullcomment .cmt").text(); + var qualName = mbr.attr("name"); + var owner = qualName.slice(0, qualName.indexOf("#")); + var name = qualName.slice(qualName.indexOf("#") + 1); + var inheritParent = inheritParents[owner]; + if (inheritParent != undefined) { + var types = $("> .types > ol", inheritParent); + if (types.length == 0) { + inheritParent.append("

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$("#linearization > li:gt(0)") : $("#linearization > li.out"); + var hiddenSuperclassesLinearization = hiddenSuperclassElementsLinearization.map(function() { + return $(this).attr("name"); + }).get(); + var hiddenSuperclassElementsImplicits = orderingInheritance ? $("#implicits > li") : $("#implicits > li.out"); + var hiddenSuperclassesImplicits = hiddenSuperclassElementsImplicits.map(function() { + return $(this).attr("name"); + }).get(); + + var hideInheritedMembers; + + if (orderingAlphabetic) { + $("#allMembers").show(); + $("#inheritedMembers").hide(); + $("#groupedMembers").hide(); + hideInheritedMembers = true; + $("#allMembers > .members").each(filterFunc); + } else if (orderingGroups) { + $("#groupedMembers").show(); + $("#inheritedMembers").hide(); + $("#allMembers").hide(); + hideInheritedMembers = true; + $("#groupedMembers > .group > .members").each(filterFunc); + $("#groupedMembers > div.group").each(function() { + $(this).show(); + if ($("> div.members", this).not(":hidden").length == 0) { + $(this).hide(); + } else { + $(this).show(); + } + }); + } else if (orderingInheritance) { + $("#inheritedMembers").show(); + $("#groupedMembers").hide(); + $("#allMembers").hide(); + hideInheritedMembers = false; + $("#inheritedMembers > .parent > .members").each(filterFunc); + $("#inheritedMembers > .conversion > .members").each(filterFunc); + } + + + function filterFunc() { + var membersVisible = false; + var members = $(this); + members.find("> ol > li").each(function() { + var mbr = $(this); + if (privateMembersHidden && mbr.attr("visbl") == "prt") { + mbr.hide(); + return; + } + var name = mbr.attr("name"); + // Owner filtering must not happen in "inherited from" member lists + if (hideInheritedMembers) { + var ownerIndex = name.indexOf("#"); + if (ownerIndex < 0) { + ownerIndex = name.lastIndexOf("."); + } + var owner = name.slice(0, ownerIndex); + for (var i = 0; i < hiddenSuperclassesLinearization.length; i++) { + if (hiddenSuperclassesLinearization[i] == owner) { + mbr.hide(); + return; + } + }; + for (var i = 0; i < hiddenSuperclassesImplicits.length; i++) { + if (hiddenSuperclassesImplicits[i] == owner) { + mbr.hide(); + return; + } + }; + } + if (query && !(queryRegExp.test(name) || queryRegExp.test(this.mbrText))) { + mbr.hide(); + return; + } + mbr.show(); + membersVisible = true; + }); + + if (membersVisible) + members.show(); + else + members.hide(); + }; + + return false; +}; + +/** Check if user agent is associated with a known mobile browser */ +function isMobile() { + return /Android|webOS|Mobi|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini/i.test(navigator.userAgent); +} diff --git a/static/stainless-library/lib/trait.svg b/static/stainless-library/lib/trait.svg new file mode 100644 index 0000000000..207a89f37f --- /dev/null +++ b/static/stainless-library/lib/trait.svg @@ -0,0 +1,54 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + t + + + + + + + diff --git a/static/stainless-library/lib/trait_comp.svg b/static/stainless-library/lib/trait_comp.svg new file mode 100644 index 0000000000..8c83dec1f1 --- /dev/null +++ b/static/stainless-library/lib/trait_comp.svg @@ -0,0 +1,57 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + t + + + + + + + + diff --git a/static/stainless-library/lib/trait_diagram.png b/static/stainless-library/lib/trait_diagram.png new file mode 100644 index 0000000000..88983254ce Binary files /dev/null and b/static/stainless-library/lib/trait_diagram.png differ diff --git a/static/stainless-library/lib/type_diagram.png b/static/stainless-library/lib/type_diagram.png new file mode 100644 index 0000000000..d8152529fd Binary files /dev/null and b/static/stainless-library/lib/type_diagram.png differ diff --git a/static/stainless-library/stainless/annotation/erasable.html b/static/stainless-library/stainless/annotation/erasable.html new file mode 100644 index 0000000000..bf2e91a7c8 --- /dev/null +++ b/static/stainless-library/stainless/annotation/erasable.html @@ -0,0 +1,666 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                    Instruct Stainless to partially evaluate calls to the annotated function.

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                    Specify that the annotated function is pure, which will be checked.

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                    Definition Classes
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                    Definition Classes
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                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
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                  Value Members

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                    Definition Classes
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                  stainless.annotation.isabelle

                  +

                  lemma + + + +

                  +

                  +
                  + +

                  + + + class + + + lemma extends Annotation with StaticAnnotation + +

                  + + +
                  Annotations
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                  StaticAnnotation, Annotation, AnyRef, Any
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                  +
                  1. + + + + + + + + + new + + + lemma(about: String) + + + +
                  +
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                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
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                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
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                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
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                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
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                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from StaticAnnotation

                  +
                  +

                  Inherited from Annotation

                  +
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                  Inherited from AnyRef

                  +
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                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
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                  +
                  +
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                  +
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                  +
                  +
                  +
                  +
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                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                  +

                  stainless.annotation.isabelle

                  +

                  noBody + + + +

                  +

                  +
                  + +

                  + + + class + + + noBody extends Annotation with StaticAnnotation + +

                  + + +
                  Annotations
                  + @ignore() + +
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                  StaticAnnotation, Annotation, AnyRef, Any
                  +
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                  Value Members

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                    Definition Classes
                    AnyRef → Any
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from StaticAnnotation

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                  +

                  Inherited from Annotation

                  +
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                  Inherited from AnyRef

                  +
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                  Inherited from Any

                  +
                  + +
                  + +
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                  Ungrouped

                  + +
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                  + +
                  + +
                  + + + +
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                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/isabelle$$proof.html b/static/stainless-library/stainless/annotation/isabelle$$proof.html new file mode 100644 index 0000000000..d5acfb2789 --- /dev/null +++ b/static/stainless-library/stainless/annotation/isabelle$$proof.html @@ -0,0 +1,648 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  Packages

                  + +
                  +
                  +
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                  +
                  c
                  +

                  stainless.annotation.isabelle

                  +

                  proof + + + +

                  +

                  +
                  + +

                  + + + class + + + proof extends Annotation with StaticAnnotation + +

                  + + +
                  Annotations
                  + @ignore() + +
                  + + Linear Supertypes + +
                  StaticAnnotation, Annotation, AnyRef, Any
                  +
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                  2. StaticAnnotation
                  3. Annotation
                  4. AnyRef
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                  Value Members

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                    Definition Classes
                    AnyRef → Any
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
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                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
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                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
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                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
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                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
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                    20. +
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                  Inherited from StaticAnnotation

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                  Inherited from Annotation

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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  +
                  +
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                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                  +

                  stainless.annotation.isabelle

                  +

                  script + + + +

                  +

                  +
                  + +

                  + + + class + + + script extends Annotation with StaticAnnotation + +

                  + + +
                  Annotations
                  + @ignore() + +
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                  StaticAnnotation, Annotation, AnyRef, Any
                  +
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                  2. StaticAnnotation
                  3. Annotation
                  4. AnyRef
                  5. Any
                    6. +
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                  1. Hide All
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                  Instance Constructors

                  +
                  1. + + + + + + + + + new + + + script(name: String, source: String) + + + +
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                  Value Members

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                    Definition Classes
                    AnyRef → Any
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
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                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
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                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
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                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from StaticAnnotation

                  +
                  +

                  Inherited from Annotation

                  +
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                  Inherited from AnyRef

                  +
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                  Inherited from Any

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                  + +
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                  Ungrouped

                  + +
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                  + +
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                  +
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                  Packages

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                  Annotations
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                  StaticAnnotation, Annotation, AnyRef, Any
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                  + Ordering +
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                  2. StaticAnnotation
                  3. Annotation
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                  5. Any
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                  Instance Constructors

                  +
                  1. + + + + + + + + + new + + + typ(name: String) + + + +
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                  + + + + + +
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                  Value Members

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                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
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                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from StaticAnnotation

                  +
                  +

                  Inherited from Annotation

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
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                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/isabelle$.html b/static/stainless-library/stainless/annotation/isabelle$.html new file mode 100644 index 0000000000..a0fecaa964 --- /dev/null +++ b/static/stainless-library/stainless/annotation/isabelle$.html @@ -0,0 +1,797 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
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                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
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                  +
                  + +
                  +
                  o
                  +

                  stainless.annotation

                  +

                  isabelle + + + +

                  +

                  +
                  + +

                  + + + object + + + isabelle + +

                  + + +
                  + + Linear Supertypes + +
                  AnyRef, Any
                  +
                  + + +
                  +
                  +
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                  +
                  +
                  + Ordering +
                    + +
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                  Type Members

                  +
                  1. + + + + + + + + + class + + + constructor extends Annotation with StaticAnnotation + + +
                    Annotations
                    + @ignore() + +
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                  2. + + + + + + + + + class + + + fullBody extends Annotation with StaticAnnotation + + +
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                  3. + + + + + + + + + class + + + function extends Annotation with StaticAnnotation + + +
                    Annotations
                    + @ignore() + +
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                  4. + + + + + + + + + class + + + lemma extends Annotation with StaticAnnotation + + +
                    Annotations
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                  5. + + + + + + + + + class + + + noBody extends Annotation with StaticAnnotation + + +
                    Annotations
                    + @ignore() + +
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                  6. + + + + + + + + + class + + + proof extends Annotation with StaticAnnotation + + +
                    Annotations
                    + @ignore() + +
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                    Annotations
                    + @ignore() + +
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                    Annotations
                    + @ignore() + +
                    +
                  +
                  + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
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                    Definition Classes
                    AnyRef
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                    + @throws( + + ... + ) + + @native() + +
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                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
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                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from AnyRef

                  +
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                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/keep.html b/static/stainless-library/stainless/annotation/keep.html new file mode 100644 index 0000000000..b94b26b68c --- /dev/null +++ b/static/stainless-library/stainless/annotation/keep.html @@ -0,0 +1,669 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
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                  Packages

                  + +
                  +
                  +
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                  +
                  c
                  +

                  stainless.annotation

                  +

                  keep + + + +

                  +

                  +
                  + +

                  + + + class + + + keep extends Annotation + +

                  + + +

                  Can be used to mark a library function/class/object so that it is not +filtered out by the keep objects. Use the command-line option --keep=g to +keep all objects marked by @keep(g) +

                  Annotations
                  + @ignore() + +
                  + + Linear Supertypes + +
                  Annotation, AnyRef, Any
                  +
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                  + Ordering +
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                  +
                  1. + + + + + + + + + new + + + keep(g: String) + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Annotation

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/law.html b/static/stainless-library/stainless/annotation/law.html new file mode 100644 index 0000000000..3063771364 --- /dev/null +++ b/static/stainless-library/stainless/annotation/law.html @@ -0,0 +1,668 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
                  +
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                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                  +

                  stainless.annotation

                  +

                  law + + + +

                  +

                  +
                  + +

                  + + + class + + + law extends Annotation + +

                  + + +

                  Mark this function as expressing a law that must be satisfied +by instances or subclasses of the enclosing class. +

                  Annotations
                  + @ignore() + +
                  + + Linear Supertypes + +
                  Annotation, AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
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                    2. +
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                  1. law
                  2. Annotation
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                  4. Any
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                    2. +
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                  1. + + + + + + + + + new + + + law() + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Annotation

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/library.html b/static/stainless-library/stainless/annotation/library.html new file mode 100644 index 0000000000..4c70843990 --- /dev/null +++ b/static/stainless-library/stainless/annotation/library.html @@ -0,0 +1,667 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
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                  +
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                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                  +

                  stainless.annotation

                  +

                  library + + + +

                  +

                  +
                  + +

                  + + + class + + + library extends Annotation + +

                  + + +

                  The annotated function or class' methods are not verified +by default (use --functions=... to override this).

                  Annotations
                  + @ignore() + +
                  + + Linear Supertypes + +
                  Annotation, AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
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                  +                   +
                    +
                  1. library
                  2. Annotation
                  3. AnyRef
                  4. Any
                    5. +
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                    2. +
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                  +
                  1. + + + + + + + + + new + + + library() + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
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                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  10. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  13. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  16. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  17. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  18. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    20. +
                  +
                  + + + + +
                  + +
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                  +

                  Inherited from Annotation

                  +
                  +

                  Inherited from AnyRef

                  +
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                  Inherited from Any

                  +
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                  + +
                  +
                  +

                  Ungrouped

                  + +
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                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/annotation/mutable.html b/static/stainless-library/stainless/annotation/mutable.html new file mode 100644 index 0000000000..b2b9cf3ca4 --- /dev/null +++ b/static/stainless-library/stainless/annotation/mutable.html @@ -0,0 +1,669 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
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                  Packages

                  + +
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                  c
                  +

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                  +

                  mutable + + + +

                  +

                  +
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                  + + + class + + + mutable extends Annotation + +

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                  Used to mark non-sealed classes that must be considered mutable. +Can also be used to mark a type parameter T to announce that it can be +instantiated with mutable types +

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                    Definition Classes
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                  + + diff --git a/static/stainless-library/stainless/annotation/opaque.html b/static/stainless-library/stainless/annotation/opaque.html new file mode 100644 index 0000000000..6330dc58ae --- /dev/null +++ b/static/stainless-library/stainless/annotation/opaque.html @@ -0,0 +1,666 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  Don't unfold the function's body during verification.

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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                  Inherited from Annotation

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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/annotation/partialEval.html b/static/stainless-library/stainless/annotation/partialEval.html new file mode 100644 index 0000000000..4f51180941 --- /dev/null +++ b/static/stainless-library/stainless/annotation/partialEval.html @@ -0,0 +1,666 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  c
                  +

                  stainless.annotation

                  +

                  partialEval + + + +

                  +

                  +
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                  + + + class + + + partialEval extends Annotation + +

                  + + +

                  Instruct Stainless to partially evaluate calls to the annotated function.

                  Annotations
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                    Definition Classes
                    AnyRef → Any
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
                    AnyRef
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                    + @throws( + + ... + ) + + @native() + +
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                  Inherited from Annotation

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                  Inherited from Any

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/annotation/pure.html b/static/stainless-library/stainless/annotation/pure.html new file mode 100644 index 0000000000..ec5332fd9f --- /dev/null +++ b/static/stainless-library/stainless/annotation/pure.html @@ -0,0 +1,674 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  c
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                  stainless.annotation

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                  pure + + + +

                  +

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                  + + + class + + + pure extends Annotation + +

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                  Specify that the annotated function is pure, which will be checked.

                  Annotations
                  + @ignore() + + @field() + + @getter() + + @setter() + + @param() + +
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                  15. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
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                    + @throws( + + ... + ) + + @native() + +
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                  Inherited from Annotation

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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/annotation/wrapping.html b/static/stainless-library/stainless/annotation/wrapping.html new file mode 100644 index 0000000000..0cae324132 --- /dev/null +++ b/static/stainless-library/stainless/annotation/wrapping.html @@ -0,0 +1,666 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  Packages

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                  c
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                  stainless.annotation

                  +

                  wrapping + + + +

                  +

                  +
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                  Disable overflow checks for sized integer arithmetic operations within the annotated function.

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                  Annotation, AnyRef, Any
                  +
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
                    AnyRef → Any
                    +
                  7. + + + + + + + + + def + + + appendInv: Boolean + + +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    Definition Classes
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                  8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
                    Definition Classes
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                  9. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  10. + + + + + + + + + def + + + balanced: Boolean + + +
                    Definition Classes
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                  11. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  12. + + + + + + + + + def + + + concInv: Boolean + + +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    Definition Classes
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                  13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
                    Definition Classes
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                  14. + + + + + + + + + def + + + content: Set[T] + + +
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                    Definition Classes
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                  18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Definition Classes
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                  19. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + +
                    Definition Classes
                    Conc
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                  20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
                    Definition Classes
                    Conc
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                  21. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
                    Definition Classes
                    Conc
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                  22. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
                    Conc
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                  23. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  24. + + + + + + + + + def + + + head: T + + +
                    Definition Classes
                    Conc
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                  25. + + + + + + + + + def + + + headOption: Option[T] + + +
                    Definition Classes
                    Conc
                    +
                  26. + + + + + + + + + def + + + isEmpty: Boolean + + +
                    Definition Classes
                    Conc
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                  27. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                  30. + + + + + + + + + val + + + left: Conc[T] + + + +
                  31. + + + + + + + + + val + + + level: BigInt + + +
                    Definition Classes
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                  32. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
                    Definition Classes
                    Conc
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                  33. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  34. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
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                  35. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
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                  36. + + + + + + + + + val + + + right: Conc[T] + + + +
                  37. + + + + + + + + + val + + + size: BigInt + + +
                    Definition Classes
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                  38. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                  39. + + + + + + + + + def + + + toList: List[T] + + +
                    Definition Classes
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                  40. + + + + + + + + + def + + + toSet: Set[T] + + +
                    Definition Classes
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                  41. + + + + + + + + + def + + + valid: Boolean + + +
                    Definition Classes
                    Conc
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                  42. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
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                  43. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
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                  44. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
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                    45. +
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                  Inherited from Serializable

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                  Inherited from Serializable

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                  Inherited from Product

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                  Inherited from Equals

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                  Inherited from Conc[T]

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                  Inherited from AnyRef

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                    Definition Classes
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                  8. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
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                  10. + + + + + + + + + def + + + flatten[T](xs: Conc[Conc[T]]): Conc[T] + + + +
                  11. + + + + + + + + + def + + + fromList[T](xs: List[T]): Conc[T] + + + +
                  12. + + + + + + + + + def + + + fromListReversed[T](xs: List[T]): Conc[T] + + + +
                  13. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
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                    Definition Classes
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                  15. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                  19. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                    Definition Classes
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                    Definition Classes
                    AnyRef
                    Annotations
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                    Definition Classes
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                    Definition Classes
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                  Inherited from AnyRef

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                  3. + + + + + + + + + def + + + ++(that: Conc[T]): Conc[T] + + + +
                  4. + + + + + + + + + def + + + :+(x: T): Conc[T] + + + +
                  5. + + + + + + + + + def + + + ::(x: T): Conc[T] + + + +
                  6. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  7. + + + + + + + + + def + + + appendInv: Boolean + + +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    +
                  8. + + + + + + + + + def + + + apply(i: BigInt): T + + + +
                  9. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  11. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
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                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
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                  12. + + + + + + + + + def + + + concInv: Boolean + + +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    +
                  13. + + + + + + + + + def + + + contains(v: T): Boolean + + + +
                  14. + + + + + + + + + def + + + content: Set[T] + + + +
                  15. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  16. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  17. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + + +
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                    protected[java.lang]
                    Definition Classes
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
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                  19. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + + +
                  20. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + + +
                  21. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + + +
                  22. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + + +
                  23. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + + +
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                    Definition Classes
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                  29. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                  31. + + + + + + + + + def + + + isNormalized: Boolean + + + +
                  32. + + + + + + + + + val + + + level: BigInt + + + +
                  33. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + + +
                  34. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  35. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                  43. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
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                    Definition Classes
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                    Definition Classes
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                    Definition Classes
                    AnyRef → Any
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                  7. + + + + + + + + + def + + + appendInv: Boolean + + +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    Definition Classes
                    Conc
                    +
                  8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
                    Definition Classes
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                    Attributes
                    protected[java.lang]
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                    + @throws( + + ... + ) + + @native() + +
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                  12. + + + + + + + + + def + + + concInv: Boolean + + +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    Definition Classes
                    Conc
                    +
                  13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
                    Definition Classes
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                  14. + + + + + + + + + def + + + content: Set[T] + + +
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                    Definition Classes
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                  18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Definition Classes
                    Conc
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                  19. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ Conc[R]): Conc[R] + + +
                    Definition Classes
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                  20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
                    Definition Classes
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                  21. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
                    Definition Classes
                    Conc
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                  22. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
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                  23. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
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                    Annotations
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                  24. + + + + + + + + + def + + + head: T + + +
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                  25. + + + + + + + + + def + + + headOption: Option[T] + + +
                    Definition Classes
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                  26. + + + + + + + + + def + + + isEmpty: Boolean + + +
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                  27. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                  28. + + + + + + + + + def + + + isLeaf: Boolean + + +
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                  29. + + + + + + + + + def + + + isNormalized: Boolean + + +
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                  30. + + + + + + + + + val + + + level: BigInt + + +
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                  31. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
                    Definition Classes
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                  32. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  33. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                  34. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
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                  35. + + + + + + + + + val + + + size: BigInt + + +
                    Definition Classes
                    Conc
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                  36. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                  37. + + + + + + + + + def + + + toList: List[T] + + +
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                    Definition Classes
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                    Definition Classes
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                  41. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
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                  42. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
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                    43. +
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                  Inherited from Serializable

                  +
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                  Inherited from Serializable

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                  Inherited from Product

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                  Inherited from Equals

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                  Inherited from Conc[T]

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/collection/ConcRope$$Single.html b/static/stainless-library/stainless/collection/ConcRope$$Single.html new file mode 100644 index 0000000000..d81a9b7a63 --- /dev/null +++ b/static/stainless-library/stainless/collection/ConcRope$$Single.html @@ -0,0 +1,1038 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                    Definition Classes
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                  7. + + + + + + + + + def + + + appendInv: Boolean + + +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    (a) Right subtree of an append node is not an append node +(b) If the tree is of the form a@Append(b@Append(_,_),_) then + a.right.level < b.right.level +(c) left and right are not empty +

                    Definition Classes
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                  8. + + + + + + + + + def + + + apply(i: BigInt): T + + +
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                    Attributes
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                    + @throws( + + ... + ) + + @native() + +
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                  12. + + + + + + + + + def + + + concInv: Boolean + + +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    (a) left and right trees of conc node should be non-empty +(b) they cannot be append nodes +

                    Definition Classes
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                  13. + + + + + + + + + def + + + contains(v: T): Boolean + + +
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                  18. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Definition Classes
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                  20. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
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                  24. + + + + + + + + + def + + + head: T + + +
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                    Definition Classes
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                  26. + + + + + + + + + def + + + isEmpty: Boolean + + +
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                  29. + + + + + + + + + def + + + isNormalized: Boolean + + +
                    Definition Classes
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                  30. + + + + + + + + + val + + + level: BigInt + + +
                    Definition Classes
                    Conc
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                  31. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): Conc[R] + + +
                    Definition Classes
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                  32. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  33. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                  34. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
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                  35. + + + + + + + + + val + + + size: BigInt + + +
                    Definition Classes
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                    Definition Classes
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                  38. + + + + + + + + + def + + + toSet: Set[T] + + +
                    Definition Classes
                    Conc
                    +
                  39. + + + + + + + + + def + + + valid: Boolean + + +
                    Definition Classes
                    Conc
                    +
                  40. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  41. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
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                    + @throws( + + ... + ) + +
                    +
                  42. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
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                    + @throws( + + ... + ) + + @native() + +
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                  43. + + + + + + + + + val + + + x: T + + + +
                    44. +
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                  Inherited from Serializable

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                  Inherited from Product

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                  Inherited from Conc[T]

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                  Inherited from AnyRef

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/collection/ConcRope$.html b/static/stainless-library/stainless/collection/ConcRope$.html new file mode 100644 index 0000000000..f993aec0f7 --- /dev/null +++ b/static/stainless-library/stainless/collection/ConcRope$.html @@ -0,0 +1,1092 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  ConcRope + + + +

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                  2. + + + + + + + + + case class + + + CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] with Product with Serializable + + +
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                    + @library() + +
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                  3. + + + + + + + + sealed abstract + class + + + Conc[T] extends AnyRef + + +
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                  4. + + + + + + + + + case class + + + Empty[T]() extends Conc[T] with Product with Serializable + + +
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                  5. + + + + + + + + + case class + + + Single[T](x: T) extends Conc[T] with Product with Serializable + + +
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                  Value Members

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                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
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                    Definition Classes
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                  5. + + + + + + + + + def + + + append[T](xs: Conc[T], x: T): Conc[T] + + + +
                  6. + + + + + + + + + def + + + appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean + + + +
                  7. + + + + + + + + + def + + + appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean + + + +
                  8. + + + + + + + + + def + + + appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
                  9. + + + + + + + + + def + + + appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] + + +

                    This is a private method and is not exposed to the +clients of conc trees +

                    +
                  10. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  12. + + + + + + + + + def + + + concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + +

                    A generic concat that applies to general concTrees +

                    +
                  13. + + + + + + + + + def + + + concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + + +
                  14. + + + + + + + + + def + + + concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] + + +

                    This concat applies only to normalized trees.

                    This concat applies only to normalized trees. +This prevents concat from being recursive +

                    +
                  15. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
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                  20. + + + + + + + + + def + + + insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] + + + +
                  21. + + + + + + + + + def + + + insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean + + + +
                  22. + + + + + + + + + def + + + insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] + + +

                    Using a different version of insert than of the library +because the library implementation in unnecessarily complicated.

                    +
                  23. + + + + + + + + + def + + + instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean + + + +
                  24. + + + + + + + + + def + + + instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean + + + +
                  25. + + + + + + + + + def + + + instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean + + + +
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                    Definition Classes
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                    Definition Classes
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                  30. + + + + + + + + + def + + + normalize[T](t: Conc[T]): Conc[T] + + + +
                  31. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
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                    + @native() + +
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                    Definition Classes
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                  33. + + + + + + + + + def + + + numTrees[T](t: Conc[T]): BigInt + + + +
                  34. + + + + + + + + + def + + + split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) + + + +
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                    Definition Classes
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                  36. + + + + + + + + + def + + + toString(): String + + +
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                    Definition Classes
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                    Definition Classes
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                  +
                  + +

                  + + + case class + + + Cons[T](h: T, t: List[T]) extends List[T] with Product with Serializable + +

                  + + +
                  Annotations
                  + @library() + + @constructor( + name = + "List.list.Cons" + ) + +
                  + + Linear Supertypes + +
                  Serializable, Serializable, Product, Equals, List[T], AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
                  +
                  +
                  + Inherited
                  +                   +
                    +
                  1. Cons
                  2. Serializable
                  3. Serializable
                  4. Product
                  5. Equals
                  6. List
                  7. AnyRef
                  8. Any
                    9. +
                  +
                  + +
                    +
                  1. Hide All
                    2. +
                  2. Show All
                    3. +
                  +
                  +
                  + Visibility +
                  1. Public
                  2. All
                  +
                  +
                  +
                  + +
                  +
                  +
                  +

                  Instance Constructors

                  +
                  1. + + + + + + + + + new + + + Cons(h: T, t: List[T]) + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.append" + ) + +
                    +
                  5. + + + + + + + + + def + + + -(e: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. removeAll x xs" + ) + +
                    +
                  6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. xs @ [x]" + ) + +
                    +
                  8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. x # xs" + ) + +
                    +
                  9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
                    Definition Classes
                    List
                    Annotations
                    + @fullBody() + +
                    +
                  11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  13. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.member" + ) + +
                    +
                  15. + + + + + + + + + def + + + content: Set[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.list.set" + ) + +
                    +
                  16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + +
                    Definition Classes
                    List
                    +
                  17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  18. + + + + + + + + + def + + + dropWhile(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  20. + + + + + + + + + def + + + evenSplit: (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  21. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
                    +
                  22. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  23. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  24. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  25. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.find P xs" + ) + +
                    +
                  26. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.bind" + ) + +
                    +
                  27. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
                    +
                  28. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%as b f. List.foldr f as b" + ) + +
                    +
                  29. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.list_all P xs" + ) + +
                    +
                  30. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  31. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + +
                    Definition Classes
                    List
                    +
                  32. + + + + + + + + + val + + + h: T + + + +
                  33. + + + + + + + + + def + + + head: T + + +
                    Definition Classes
                    List
                    +
                  34. + + + + + + + + + def + + + headOption: Option[T] + + +
                    Definition Classes
                    List
                    +
                  35. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + +
                    Definition Classes
                    List
                    +
                  36. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + +
                    Definition Classes
                    List
                    +
                  37. + + + + + + + + + def + + + init: List[T] + + +
                    Definition Classes
                    List
                    +
                  38. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  39. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  40. + + + + + + + + + def + + + isEmpty: Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.null" + ) + +
                    +
                  41. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  42. + + + + + + + + + def + + + last: T + + +
                    Definition Classes
                    List
                    +
                  43. + + + + + + + + + def + + + lastOption: Option[T] + + +
                    Definition Classes
                    List
                    +
                  44. + + + + + + + + + def + + + length: BigInt + + +
                    Definition Classes
                    List
                    +
                  45. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs f. List.list.map f xs" + ) + +
                    +
                  46. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  47. + + + + + + + + + def + + + nonEmpty: Boolean + + +
                    Definition Classes
                    List
                    +
                  48. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  49. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  50. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  51. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  52. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  53. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  54. + + + + + + + + + def + + + reverse: List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.rev" + ) + +
                    +
                  55. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  56. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    +
                  57. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    +
                  58. + + + + + + + + + def + + + size: BigInt + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "Int.int o List.length" + ) + +
                    +
                  59. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  60. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  61. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  62. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  63. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  64. + + + + + + + + + val + + + t: List[T] + + + +
                  65. + + + + + + + + + def + + + tail: List[T] + + +
                    Definition Classes
                    List
                    +
                  66. + + + + + + + + + def + + + tailOption: Option[List[T]] + + +
                    Definition Classes
                    List
                    +
                  67. + + + + + + + + + def + + + take(i: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  68. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  69. + + + + + + + + + def + + + toSet: Set[T] + + +
                    Definition Classes
                    List
                    +
                  70. + + + + + + + + + def + + + unique: List[T] + + +
                    Definition Classes
                    List
                    +
                  71. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  72. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  73. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  74. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  75. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  76. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.zip" + ) + +
                    +
                    77. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Product

                  +
                  +

                  Inherited from Equals

                  +
                  +

                  Inherited from List[T]

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/collection/List$.html b/static/stainless-library/stainless/collection/List$.html new file mode 100644 index 0000000000..7c895b96c0 --- /dev/null +++ b/static/stainless-library/stainless/collection/List$.html @@ -0,0 +1,711 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  o
                   +

                  stainless.collection

                  +

                  List + + + +

                  +

                  + Companion class List +

                  +
                  + +

                  + + + object + + + List + +

                  + + +
                  + + Linear Supertypes + +
                  AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
                  +
                  +
                  + Inherited
                  +                   +
                    +
                  1. List
                  2. AnyRef
                  3. Any
                    4. +
                  +
                  + +
                    +
                  1. Hide All
                    2. +
                  2. Show All
                    3. +
                  +
                  +
                  + Visibility +
                  1. Public
                  2. All
                  +
                  +
                  +
                  + +
                  +
                  + + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + + def + + + apply[T](elems: T*): List[T] + + +
                    Annotations
                    + @ignore() + +
                    +
                  5. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  6. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  7. + + + + + + + + + def + + + empty[T]: List[T] + + +
                    Annotations
                    + @library() + +
                    +
                  8. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  9. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  10. + + + + + + + + + def + + + fill[T](n: BigInt)(x: T): List[T] + + +
                    Annotations
                    + @library() + +
                    +
                  11. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  12. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  13. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  14. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  15. + + + + + + + + + def + + + mkString[A](l: List[A], mid: String, f: (A) ⇒ String): String + + +
                    Annotations
                    + @library() + +
                    +
                  16. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  17. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  19. + + + + + + + + + def + + + range(start: BigInt, until: BigInt): List[BigInt] + + +
                    Annotations
                    + @library() + +
                    +
                  20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  21. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  22. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    25. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/collection/List.html b/static/stainless-library/stainless/collection/List.html new file mode 100644 index 0000000000..71b11bb0f3 --- /dev/null +++ b/static/stainless-library/stainless/collection/List.html @@ -0,0 +1,1662 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                   +

                  stainless.collection

                  +

                  List + + + +

                  +

                  + Companion object List +

                  +
                  + +

                  + + sealed abstract + class + + + List[T] extends AnyRef + +

                  + + +
                  Annotations
                  + @library() + + @typ( + name = + "List.list" + ) + +
                  + + Linear Supertypes + +
                  AnyRef, Any
                  +
                  + + Known Subclasses + +
                  Cons, Nil
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
                  +
                  +
                  + Inherited
                  +                   +
                    +
                  1. List
                  2. AnyRef
                  3. Any
                    4. +
                  +
                  + +
                    +
                  1. Hide All
                    2. +
                  2. Show All
                    3. +
                  +
                  +
                  + Visibility +
                  1. Public
                  2. All
                  +
                  +
                  +
                  + +
                  +
                  + + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + + +
                  4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
                    Annotations
                    + @function( + term = + "List.append" + ) + +
                    +
                  5. + + + + + + + + + def + + + -(e: T): List[T] + + +
                    Annotations
                    + @function( + term = + "%xs x. removeAll x xs" + ) + +
                    +
                  6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + + +
                  7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
                    Annotations
                    + @function( + term = + "%xs x. xs @ [x]" + ) + +
                    +
                  8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
                    Annotations
                    + @function( + term = + "%xs x. x # xs" + ) + +
                    +
                  9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
                    Annotations
                    + @fullBody() + +
                    +
                  11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + + +
                  13. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
                    Annotations
                    + @function( + term = + "List.member" + ) + +
                    +
                  15. + + + + + + + + + def + + + content: Set[T] + + +
                    Annotations
                    + @function( + term = + "List.list.set" + ) + +
                    +
                  16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + + +
                  17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + + +
                  18. + + + + + + + + + def + + + dropWhile(p: (T) ⇒ Boolean): List[T] + + + +
                  19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  20. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
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                    +
                  21. + + + + + + + + + def + + + evenSplit: (List[T], List[T]) + + + +
                  22. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
                    Annotations
                    + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
                    +
                  23. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + + +
                  24. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + + +
                  25. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  26. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Annotations
                    + @function( + term = + "%xs P. List.find P xs" + ) + +
                    +
                  27. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
                    Annotations
                    + @function( + term = + "List.bind" + ) + +
                    +
                  28. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
                    Annotations
                    + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
                    +
                  29. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
                    Annotations
                    + @function( + term = + "%as b f. List.foldr f as b" + ) + +
                    +
                  30. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
                    Annotations
                    + @function( + term = + "%xs P. List.list_all P xs" + ) + +
                    +
                  31. + + + + + + + + final + def + + + getClass(): Class[_] + + +
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                  32. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + + +
                  33. + + + + + + + + + def + + + hashCode(): Int + + +
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                  34. + + + + + + + + + def + + + head: T + + + +
                  35. + + + + + + + + + def + + + headOption: Option[T] + + + +
                  36. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + + +
                  37. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + + +
                  38. + + + + + + + + + def + + + init: List[T] + + + +
                  39. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + + +
                  40. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + + +
                  41. + + + + + + + + + def + + + isEmpty: Boolean + + +
                    Annotations
                    + @function( + term = + "List.null" + ) + +
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                  42. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
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                  43. + + + + + + + + + def + + + last: T + + + +
                  44. + + + + + + + + + def + + + lastOption: Option[T] + + + +
                  45. + + + + + + + + + def + + + length: BigInt + + + +
                  46. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
                    Annotations
                    + @function( + term = + "%xs f. List.list.map f xs" + ) + +
                    +
                  47. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  48. + + + + + + + + + def + + + nonEmpty: Boolean + + + +
                  49. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                  50. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
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                    + @native() + +
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                  51. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + + +
                  52. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + + +
                  53. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + + +
                  54. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + + +
                  55. + + + + + + + + + def + + + reverse: List[T] + + +
                    Annotations
                    + @function( + term = + "List.rev" + ) + +
                    +
                  56. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + + +
                  57. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + + +
                  58. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + + +
                  59. + + + + + + + + + def + + + size: BigInt + + +
                    Annotations
                    + @function( + term = + "Int.int o List.length" + ) + +
                    +
                  60. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + + +
                  61. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + + +
                  62. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + + +
                  63. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + + +
                  64. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                  65. + + + + + + + + + def + + + tail: List[T] + + + +
                  66. + + + + + + + + + def + + + tailOption: Option[List[T]] + + + +
                  67. + + + + + + + + + def + + + take(i: BigInt): List[T] + + + +
                  68. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + + +
                  69. + + + + + + + + + def + + + toSet: Set[T] + + + +
                  70. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
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                    +
                  71. + + + + + + + + + def + + + unique: List[T] + + + +
                  72. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + + +
                  73. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
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                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  74. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
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                    + @throws( + + ... + ) + +
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                  75. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
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                    + @throws( + + ... + ) + + @native() + +
                    +
                  76. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + + +
                  77. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
                    Annotations
                    + @function( + term = + "List.zip" + ) + +
                    +
                    78. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  +
                  + + diff --git a/static/stainless-library/stainless/collection/ListOps$.html b/static/stainless-library/stainless/collection/ListOps$.html new file mode 100644 index 0000000000..3a5f27c0d0 --- /dev/null +++ b/static/stainless-library/stainless/collection/ListOps$.html @@ -0,0 +1,703 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  + + + object + + + ListOps + +

                  + + +
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                  + @library() + +
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                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                  7. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
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                    Attributes
                    protected[java.lang]
                    Definition Classes
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + + def + + + flatten[T](ls: List[List[T]]): List[T] + + +
                    Annotations
                    + @function( + term = + "List.concat" + ) + +
                    +
                  10. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
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                  11. + + + + + + + + + def + + + hashCode(): Int + + +
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                  12. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                  13. + + + + + + + + + def + + + isSorted(ls: List[BigInt]): Boolean + + + +
                  14. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
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                    +
                  15. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                    + @native() + +
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                  16. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
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                    + @native() + +
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                  17. + + + + + + + + + def + + + sorted(ls: List[BigInt]): List[BigInt] + + + +
                  18. + + + + + + + + + def + + + sum(l: List[BigInt]): BigInt + + + +
                  19. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                    +
                  20. + + + + + + + + + def + + + toMap[K, V](l: List[(K, V)]): Map[K, V] + + + +
                  21. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
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                    +
                  22. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
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                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    25. +
                  +
                  + + + + +
                  + +
                  +
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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/collection/ListSpecs$.html b/static/stainless-library/stainless/collection/ListSpecs$.html new file mode 100644 index 0000000000..fb3eb8607a --- /dev/null +++ b/static/stainless-library/stainless/collection/ListSpecs$.html @@ -0,0 +1,1007 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  ListSpecs + + + +

                  +

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                  + + + object + + + ListSpecs + +

                  + + +
                  Annotations
                  + @library() + +
                  + + Linear Supertypes + +
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                    Definition Classes
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + + def + + + appendAssoc[T](l1: List[T], l2: List[T], l3: List[T]): Boolean + + + +
                  5. + + + + + + + + + def + + + appendContent[A](l1: List[A], l2: List[A]): Boolean + + + +
                  6. + + + + + + + + + def + + + appendIndex[T](l1: List[T], l2: List[T], i: BigInt): Boolean + + + +
                  7. + + + + + + + + + def + + + appendInsert[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
                  8. + + + + + + + + + def + + + appendTakeDrop[T](l1: List[T], l2: List[T], n: BigInt): Boolean + + + +
                  9. + + + + + + + + + def + + + appendUpdate[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean + + + +
                  10. + + + + + + + + + def + + + applyForAll[T](l: List[T], i: BigInt, p: (T) ⇒ Boolean): Boolean + + +

                    A way to apply the forall axiom

                    +
                  11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  13. + + + + + + + + + def + + + consIndex[T](h: T, t: List[T], i: BigInt): Boolean + + +
                    Annotations
                    + @lemma( + about = + "stainless.collection.List.apply" + ) + +
                    +
                  14. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  15. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
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                  16. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  17. + + + + + + + + + def + + + flattenPreservesContent[T](ls: List[List[T]]): Boolean + + + +
                  18. + + + + + + + + + def + + + folds[A, B](xs: List[A], z: B, f: (B, A) ⇒ B): Boolean + + + +
                  19. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  20. + + + + + + + + + def + + + hashCode(): Int + + +
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                    + @native() + +
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                  21. + + + + + + + + + def + + + headReverseLast[T](l: List[T]): Boolean + + + +
                  22. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                    +
                  23. + + + + + + + + + def + + + leftUnitAppend[T](l1: List[T]): Boolean + + + +
                  24. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  25. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
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                  26. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  27. + + + + + + + + + def + + + reverseAppend[T](l1: List[T], l2: List[T]): Boolean + + + +
                  28. + + + + + + + + + def + + + reverseIndex[T](l: List[T], i: BigInt): Boolean + + + +
                  29. + + + + + + + + + def + + + reverseReverse[T](l: List[T]): Boolean + + + +
                  30. + + + + + + + + + def + + + rightUnitAppend[T](l1: List[T]): Boolean + + + +
                  31. + + + + + + + + + def + + + scanVsFoldLeft[A, B](l: List[A], z: B, f: (B, A) ⇒ B): Boolean + + + +
                  32. + + + + + + + + + def + + + scanVsFoldRight[A, B](l: List[A], z: B, f: (A, B) ⇒ B): Boolean + + + +
                  33. + + + + + + + + + def + + + snocAfterAppend[T](l1: List[T], l2: List[T], t: T): Boolean + + + +
                  34. + + + + + + + + + def + + + snocFoldRight[A, B](xs: List[A], y: A, z: B, f: (A, B) ⇒ B): Boolean + + + +
                  35. + + + + + + + + + def + + + snocIndex[T](l: List[T], t: T, i: BigInt): Boolean + + + +
                  36. + + + + + + + + + def + + + snocIsAppend[T](l: List[T], t: T): Boolean + + + +
                  37. + + + + + + + + + def + + + snocLast[T](l: List[T], x: T): Boolean + + + +
                  38. + + + + + + + + + def + + + snocReverse[T](l: List[T], t: T): Boolean + + + +
                  39. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                    +
                  40. + + + + + + + + + def + + + toString(): String + + +
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                  41. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
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                    + @throws( + + ... + ) + +
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                  42. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
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                  43. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
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                  Ungrouped

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                  + + diff --git a/static/stainless-library/stainless/collection/Nil.html b/static/stainless-library/stainless/collection/Nil.html new file mode 100644 index 0000000000..d48a3213ea --- /dev/null +++ b/static/stainless-library/stainless/collection/Nil.html @@ -0,0 +1,1633 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  Nil + + + +

                  +

                  +
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                  + + + case class + + + Nil[T]() extends List[T] with Product with Serializable + +

                  + + +
                  Annotations
                  + @library() + + @constructor( + name = + "List.list.Nil" + ) + +
                  + + Linear Supertypes + +
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                  + Visibility +
                  1. Public
                  2. All
                  +
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                  Instance Constructors

                  +
                  1. + + + + + + + + + new + + + Nil() + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + + def + + + &(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  4. + + + + + + + + + def + + + ++(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.append" + ) + +
                    +
                  5. + + + + + + + + + def + + + -(e: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. removeAll x xs" + ) + +
                    +
                  6. + + + + + + + + + def + + + --(that: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  7. + + + + + + + + + def + + + :+(t: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. xs @ [x]" + ) + +
                    +
                  8. + + + + + + + + + def + + + ::(t: T): List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs x. x # xs" + ) + +
                    +
                  9. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  10. + + + + + + + + + def + + + apply(index: BigInt): T + + +
                    Definition Classes
                    List
                    Annotations
                    + @fullBody() + +
                    +
                  11. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  12. + + + + + + + + + def + + + chunks(s: BigInt): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  13. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  14. + + + + + + + + + def + + + contains(v: T): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.member" + ) + +
                    +
                  15. + + + + + + + + + def + + + content: Set[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.list.set" + ) + +
                    +
                  16. + + + + + + + + + def + + + count(p: (T) ⇒ Boolean): BigInt + + +
                    Definition Classes
                    List
                    +
                  17. + + + + + + + + + def + + + drop(i: BigInt): List[T] + + +
                    Definition Classes
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                    +
                  18. + + + + + + + + + def + + + dropWhile(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
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                    +
                  19. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  20. + + + + + + + + + def + + + evenSplit: (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  21. + + + + + + + + + def + + + exists(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.list_ex P xs" + ) + +
                    +
                  22. + + + + + + + + + def + + + filter(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  23. + + + + + + + + + def + + + filterNot(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  24. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  25. + + + + + + + + + def + + + find(p: (T) ⇒ Boolean): Option[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.find P xs" + ) + +
                    +
                  26. + + + + + + + + + def + + + flatMap[R](f: (T) ⇒ List[R]): List[R] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.bind" + ) + +
                    +
                  27. + + + + + + + + + def + + + foldLeft[R](z: R)(f: (R, T) ⇒ R): R + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%bs a f. List.foldl f a bs" + ) + +
                    +
                  28. + + + + + + + + + def + + + foldRight[R](z: R)(f: (T, R) ⇒ R): R + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%as b f. List.foldr f as b" + ) + +
                    +
                  29. + + + + + + + + + def + + + forall(p: (T) ⇒ Boolean): Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs P. List.list_all P xs" + ) + +
                    +
                  30. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  31. + + + + + + + + + def + + + groupBy[R](f: (T) ⇒ R): Map[R, List[T]] + + +
                    Definition Classes
                    List
                    +
                  32. + + + + + + + + + def + + + head: T + + +
                    Definition Classes
                    List
                    +
                  33. + + + + + + + + + def + + + headOption: Option[T] + + +
                    Definition Classes
                    List
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                  34. + + + + + + + + + def + + + indexOf(elem: T): BigInt + + +
                    Definition Classes
                    List
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                  35. + + + + + + + + + def + + + indexWhere(p: (T) ⇒ Boolean): BigInt + + +
                    Definition Classes
                    List
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                  36. + + + + + + + + + def + + + init: List[T] + + +
                    Definition Classes
                    List
                    +
                  37. + + + + + + + + + def + + + insertAt(pos: BigInt, e: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  38. + + + + + + + + + def + + + insertAt(pos: BigInt, l: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  39. + + + + + + + + + def + + + isEmpty: Boolean + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.null" + ) + +
                    +
                  40. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  41. + + + + + + + + + def + + + last: T + + +
                    Definition Classes
                    List
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                  42. + + + + + + + + + def + + + lastOption: Option[T] + + +
                    Definition Classes
                    List
                    +
                  43. + + + + + + + + + def + + + length: BigInt + + +
                    Definition Classes
                    List
                    +
                  44. + + + + + + + + + def + + + map[R](f: (T) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "%xs f. List.list.map f xs" + ) + +
                    +
                  45. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  46. + + + + + + + + + def + + + nonEmpty: Boolean + + +
                    Definition Classes
                    List
                    +
                  47. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  48. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  49. + + + + + + + + + def + + + padTo(s: BigInt, e: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  50. + + + + + + + + + def + + + partition(p: (T) ⇒ Boolean): (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  51. + + + + + + + + + def + + + replace(from: T, to: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  52. + + + + + + + + + def + + + replaceAt(pos: BigInt, l: List[T]): List[T] + + +
                    Definition Classes
                    List
                    +
                  53. + + + + + + + + + def + + + reverse: List[T] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.rev" + ) + +
                    +
                  54. + + + + + + + + + def + + + rotate(s: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  55. + + + + + + + + + def + + + scanLeft[R](z: R)(f: (R, T) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    +
                  56. + + + + + + + + + def + + + scanRight[R](z: R)(f: (T, R) ⇒ R): List[R] + + +
                    Definition Classes
                    List
                    +
                  57. + + + + + + + + + def + + + size: BigInt + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "Int.int o List.length" + ) + +
                    +
                  58. + + + + + + + + + def + + + slice(from: BigInt, to: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  59. + + + + + + + + + def + + + split(seps: List[T]): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  60. + + + + + + + + + def + + + splitAt(e: T): List[List[T]] + + +
                    Definition Classes
                    List
                    +
                  61. + + + + + + + + + def + + + splitAtIndex(index: BigInt): (List[T], List[T]) + + +
                    Definition Classes
                    List
                    +
                  62. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  63. + + + + + + + + + def + + + tail: List[T] + + +
                    Definition Classes
                    List
                    +
                  64. + + + + + + + + + def + + + tailOption: Option[List[T]] + + +
                    Definition Classes
                    List
                    +
                  65. + + + + + + + + + def + + + take(i: BigInt): List[T] + + +
                    Definition Classes
                    List
                    +
                  66. + + + + + + + + + def + + + takeWhile(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  67. + + + + + + + + + def + + + toSet: Set[T] + + +
                    Definition Classes
                    List
                    +
                  68. + + + + + + + + + def + + + unique: List[T] + + +
                    Definition Classes
                    List
                    +
                  69. + + + + + + + + + def + + + updated(i: BigInt, y: T): List[T] + + +
                    Definition Classes
                    List
                    +
                  70. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  71. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  72. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  73. + + + + + + + + + def + + + withFilter(p: (T) ⇒ Boolean): List[T] + + +
                    Definition Classes
                    List
                    +
                  74. + + + + + + + + + def + + + zip[B](that: List[B]): List[(T, B)] + + +
                    Definition Classes
                    List
                    Annotations
                    + @function( + term = + "List.zip" + ) + +
                    +
                    75. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Product

                  +
                  +

                  Inherited from Equals

                  +
                  +

                  Inherited from List[T]

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/collection/Queue$.html b/static/stainless-library/stainless/collection/Queue$.html new file mode 100644 index 0000000000..779d4f4eed --- /dev/null +++ b/static/stainless-library/stainless/collection/Queue$.html @@ -0,0 +1,639 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
                  +
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                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  o
                   +

                  stainless.collection

                  +

                  Queue + + + +

                  +

                  + Companion class Queue +

                  +
                  + +

                  + + + object + + + Queue extends Serializable + +

                  + + +
                  Annotations
                  + @library() + +
                  + + Linear Supertypes + +
                  Serializable, Serializable, AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
                  +
                  +
                  + Inherited
                  +                   +
                    +
                  1. Queue
                  2. Serializable
                  3. Serializable
                  4. AnyRef
                  5. Any
                    6. +
                  +
                  + +
                    +
                  1. Hide All
                    2. +
                  2. Show All
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                  2. All
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                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  6. + + + + + + + + + def + + + empty[A]: Queue[A] + + + +
                  7. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  8. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  9. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  10. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  11. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  12. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  13. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  14. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  15. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  16. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  17. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  18. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  19. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  20. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    21. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

                  + +
                  +
                  + +
                  + +
                  + + + +
                  +
                  +
                  + + diff --git a/static/stainless-library/stainless/collection/Queue.html b/static/stainless-library/stainless/collection/Queue.html new file mode 100644 index 0000000000..4a98cf45e5 --- /dev/null +++ b/static/stainless-library/stainless/collection/Queue.html @@ -0,0 +1,723 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +
                  +

                  Packages

                  + +
                  +
                  +
                  + +
                  +
                  c
                   +

                  stainless.collection

                  +

                  Queue + + + +

                  +

                  + Companion object Queue +

                  +
                  + +

                  + + + case class + + + Queue[A](front: List[A], rear: List[A]) extends Product with Serializable + +

                  + + +
                  Annotations
                  + @library() + +
                  + + Linear Supertypes + +
                  Serializable, Serializable, Product, Equals, AnyRef, Any
                  +
                  + + +
                  +
                  +
                  + + + + + +
                  +
                  +
                  + Ordering +
                    + +
                  1. Alphabetic
                    2. +
                  2. By Inheritance
                    3. +
                  +
                  +
                  + Inherited
                  +                   +
                    +
                  1. Queue
                  2. Serializable
                  3. Serializable
                  4. Product
                  5. Equals
                  6. AnyRef
                  7. Any
                    8. +
                  +
                  + +
                    +
                  1. Hide All
                    2. +
                  2. Show All
                    3. +
                  +
                  +
                  + Visibility +
                  1. Public
                  2. All
                  +
                  +
                  +
                  + +
                  +
                  +
                  +

                  Instance Constructors

                  +
                  1. + + + + + + + + + new + + + Queue(front: List[A], rear: List[A]) + + + +
                  +
                  + + + + + +
                  +

                  Value Members

                  +
                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  4. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
                    Any
                    +
                  5. + + + + + + + + + def + + + asList: List[A] + + + +
                  6. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                  7. + + + + + + + + + def + + + enqueue(elem: A): Queue[A] + + + +
                  8. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  9. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  10. + + + + + + + + + val + + + front: List[A] + + + +
                  11. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  12. + + + + + + + + + def + + + head: A + + + +
                  13. + + + + + + + + + def + + + isAmortized: Boolean + + + +
                  14. + + + + + + + + + def + + + isEmpty: Boolean + + + +
                  15. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  16. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
                    +
                  17. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  19. + + + + + + + + + val + + + rear: List[A] + + + +
                  20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
                    +
                  21. + + + + + + + + + def + + + tail: Queue[A] + + + +
                  22. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  24. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    25. +
                  +
                  + + + + +
                  + +
                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Serializable

                  +
                  +

                  Inherited from Product

                  +
                  +

                  Inherited from Equals

                  +
                  +

                  Inherited from AnyRef

                  +
                  +

                  Inherited from Any

                  +
                  + +
                  + +
                  +
                  +

                  Ungrouped

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                  +
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                    Open a new stream to read from filename, if it exists.

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                    Test whether the stream is opened or not.

                    Test whether the stream is opened or not.

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                    Open a new stream to write into filename, erasing any previous +content of the file or creating a new one if needed.

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                    Close the stream; return true on success.

                    Close the stream; return true on success.

                    NOTE The stream must not be used afterward, even on failure. +

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                    Definition Classes
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                    Test whether the stream is opened or not.

                    Test whether the stream is opened or not.

                    NOTE This is a requirement for all write operations. +

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                    Append a string to the stream and return true on success.

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                    Append a character to the stream and return true on success.

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                    Append an integer to the stream and return true on success.

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                    Reads the next signed decimal integer

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                    Attributes
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                    Definition Classes
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                  11. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
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                    Definition Classes
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                  13. + + + + + + + + + def + + + get(a: T): BigInt + + + +
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                    Definition Classes
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                    Definition Classes
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                  20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                  21. + + + + + + + + + val + + + theBag: scala.collection.immutable.Map[T, BigInt] + + + +
                  22. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
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                    + @throws( + + ... + ) + +
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                  23. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
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                    Definition Classes
                    AnyRef
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                    25. +
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                  Inherited from Serializable

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                  Inherited from Serializable

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                  Inherited from Product

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                  Inherited from Equals

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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  Packages

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                    Definition Classes
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                    Definition Classes
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                    Attributes
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                  6. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
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                    Definition Classes
                    AnyRef → Any
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                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
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                  9. + + + + + + + + + def + + + flatMap[C](f: (B) ⇒ Either[A, C]): Either[A, C] + + + +
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                  11. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
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                  12. + + + + + + + + + def + + + hashCode(): Int + + +
                    Definition Classes
                    AnyRef → Any
                    Annotations
                    + @native() + +
                    +
                  13. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
                    +
                  14. + + + + + + + + + def + + + map[C](f: (B) ⇒ C): Either[A, C] + + + +
                  15. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  16. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
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                    Definition Classes
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                  18. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
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                  19. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
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                  20. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  21. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
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                  22. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    23. +
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                  + + + + +
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                  Inherited from AnyRef

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                  Inherited from Any

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                  Ungrouped

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                  c
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                  stainless.lang

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                  Left + + + +

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                  + + + case class + + + Left[A, B](content: A) extends Either[A, B] with Product with Serializable + +

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                  +
                  + + + + + +
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                  Value Members

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                    +
                  1. + + + + + + + + final + def + + + !=(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  2. + + + + + + + + final + def + + + ##(): Int + + +
                    Definition Classes
                    AnyRef → Any
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                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
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                    Definition Classes
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                    Attributes
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                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
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                  6. + + + + + + + + + val + + + content: A + + + +
                  7. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  8. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + classOf[java.lang.Throwable] + ) + +
                    +
                  9. + + + + + + + + + def + + + flatMap[C](f: (B) ⇒ Either[A, C]): Either[A, C] + + +
                    Definition Classes
                    Either
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                  10. + + + + + + + + + def + + + get: B + + +
                    Definition Classes
                    Either
                    +
                  11. + + + + + + + + final + def + + + getClass(): Class[_] + + +
                    Definition Classes
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                    Annotations
                    + @native() + +
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                  12. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
                    Any
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                  13. + + + + + + + + + def + + + isLeft: Boolean + + +
                    Definition Classes
                    Left → Either
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                  14. + + + + + + + + + def + + + isRight: Boolean + + +
                    Definition Classes
                    Left → Either
                    +
                  15. + + + + + + + + + def + + + map[C](f: (B) ⇒ C): Either[A, C] + + +
                    Definition Classes
                    Either
                    +
                  16. + + + + + + + + final + def + + + ne(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  17. + + + + + + + + final + def + + + notify(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
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                  18. + + + + + + + + final + def + + + notifyAll(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @native() + +
                    +
                  19. + + + + + + + + + def + + + swap: Right[B, A] + + +
                    Definition Classes
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                  20. + + + + + + + + final + def + + + synchronized[T0](arg0: ⇒ T0): T0 + + +
                    Definition Classes
                    AnyRef
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                  21. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  22. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  23. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
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                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    24. +
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                  Inherited from Serializable

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                  Inherited from Product

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                  Inherited from Equals

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                  Inherited from Either[A, B]

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                  Packages

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                  stainless.lang

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                  Map + + + +

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                    Definition Classes
                    AnyRef → Any
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                    Definition Classes
                    AnyRef → Any
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                  3. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
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                  4. + + + + + + + + + def + + + apply[A, B](elems: (A, B)*): Map[A, B] + + +
                    Annotations
                    + @ignore() + +
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                  5. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
                    Definition Classes
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                  6. + + + + + + + + + def + + + clone(): AnyRef + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
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                  7. + + + + + + + + + def + + + empty[A, B]: Map[A, B] + + +
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                  8. + + + + + + + + final + def + + + eq(arg0: AnyRef): Boolean + + +
                    Definition Classes
                    AnyRef
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                  9. + + + + + + + + + def + + + equals(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  10. + + + + + + + + + def + + + finalize(): Unit + + +
                    Attributes
                    protected[java.lang]
                    Definition Classes
                    AnyRef
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                    + @throws( + + classOf[java.lang.Throwable] + ) + +
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                    Definition Classes
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                    + @native() + +
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                    Definition Classes
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                    + @native() + +
                    +
                  13. + + + + + + + + final + def + + + isInstanceOf[T0]: Boolean + + +
                    Definition Classes
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                    +
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                    Definition Classes
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                  19. + + + + + + + + + def + + + toString(): String + + +
                    Definition Classes
                    AnyRef → Any
                    +
                  20. + + + + + + + + final + def + + + wait(): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
                    +
                  21. + + + + + + + + final + def + + + wait(arg0: Long, arg1: Int): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + +
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                  22. + + + + + + + + final + def + + + wait(arg0: Long): Unit + + +
                    Definition Classes
                    AnyRef
                    Annotations
                    + @throws( + + ... + ) + + @native() + +
                    +
                    23. +
                  +
                  + + + + +
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                  Inherited from Serializable

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                  +

                  Inherited from Serializable

                  +
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                  Inherited from AnyRef

                  +
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                  Inherited from Any

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                  Ungrouped

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                  Packages

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                  c
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                  stainless.lang

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                  Map + + + +

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                  + Companion object Map +

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                  + + + case class + + + Map[A, B](theMap: scala.collection.immutable.Map[A, B]) extends Product with Serializable + +

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                  Value Members

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                    Definition Classes
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                    Definition Classes
                    AnyRef → Any
                    +
                  3. + + + + + + + + + def + + + +(k: A, v: B): Map[A, B] + + + +
                  4. + + + + + + + + + def + + + +(kv: (A, B)): Map[A, B] + + + +
                  5. + + + + + + + + + def + + + ++(b: Map[A, B]): Map[A, B] + + + +
                  6. + + + + + + + + + def + + + -(k: A): Map[A, B] + + + +
                  7. + + + + + + + + + def + + + --(b: Set[A]): Map[A, B] + + + +
                  8. + + + + + + + + final + def + + + ==(arg0: Any): Boolean + + +
                    Definition Classes
                    AnyRef → Any
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                  21. + + + + + + + + + def + + + |(that: RelReasoning[B]): RelReasoning[B] + + +

                    Close a proof.

                    +
                  22. + + + + + + + + + def + + + |[C](that: WithRel[B, C]): WithRel[B, C] + + +

                    Close a proof.

                    +
                  23. + + + + + + + + + def + + + |[C](that: WithProof[B, C]): WithProof[B, C] + + +

                    Close a proof.

                    +
                    24. +
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                  Inherited from Serializable

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                  + + diff --git a/static/stainless-library/stainless/proof/Internal$$WithRel.html b/static/stainless-library/stainless/proof/Internal$$WithRel.html new file mode 100644 index 0000000000..6dde77d4fe --- /dev/null +++ b/static/stainless-library/stainless/proof/Internal$$WithRel.html @@ -0,0 +1,689 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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                  + + + case class + + + WithRel[A, B](x: A, r: (A, B) ⇒ Boolean, prop: Boolean) extends Product with Serializable + +

                  + + +

                  * Helper classes for relational reasoning **

                  Annotations
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                  4. + + + + + + + + + def + + + ==|(proof: Boolean): WithProof[A, A] + + +

                    Short-hand for equational reasoning.

                    +
                  5. + + + + + + + + + def + + + ^^(y: B): RelReasoning[B] + + +

                    Continue with the next relation.

                    +
                  6. + + + + + + + + + def + + + ^^|(proof: Boolean): WithProof[A, B] + + +

                    Add a proof.

                    +
                  7. + + + + + + + + final + def + + + asInstanceOf[T0]: T0 + + +
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                    * Helper classes for relational reasoning **

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                    Relational reasoning.

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                  Relational reasoning.

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                    Short-hand for equational reasoning.

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                  AbstractRefinementMap.scala [raw]


                  +
                  import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+
+object AbstractRefinementMap {
+
+  case class ~>[A,B](private val f: A => B, ens: B => Boolean) {
+    require(forall((x: B) => ens.pre(x)) && forall((x: A) => f.pre(x) ==> ens(f(x))))
+
+    lazy val pre = f.pre
+
+    def apply(x: A): B = {
+      require(f.pre(x))
+      f(x)
+    } ensuring(ens)
+  }
+
+  def map[A, B](l: List[A], f: A ~> B): List[B] = {
+    require(forall((x:A) => l.contains(x) ==> f.pre(x)))
+    l match {
+      case Cons(x, xs) => Cons[B](f(x), map(xs, f))
+      case Nil() => Nil[B]()
+    }
+  } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) }
+}
+
+
                  +

                  back

                  diff --git a/static/valid/AbstractRefinementMap.scala b/static/valid/AbstractRefinementMap.scala new file mode 100644 index 0000000000..48cb2ec848 --- /dev/null +++ b/static/valid/AbstractRefinementMap.scala @@ -0,0 +1,26 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ + +object AbstractRefinementMap { + + case class ~>[A,B](private val f: A => B, ens: B => Boolean) { + require(forall((x: B) => ens.pre(x)) && forall((x: A) => f.pre(x) ==> ens(f(x)))) + + lazy val pre = f.pre + + def apply(x: A): B = { + require(f.pre(x)) + f(x) + } ensuring(ens) + } + + def map[A, B](l: List[A], f: A ~> B): List[B] = { + require(forall((x:A) => l.contains(x) ==> f.pre(x))) + l match { + case Cons(x, xs) => Cons[B](f(x), map(xs, f)) + case Nil() => Nil[B]() + } + } ensuring { res => forall((x: B) => res.contains(x) ==> f.ens(x)) } +} + diff --git a/static/valid/AddingPositiveNumbers.html b/static/valid/AddingPositiveNumbers.html new file mode 100644 index 0000000000..d7122e0fab --- /dev/null +++ b/static/valid/AddingPositiveNumbers.html @@ -0,0 +1,20 @@ + + + +valid/AddingPositiveNumbers.scala + + +

                  AddingPositiveNumbers.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+object AddingPositiveNumbers {
+
+  //this should not overflow
+  def additionSound(x: BigInt, y: BigInt): BigInt = {
+    require(x >= 0 && y >= 0)
+    x + y
+  } ensuring(_ >= 0)
+
+}
+
                  +

                  back

                  diff --git a/static/valid/AddingPositiveNumbers.scala b/static/valid/AddingPositiveNumbers.scala new file mode 100644 index 0000000000..84fca5dc63 --- /dev/null +++ b/static/valid/AddingPositiveNumbers.scala @@ -0,0 +1,11 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +object AddingPositiveNumbers { + + //this should not overflow + def additionSound(x: BigInt, y: BigInt): BigInt = { + require(x >= 0 && y >= 0) + x + y + } ensuring(_ >= 0) + +} diff --git a/static/valid/AssociativeList.html b/static/valid/AssociativeList.html new file mode 100644 index 0000000000..bade03ed99 --- /dev/null +++ b/static/valid/AssociativeList.html @@ -0,0 +1,60 @@ + + + +valid/AssociativeList.scala + + +

                  AssociativeList.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object AssociativeList { 
+  sealed abstract class KeyValuePairAbs
+  case class KeyValuePair(key: Int, value: Int) extends KeyValuePairAbs
+
+  sealed abstract class List
+  case class Cons(head: KeyValuePairAbs, tail: List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptionInt
+  case class Some(i: Int) extends OptionInt
+  case class None() extends OptionInt
+
+  def domain(l: List): Set[Int] = l match {
+    case Nil() => Set.empty[Int]
+    case Cons(KeyValuePair(k,_), xs) => Set(k) ++ domain(xs)
+  }
+
+  def find(l: List, e: Int): OptionInt = l match {
+    case Nil() => None()
+    case Cons(KeyValuePair(k, v), xs) => if (k == e) Some(v) else find(xs, e)
+  }
+
+  def noDuplicates(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(KeyValuePair(k, v), xs) => find(xs, k) == None() && noDuplicates(xs)
+  }
+
+  def updateAll(l1: List, l2: List): List = (l2 match {
+    case Nil() => l1
+    case Cons(x, xs) => updateAll(updateElem(l1, x), xs)
+  }) ensuring(domain(_) == domain(l1) ++ domain(l2))
+
+  def updateElem(l: List, e: KeyValuePairAbs): List = (l match {
+    case Nil() => Cons(e, Nil())
+    case Cons(KeyValuePair(k, v), xs) => e match {
+      case KeyValuePair(ek, ev) => if (ek == k) Cons(KeyValuePair(ek, ev), xs) else Cons(KeyValuePair(k, v), updateElem(xs, e))
+    }
+  }) ensuring(res => e match {
+    case KeyValuePair(k, v) => domain(res) == domain(l) ++ Set[Int](k)
+  })
+
+  @induct
+  def readOverWrite(l: List, k1: Int, k2: Int, e: Int) : Boolean = {
+    find(updateElem(l, KeyValuePair(k2,e)), k1) == (if (k1 == k2) Some(e) else find(l, k1))
+  }.holds
+}
+
                  +

                  back

                  diff --git a/static/valid/AssociativeList.scala b/static/valid/AssociativeList.scala new file mode 100644 index 0000000000..45ac711a12 --- /dev/null +++ b/static/valid/AssociativeList.scala @@ -0,0 +1,51 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object AssociativeList { + sealed abstract class KeyValuePairAbs + case class KeyValuePair(key: Int, value: Int) extends KeyValuePairAbs + + sealed abstract class List + case class Cons(head: KeyValuePairAbs, tail: List) extends List + case class Nil() extends List + + sealed abstract class OptionInt + case class Some(i: Int) extends OptionInt + case class None() extends OptionInt + + def domain(l: List): Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(KeyValuePair(k,_), xs) => Set(k) ++ domain(xs) + } + + def find(l: List, e: Int): OptionInt = l match { + case Nil() => None() + case Cons(KeyValuePair(k, v), xs) => if (k == e) Some(v) else find(xs, e) + } + + def noDuplicates(l: List): Boolean = l match { + case Nil() => true + case Cons(KeyValuePair(k, v), xs) => find(xs, k) == None() && noDuplicates(xs) + } + + def updateAll(l1: List, l2: List): List = (l2 match { + case Nil() => l1 + case Cons(x, xs) => updateAll(updateElem(l1, x), xs) + }) ensuring(domain(_) == domain(l1) ++ domain(l2)) + + def updateElem(l: List, e: KeyValuePairAbs): List = (l match { + case Nil() => Cons(e, Nil()) + case Cons(KeyValuePair(k, v), xs) => e match { + case KeyValuePair(ek, ev) => if (ek == k) Cons(KeyValuePair(ek, ev), xs) else Cons(KeyValuePair(k, v), updateElem(xs, e)) + } + }) ensuring(res => e match { + case KeyValuePair(k, v) => domain(res) == domain(l) ++ Set[Int](k) + }) + + @induct + def readOverWrite(l: List, k1: Int, k2: Int, e: Int) : Boolean = { + find(updateElem(l, KeyValuePair(k2,e)), k1) == (if (k1 == k2) Some(e) else find(l, k1)) + }.holds +} diff --git a/static/valid/AssociativityProperties.html b/static/valid/AssociativityProperties.html new file mode 100644 index 0000000000..9455bffcdf --- /dev/null +++ b/static/valid/AssociativityProperties.html @@ -0,0 +1,42 @@ + + + +valid/AssociativityProperties.scala + + +

                  AssociativityProperties.scala [raw]


                  +
                  import stainless.lang._
+
+object AssociativityProperties {
+
+  def isAssociative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z)))
+  }
+
+  def isCommutative[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A) => f(x, y) == f(y, x))
+  }
+
+  def isRotate[A](f: (A,A) => A): Boolean = {
+    forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x))
+  }
+
+  def assocPairs[A,B](f1: (A,A) => A, f2: (B,B) => B) = {
+    require(isAssociative(f1) && isAssociative(f2))
+    val fp = ((p1: (A,B), p2: (A,B)) => (f1(p1._1, p2._1), f2(p1._2, p2._2)))
+    isAssociative(fp)
+  }.holds
+
+  def assocRotate[A](f: (A,A) => A): Boolean = {
+    require(isCommutative(f) && isRotate(f))
+    isAssociative(f)
+  }.holds
+
+  def assocRotateInt(f: (BigInt, BigInt) => BigInt): Boolean = {
+    require(isCommutative(f) && isRotate(f))
+    isAssociative(f)
+  }.holds
+
+}
+
                  +

                  back

                  diff --git a/static/valid/AssociativityProperties.scala b/static/valid/AssociativityProperties.scala new file mode 100644 index 0000000000..c92d44ae10 --- /dev/null +++ b/static/valid/AssociativityProperties.scala @@ -0,0 +1,33 @@ +import stainless.lang._ + +object AssociativityProperties { + + def isAssociative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(x, f(y, z))) + } + + def isCommutative[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A) => f(x, y) == f(y, x)) + } + + def isRotate[A](f: (A,A) => A): Boolean = { + forall((x: A, y: A, z: A) => f(f(x, y), z) == f(f(y, z), x)) + } + + def assocPairs[A,B](f1: (A,A) => A, f2: (B,B) => B) = { + require(isAssociative(f1) && isAssociative(f2)) + val fp = ((p1: (A,B), p2: (A,B)) => (f1(p1._1, p2._1), f2(p1._2, p2._2))) + isAssociative(fp) + }.holds + + def assocRotate[A](f: (A,A) => A): Boolean = { + require(isCommutative(f) && isRotate(f)) + isAssociative(f) + }.holds + + def assocRotateInt(f: (BigInt, BigInt) => BigInt): Boolean = { + require(isCommutative(f) && isRotate(f)) + isAssociative(f) + }.holds + +} diff --git a/static/valid/BinarySearchTreeQuant.html b/static/valid/BinarySearchTreeQuant.html new file mode 100644 index 0000000000..72c2c4ddd4 --- /dev/null +++ b/static/valid/BinarySearchTreeQuant.html @@ -0,0 +1,53 @@ + + + +valid/BinarySearchTreeQuant.scala + + +

                  BinarySearchTreeQuant.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.collection._
+
+object BSTSimpler {
+  sealed abstract class Tree
+  case class Node(left: Tree, value: BigInt, right: Tree) extends Tree
+  case class Leaf() extends Tree
+
+  def content(tree: Tree): Set[BigInt] = tree match {
+    case Leaf() => Set.empty[BigInt]
+    case Node(l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def isBST(tree: Tree) : Boolean = tree match {
+    case Leaf() => true
+    case Node(left, v, right) => {
+      isBST(left) && isBST(right) &&
+      forall((x:BigInt) => (content(left).contains(x) ==> x < v)) &&
+      forall((x:BigInt) => (content(right).contains(x) ==> v < x))
+    }
+  }
+
+  def emptySet(): Tree = Leaf()
+
+  def insert(tree: Tree, value: BigInt): Node = {
+    require(isBST(tree))
+    tree match {
+      case Leaf() => Node(Leaf(), value, Leaf())
+      case Node(l, v, r) => (if (v < value) {
+        Node(l, v, insert(r, value))
+      } else if (v > value) {
+        Node(insert(l, value), v, r)
+      } else {
+        Node(l, v, r)
+      })
+    }
+  } ensuring(res => isBST(res) && content(res) == content(tree) ++ Set(value))
+
+  def createRoot(v: BigInt): Node = {
+    Node(Leaf(), v, Leaf())
+  } ensuring (content(_) == Set(v))
+}
+
                  +

                  back

                  diff --git a/static/valid/BinarySearchTreeQuant.scala b/static/valid/BinarySearchTreeQuant.scala new file mode 100644 index 0000000000..36f80d7d8b --- /dev/null +++ b/static/valid/BinarySearchTreeQuant.scala @@ -0,0 +1,44 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.collection._ + +object BSTSimpler { + sealed abstract class Tree + case class Node(left: Tree, value: BigInt, right: Tree) extends Tree + case class Leaf() extends Tree + + def content(tree: Tree): Set[BigInt] = tree match { + case Leaf() => Set.empty[BigInt] + case Node(l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def isBST(tree: Tree) : Boolean = tree match { + case Leaf() => true + case Node(left, v, right) => { + isBST(left) && isBST(right) && + forall((x:BigInt) => (content(left).contains(x) ==> x < v)) && + forall((x:BigInt) => (content(right).contains(x) ==> v < x)) + } + } + + def emptySet(): Tree = Leaf() + + def insert(tree: Tree, value: BigInt): Node = { + require(isBST(tree)) + tree match { + case Leaf() => Node(Leaf(), value, Leaf()) + case Node(l, v, r) => (if (v < value) { + Node(l, v, insert(r, value)) + } else if (v > value) { + Node(insert(l, value), v, r) + } else { + Node(l, v, r) + }) + } + } ensuring(res => isBST(res) && content(res) == content(tree) ++ Set(value)) + + def createRoot(v: BigInt): Node = { + Node(Leaf(), v, Leaf()) + } ensuring (content(_) == Set(v)) +} diff --git a/static/valid/ChooseWithWitness.html b/static/valid/ChooseWithWitness.html new file mode 100644 index 0000000000..dacc364f12 --- /dev/null +++ b/static/valid/ChooseWithWitness.html @@ -0,0 +1,60 @@ + + + +valid/ChooseWithWitness.scala + + +

                  ChooseWithWitness.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ChooseWithWitness {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def createListOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        Cons(0, createListOfSize(i - 1))
+      }
+    } ensuring ( size(_) == i )
+
+    def listOfSize(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i == BigInt(0)) {
+        Nil()
+      } else {
+        assert(size(createListOfSize(i)) == i) // provides choose quantification with a matcher
+        choose[List] { (res: List) => size(res) == i }
+      }
+    } ensuring ( size(_) == i )
+
+    def listOfSize2(i: BigInt): List = {
+      require(i >= 0)
+
+      if (i > 0) {
+        Cons(0, listOfSize(i-1))
+      } else {
+        Nil()
+      }
+    } ensuring ( size(_) == i )
+}
+
                  +

                  back

                  diff --git a/static/valid/ChooseWithWitness.scala b/static/valid/ChooseWithWitness.scala new file mode 100644 index 0000000000..3d6c1c1d31 --- /dev/null +++ b/static/valid/ChooseWithWitness.scala @@ -0,0 +1,51 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ChooseWithWitness { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def createListOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + Cons(0, createListOfSize(i - 1)) + } + } ensuring ( size(_) == i ) + + def listOfSize(i: BigInt): List = { + require(i >= 0) + + if (i == BigInt(0)) { + Nil() + } else { + assert(size(createListOfSize(i)) == i) // provides choose quantification with a matcher + choose[List] { (res: List) => size(res) == i } + } + } ensuring ( size(_) == i ) + + def listOfSize2(i: BigInt): List = { + require(i >= 0) + + if (i > 0) { + Cons(0, listOfSize(i-1)) + } else { + Nil() + } + } ensuring ( size(_) == i ) +} diff --git a/static/valid/ConcRope.html b/static/valid/ConcRope.html new file mode 100644 index 0000000000..29bc4359d4 --- /dev/null +++ b/static/valid/ConcRope.html @@ -0,0 +1,470 @@ +

                  ConcRope.scala [raw]


                  +
                  package conc
+// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL
+
+import stainless.collection._
+import stainless.lang._
+import ListSpecs._
+import stainless.annotation._
+
+object ConcRope {
+
+  def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y
+  def abs(x: BigInt): BigInt = if (x < 0) -x else x
+
+  sealed abstract class Conc[T] {
+
+    def isEmpty: Boolean = {
+      this == Empty[T]()
+    }
+
+    def isLeaf: Boolean = {
+      this match {
+        case Empty() => true
+        case Single(_) => true
+        case _ => false
+      }
+    }
+
+    def isNormalized: Boolean = this match {
+      case Append(_, _) => false
+      case _ => true
+    }
+
+    def valid: Boolean = {
+      concInv && balanced && appendInv
+    }
+
+    /**
+     * (a) left and right trees of conc node should be non-empty
+     * (b) they cannot be append nodes
+     */
+    def concInv: Boolean = this match {
+      case CC(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.isNormalized && r.isNormalized &&
+          l.concInv && r.concInv
+      case _ => true
+    }
+
+    def balanced: Boolean = {
+      this match {
+        case CC(l, r) =>
+          l.level - r.level >= -1 && l.level - r.level <= 1 &&
+            l.balanced && r.balanced
+        case _ => true
+      }
+    }
+
+    /**
+     * (a) Right subtree of an append node is not an append node
+     * (b) If the tree is of the form a@Append(b@Append(_,_),_) then
+     * 		a.right.level < b.right.level
+     * (c) left and right are not empty
+     */
+    def appendInv: Boolean = this match {
+      case Append(l, r) =>
+        !l.isEmpty && !r.isEmpty &&
+          l.valid && r.valid &&
+          r.isNormalized &&
+          (l match {
+            case Append(_, lr) =>
+              lr.level > r.level
+            case _ =>
+              l.level > r.level
+          })
+      case _ => true
+    }
+
+    val level: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 0
+        case CC(l, r) =>
+          1 + max(l.level, r.level)
+        case Append(l, r) =>
+          1 + max(l.level, r.level)
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    val size: BigInt = {
+      (this match {
+        case Empty() => 0
+        case Single(x) => 1
+        case CC(l, r) =>
+          l.size + r.size
+        case Append(l, r) =>
+          l.size + r.size
+      }): BigInt
+    } ensuring (_ >= 0)
+
+    def toList: List[T] = {
+      this match {
+        case Empty() => Nil[T]()
+        case Single(x) => Cons(x, Nil[T]())
+        case CC(l, r) =>
+          l.toList ++ r.toList // note: left elements precede the right elements in the list
+        case Append(l, r) =>
+          l.toList ++ r.toList
+      }
+    } ensuring (res => res.size == this.size)
+  }
+
+  case class Empty[T]() extends Conc[T]
+  case class Single[T](x: T) extends Conc[T]
+  case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+  case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T]
+
+  def lookup[T](xs: Conc[T], i: BigInt): T = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => x
+      case CC(l, r) =>
+        if (i < l.size) lookup(l, i)
+       else lookup(r, i - l.size)          
+      case Append(l, r) =>
+        if (i < l.size) lookup(l, i)
+        else lookup(r, i - l.size)          
+    }
+  } ensuring (res =>  instAppendIndexAxiom(xs, i) &&  // an auxiliary axiom instantiation that required for the proof
+    res == xs.toList(i)) // correctness
+    
+
+  def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = {
+    require(0 <= i && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case Append(l, r) =>
+        appendIndex(l.toList, r.toList, i)
+      case _ => true
+    }
+  }.holds
+
+  def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size)
+    xs match {
+      case Single(x) => Single(y)
+      case CC(l, r) =>
+        if (i < l.size) CC(update(l, i, y), r)
+        else CC(l, update(r, i - l.size, y))
+      case Append(l, r) =>
+        if (i < l.size) {          
+          Append(update(l, i, y), r)
+        } else         
+          Append(l, update(r, i - l.size, y))
+    }
+  } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation
+    res.level == xs.level && // heights of the input and output trees are equal
+    res.valid && // tree invariants are preserved    
+    res.toList == xs.toList.updated(i, y) && // correctness
+    numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function     
+
+  def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i < xs.size)
+    xs match {
+      case CC(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case Append(l, r) =>
+        appendUpdate(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  /**
+   * A generic concat that applies to general concTrees
+   */  
+  def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid)    
+    concatNormalized(normalize(xs), normalize(ys))    
+  }
+
+  /**
+   * This concat applies only to normalized trees.
+   * This prevents concat from being recursive
+   */
+  def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized)
+    (xs, ys) match {
+      case (xs, Empty()) => xs
+      case (Empty(), ys) => ys
+      case _ =>
+        concatNonEmpty(xs, ys)
+    }
+  } ensuring (res => res.valid && // tree invariants
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    (res.toList == xs.toList ++ ys.toList) && // correctness
+    res.isNormalized //auxiliary properties    
+    )
+
+  def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid &&
+      xs.isNormalized && ys.isNormalized &&
+      !xs.isEmpty && !ys.isEmpty)
+
+    val diff = ys.level - xs.level
+    if (diff >= -1 && diff <= 1) 
+      CC(xs, ys)
+    else if (diff < -1) {
+      // ys is smaller than xs
+      xs match {
+        case CC(l, r) =>
+          if (l.level >= r.level) 
+            CC(l, concatNonEmpty(r, ys))
+          else {
+            r match {
+              case CC(rl, rr) =>
+                val nrr = concatNonEmpty(rr, ys)
+                if (nrr.level == xs.level - 3) {
+                  CC(l, CC(rl, nrr))
+                } else {
+                  CC(CC(l, rl), nrr)
+                }
+            }
+          }
+      }
+    } else {
+      ys match {
+        case CC(l, r) =>
+          if (r.level >= l.level) {
+            CC(concatNonEmpty(xs, l), r)
+          } else {
+            l match {
+              case CC(ll, lr) =>
+                val nll = concatNonEmpty(xs, ll)
+                if (nll.level == ys.level - 3) {                  
+                  CC(CC(nll, lr), r)
+                } else {                  
+                  CC(nll, CC(lr, r))
+                }
+            }
+          }
+      }
+    }
+  } ensuring (res =>  
+    appendAssocInst(xs, ys) && // instantiation of an axiom
+    res.level <= max(xs.level, ys.level) + 1 && // height invariants
+    res.level >= max(xs.level, ys.level) &&
+    res.balanced && res.appendInv && res.concInv && //this is should not be needed
+    res.valid && // tree invariant is preserved
+    res.toList == xs.toList ++ ys.toList && // correctness
+    res.isNormalized // auxiliary properties    
+    )
+
+  
+  def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    (xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation              
+          (r match {
+            case CC(rl, rr) =>
+              appendAssoc(rl.toList, rr.toList, ys.toList) &&
+                appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList)
+            case _ => true
+          })
+      case _ => true
+    }) &&
+      (ys match {
+        case CC(l, r) =>
+          appendAssoc(xs.toList, l.toList, r.toList) &&
+            (l match {
+              case CC(ll, lr) =>
+                appendAssoc(xs.toList, ll.toList, lr.toList) &&
+                  appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList)
+              case _ => true
+            })
+        case _ => true
+      })
+  }.holds
+
+  
+  def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = {
+    require(xs.valid && i >= 0 && i <= xs.size &&
+      xs.isNormalized) //note the precondition
+    xs match {
+      case Empty() => Single(y)
+      case Single(x) =>
+        if (i == 0)
+          CC(Single(y), xs)
+        else
+          CC(xs, Single(y))
+      case CC(l, r) if i < l.size =>
+        concatNonEmpty(insert(l, i, y), r)        
+      case CC(l, r) =>
+       concatNonEmpty(l, insert(r, i - l.size, y))      
+    }
+  } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom 
+    res.valid && res.isNormalized && // tree invariants            
+    res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree    
+    res.toList == insertAtIndex(xs.toList, i, y) // correctness    
+    )
+
+  /**
+   * Using a different version of insert than of the library
+   * because the library implementation in unnecessarily complicated.  
+   */
+  def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = {
+    require(0 <= i && i <= l.size)
+    l match {
+      case Nil() =>
+        Cons[T](y, Nil())
+      case _ if i == 0 =>
+        Cons[T](y, l)
+      case Cons(x, tail) =>
+        Cons[T](x, insertAtIndex(tail, i - 1, y))
+    }
+  }
+
+  // A lemma about `append` and `insertAtIndex`
+  def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = {
+    require(0 <= i && i <= l1.size + l2.size)
+    (l1 match {
+      case Nil() => true
+      case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y)
+    }) &&
+      // lemma
+      (insertAtIndex((l1 ++ l2), i, y) == (
+        if (i < l1.size) insertAtIndex(l1, i, y) ++ l2
+        else l1 ++ insertAtIndex(l2, (i - l1.size), y)))
+  }.holds
+
+  def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = {
+    require(i >= 0 && i <= xs.size)
+    xs match {
+      case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y)
+      case _ => true
+    }
+  }.holds
+
+  def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = {
+    require(xs.valid && xs.isNormalized)
+    xs match {
+      case Empty() =>
+        (Empty[T](), Empty[T]())
+      case s @ Single(x) =>
+        if (n <= 0) { 
+          (Empty[T](), s)
+        } else {
+          (s, Empty[T]())
+        }
+      case CC(l, r) =>
+        if (n < l.size) {
+          val (ll, lr) = split(l, n)          
+          (ll, concatNormalized(lr, r))
+        } else if (n > l.size) {
+          val (rl, rr) = split(r, n - l.size)          
+          (concatNormalized(l, rl), rr)
+        } else {
+          (l, r)
+        }
+    }
+  } ensuring (res  => instSplitAxiom(xs, n) && // instantiation of an axiom     
+    res._1.valid && res._2.valid && // tree invariants are preserved
+    res._1.isNormalized && res._2.isNormalized &&
+    xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree
+    res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness    
+    )
+
+  def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendTakeDrop(l.toList, r.toList, n)
+      case _ => true
+    }
+  }.holds
+
+  def append[T](xs: Conc[T], x: T): Conc[T] = {
+    require(xs.valid)
+    val ys = Single[T](x)
+    xs match {
+      case xs @ Append(_, _) =>
+        appendPriv(xs, ys)
+      case CC(_, _) =>
+        Append(xs, ys) //creating an append node
+      case Empty() => ys
+      case Single(_) => CC(xs, ys)
+    }
+  } ensuring (res => res.valid && //conctree invariants
+    res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness
+    res.level <= xs.level + 1 
+  )
+
+  /**
+   * This is a private method and is not exposed to the
+   * clients of conc trees
+   */
+  def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T]  = {
+    require(xs.valid && ys.valid &&
+      !ys.isEmpty && ys.isNormalized &&
+      xs.right.level >= ys.level)
+
+    if (xs.right.level > ys.level)
+      Append(xs, ys)
+    else {
+      val zs = CC(xs.right, ys)
+      xs.left match {
+        case l @ Append(_, _) => appendPriv(l, zs)          
+        case l if l.level <= zs.level => //note: here < is not possible           
+          CC(l, zs)
+        case l =>
+          Append(l, zs)
+      }
+    }
+  } ensuring (res => appendAssocInst2(xs, ys) && 
+    res.valid && //conc tree invariants
+    res.toList == xs.toList ++ ys.toList && //correctness invariants
+    res.level <= xs.level + 1 )
+
+  def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = {
+    xs match {
+      case CC(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case Append(l, r) =>
+        appendAssoc(l.toList, r.toList, ys.toList)
+      case _ => true
+    }
+  }.holds
+
+  def numTrees[T](t: Conc[T]): BigInt = {
+    t match {
+      case Append(l, r) => numTrees(l) + 1
+      case _ => BigInt(1)
+    }
+  } ensuring (res => res >= 0)
+
+  def normalize[T](t: Conc[T]): Conc[T] = {
+    require(t.valid)
+    t match {
+      case Append(l @ Append(_, _), r) =>
+        wrap(l, r)
+      case Append(l, r) =>
+        concatNormalized(l, r)
+      case _ => t
+    }
+  } ensuring (res => res.valid &&
+    res.isNormalized &&
+    res.toList == t.toList && //correctness
+    res.size == t.size && res.level <= t.level //normalize preserves level and size  
+    )
+
+  def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = {
+    require(xs.valid && ys.valid && ys.isNormalized &&
+      xs.right.level >= ys.level)
+    val nr  = concatNormalized(xs.right, ys)
+    xs.left match {
+      case l @ Append(_, _) => wrap(l, nr)      
+      case l =>
+        concatNormalized(l, nr)        
+    }
+  } ensuring (res => 
+    appendAssocInst2(xs, ys) && //some lemma instantiations   
+    res.valid &&
+    res.isNormalized &&
+    res.toList == xs.toList ++ ys.toList && //correctness
+    res.size == xs.size + ys.size && //other auxiliary properties
+    res.level <= xs.level    
+    ) 
+}
+
                  diff --git a/static/valid/ConcRope.scala b/static/valid/ConcRope.scala new file mode 100644 index 0000000000..932bd11494 --- /dev/null +++ b/static/valid/ConcRope.scala @@ -0,0 +1,468 @@ +package conc +// By Ravi Kandhadai Madhavan @ LARA, EPFL. (c) EPFL + +import stainless.collection._ +import stainless.lang._ +import ListSpecs._ +import stainless.annotation._ + +object ConcRope { + + def max(x: BigInt, y: BigInt): BigInt = if (x >= y) x else y + def abs(x: BigInt): BigInt = if (x < 0) -x else x + + sealed abstract class Conc[T] { + + def isEmpty: Boolean = { + this == Empty[T]() + } + + def isLeaf: Boolean = { + this match { + case Empty() => true + case Single(_) => true + case _ => false + } + } + + def isNormalized: Boolean = this match { + case Append(_, _) => false + case _ => true + } + + def valid: Boolean = { + concInv && balanced && appendInv + } + + /** + * (a) left and right trees of conc node should be non-empty + * (b) they cannot be append nodes + */ + def concInv: Boolean = this match { + case CC(l, r) => + !l.isEmpty && !r.isEmpty && + l.isNormalized && r.isNormalized && + l.concInv && r.concInv + case _ => true + } + + def balanced: Boolean = { + this match { + case CC(l, r) => + l.level - r.level >= -1 && l.level - r.level <= 1 && + l.balanced && r.balanced + case _ => true + } + } + + /** + * (a) Right subtree of an append node is not an append node + * (b) If the tree is of the form a@Append(b@Append(_,_),_) then + * a.right.level < b.right.level + * (c) left and right are not empty + */ + def appendInv: Boolean = this match { + case Append(l, r) => + !l.isEmpty && !r.isEmpty && + l.valid && r.valid && + r.isNormalized && + (l match { + case Append(_, lr) => + lr.level > r.level + case _ => + l.level > r.level + }) + case _ => true + } + + val level: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 0 + case CC(l, r) => + 1 + max(l.level, r.level) + case Append(l, r) => + 1 + max(l.level, r.level) + }): BigInt + } ensuring (_ >= 0) + + val size: BigInt = { + (this match { + case Empty() => 0 + case Single(x) => 1 + case CC(l, r) => + l.size + r.size + case Append(l, r) => + l.size + r.size + }): BigInt + } ensuring (_ >= 0) + + def toList: List[T] = { + this match { + case Empty() => Nil[T]() + case Single(x) => Cons(x, Nil[T]()) + case CC(l, r) => + l.toList ++ r.toList // note: left elements precede the right elements in the list + case Append(l, r) => + l.toList ++ r.toList + } + } ensuring (res => res.size == this.size) + } + + case class Empty[T]() extends Conc[T] + case class Single[T](x: T) extends Conc[T] + case class CC[T](left: Conc[T], right: Conc[T]) extends Conc[T] + case class Append[T](left: Conc[T], right: Conc[T]) extends Conc[T] + + def lookup[T](xs: Conc[T], i: BigInt): T = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => x + case CC(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + case Append(l, r) => + if (i < l.size) lookup(l, i) + else lookup(r, i - l.size) + } + } ensuring (res => instAppendIndexAxiom(xs, i) && // an auxiliary axiom instantiation that required for the proof + res == xs.toList(i)) // correctness + + + def instAppendIndexAxiom[T](xs: Conc[T], i: BigInt): Boolean = { + require(0 <= i && i < xs.size) + xs match { + case CC(l, r) => + appendIndex(l.toList, r.toList, i) + case Append(l, r) => + appendIndex(l.toList, r.toList, i) + case _ => true + } + }.holds + + def update[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && !xs.isEmpty && i >= 0 && i < xs.size) + xs match { + case Single(x) => Single(y) + case CC(l, r) => + if (i < l.size) CC(update(l, i, y), r) + else CC(l, update(r, i - l.size, y)) + case Append(l, r) => + if (i < l.size) { + Append(update(l, i, y), r) + } else + Append(l, update(r, i - l.size, y)) + } + } ensuring (res => instAppendUpdateAxiom(xs, i, y) && // an auxiliary axiom instantiation + res.level == xs.level && // heights of the input and output trees are equal + res.valid && // tree invariants are preserved + res.toList == xs.toList.updated(i, y) && // correctness + numTrees(res) == numTrees(xs)) //auxiliary property that preserves the potential function + + def instAppendUpdateAxiom[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i < xs.size) + xs match { + case CC(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case Append(l, r) => + appendUpdate(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + /** + * A generic concat that applies to general concTrees + */ + def concat[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid) + concatNormalized(normalize(xs), normalize(ys)) + } + + /** + * This concat applies only to normalized trees. + * This prevents concat from being recursive + */ + def concatNormalized[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized) + (xs, ys) match { + case (xs, Empty()) => xs + case (Empty(), ys) => ys + case _ => + concatNonEmpty(xs, ys) + } + } ensuring (res => res.valid && // tree invariants + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + (res.toList == xs.toList ++ ys.toList) && // correctness + res.isNormalized //auxiliary properties + ) + + def concatNonEmpty[T](xs: Conc[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + xs.isNormalized && ys.isNormalized && + !xs.isEmpty && !ys.isEmpty) + + val diff = ys.level - xs.level + if (diff >= -1 && diff <= 1) + CC(xs, ys) + else if (diff < -1) { + // ys is smaller than xs + xs match { + case CC(l, r) => + if (l.level >= r.level) + CC(l, concatNonEmpty(r, ys)) + else { + r match { + case CC(rl, rr) => + val nrr = concatNonEmpty(rr, ys) + if (nrr.level == xs.level - 3) { + CC(l, CC(rl, nrr)) + } else { + CC(CC(l, rl), nrr) + } + } + } + } + } else { + ys match { + case CC(l, r) => + if (r.level >= l.level) { + CC(concatNonEmpty(xs, l), r) + } else { + l match { + case CC(ll, lr) => + val nll = concatNonEmpty(xs, ll) + if (nll.level == ys.level - 3) { + CC(CC(nll, lr), r) + } else { + CC(nll, CC(lr, r)) + } + } + } + } + } + } ensuring (res => + appendAssocInst(xs, ys) && // instantiation of an axiom + res.level <= max(xs.level, ys.level) + 1 && // height invariants + res.level >= max(xs.level, ys.level) && + res.balanced && res.appendInv && res.concInv && //this is should not be needed + res.valid && // tree invariant is preserved + res.toList == xs.toList ++ ys.toList && // correctness + res.isNormalized // auxiliary properties + ) + + + def appendAssocInst[T](xs: Conc[T], ys: Conc[T]): Boolean = { + (xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) && //instantiation of associativity of concatenation + (r match { + case CC(rl, rr) => + appendAssoc(rl.toList, rr.toList, ys.toList) && + appendAssoc(l.toList, rl.toList, rr.toList ++ ys.toList) + case _ => true + }) + case _ => true + }) && + (ys match { + case CC(l, r) => + appendAssoc(xs.toList, l.toList, r.toList) && + (l match { + case CC(ll, lr) => + appendAssoc(xs.toList, ll.toList, lr.toList) && + appendAssoc(xs.toList ++ ll.toList, lr.toList, r.toList) + case _ => true + }) + case _ => true + }) + }.holds + + + def insert[T](xs: Conc[T], i: BigInt, y: T): Conc[T] = { + require(xs.valid && i >= 0 && i <= xs.size && + xs.isNormalized) //note the precondition + xs match { + case Empty() => Single(y) + case Single(x) => + if (i == 0) + CC(Single(y), xs) + else + CC(xs, Single(y)) + case CC(l, r) if i < l.size => + concatNonEmpty(insert(l, i, y), r) + case CC(l, r) => + concatNonEmpty(l, insert(r, i - l.size, y)) + } + } ensuring (res => insertAppendAxiomInst(xs, i, y) && // instantiation of an axiom + res.valid && res.isNormalized && // tree invariants + res.level - xs.level <= 1 && res.level >= xs.level && // height of the output tree is at most 1 greater than that of the input tree + res.toList == insertAtIndex(xs.toList, i, y) // correctness + ) + + /** + * Using a different version of insert than of the library + * because the library implementation in unnecessarily complicated. + */ + def insertAtIndex[T](l: List[T], i: BigInt, y: T): List[T] = { + require(0 <= i && i <= l.size) + l match { + case Nil() => + Cons[T](y, Nil()) + case _ if i == 0 => + Cons[T](y, l) + case Cons(x, tail) => + Cons[T](x, insertAtIndex(tail, i - 1, y)) + } + } + + // A lemma about `append` and `insertAtIndex` + def appendInsertIndex[T](l1: List[T], l2: List[T], i: BigInt, y: T): Boolean = { + require(0 <= i && i <= l1.size + l2.size) + (l1 match { + case Nil() => true + case Cons(x, xs) => if (i == 0) true else appendInsertIndex[T](xs, l2, i - 1, y) + }) && + // lemma + (insertAtIndex((l1 ++ l2), i, y) == ( + if (i < l1.size) insertAtIndex(l1, i, y) ++ l2 + else l1 ++ insertAtIndex(l2, (i - l1.size), y))) + }.holds + + def insertAppendAxiomInst[T](xs: Conc[T], i: BigInt, y: T): Boolean = { + require(i >= 0 && i <= xs.size) + xs match { + case CC(l, r) => appendInsertIndex(l.toList, r.toList, i, y) + case _ => true + } + }.holds + + def split[T](xs: Conc[T], n: BigInt): (Conc[T], Conc[T]) = { + require(xs.valid && xs.isNormalized) + xs match { + case Empty() => + (Empty[T](), Empty[T]()) + case s @ Single(x) => + if (n <= 0) { + (Empty[T](), s) + } else { + (s, Empty[T]()) + } + case CC(l, r) => + if (n < l.size) { + val (ll, lr) = split(l, n) + (ll, concatNormalized(lr, r)) + } else if (n > l.size) { + val (rl, rr) = split(r, n - l.size) + (concatNormalized(l, rl), rr) + } else { + (l, r) + } + } + } ensuring (res => instSplitAxiom(xs, n) && // instantiation of an axiom + res._1.valid && res._2.valid && // tree invariants are preserved + res._1.isNormalized && res._2.isNormalized && + xs.level >= res._1.level && xs.level >= res._2.level && // height bounds of the resulting tree + res._1.toList == xs.toList.take(n) && res._2.toList == xs.toList.drop(n) // correctness + ) + + def instSplitAxiom[T](xs: Conc[T], n: BigInt): Boolean = { + xs match { + case CC(l, r) => + appendTakeDrop(l.toList, r.toList, n) + case _ => true + } + }.holds + + def append[T](xs: Conc[T], x: T): Conc[T] = { + require(xs.valid) + val ys = Single[T](x) + xs match { + case xs @ Append(_, _) => + appendPriv(xs, ys) + case CC(_, _) => + Append(xs, ys) //creating an append node + case Empty() => ys + case Single(_) => CC(xs, ys) + } + } ensuring (res => res.valid && //conctree invariants + res.toList == xs.toList ++ Cons(x, Nil[T]()) && //correctness + res.level <= xs.level + 1 + ) + + /** + * This is a private method and is not exposed to the + * clients of conc trees + */ + def appendPriv[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && + !ys.isEmpty && ys.isNormalized && + xs.right.level >= ys.level) + + if (xs.right.level > ys.level) + Append(xs, ys) + else { + val zs = CC(xs.right, ys) + xs.left match { + case l @ Append(_, _) => appendPriv(l, zs) + case l if l.level <= zs.level => //note: here < is not possible + CC(l, zs) + case l => + Append(l, zs) + } + } + } ensuring (res => appendAssocInst2(xs, ys) && + res.valid && //conc tree invariants + res.toList == xs.toList ++ ys.toList && //correctness invariants + res.level <= xs.level + 1 ) + + def appendAssocInst2[T](xs: Conc[T], ys: Conc[T]): Boolean = { + xs match { + case CC(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case Append(l, r) => + appendAssoc(l.toList, r.toList, ys.toList) + case _ => true + } + }.holds + + def numTrees[T](t: Conc[T]): BigInt = { + t match { + case Append(l, r) => numTrees(l) + 1 + case _ => BigInt(1) + } + } ensuring (res => res >= 0) + + def normalize[T](t: Conc[T]): Conc[T] = { + require(t.valid) + t match { + case Append(l @ Append(_, _), r) => + wrap(l, r) + case Append(l, r) => + concatNormalized(l, r) + case _ => t + } + } ensuring (res => res.valid && + res.isNormalized && + res.toList == t.toList && //correctness + res.size == t.size && res.level <= t.level //normalize preserves level and size + ) + + def wrap[T](xs: Append[T], ys: Conc[T]): Conc[T] = { + require(xs.valid && ys.valid && ys.isNormalized && + xs.right.level >= ys.level) + val nr = concatNormalized(xs.right, ys) + xs.left match { + case l @ Append(_, _) => wrap(l, nr) + case l => + concatNormalized(l, nr) + } + } ensuring (res => + appendAssocInst2(xs, ys) && //some lemma instantiations + res.valid && + res.isNormalized && + res.toList == xs.toList ++ ys.toList && //correctness + res.size == xs.size + ys.size && //other auxiliary properties + res.level <= xs.level + ) +} diff --git a/static/valid/FlatMap.html b/static/valid/FlatMap.html new file mode 100644 index 0000000000..8025c50fbb --- /dev/null +++ b/static/valid/FlatMap.html @@ -0,0 +1,61 @@ + + + +valid/FlatMap.scala + + +

                  FlatMap.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.proof._
+import stainless.collection._
+
+object FlatMap {
+
+  def append[T](l1: List[T], l2: List[T]): List[T] = l1 match {
+    case Cons(head, tail) => Cons(head, append(tail, l2))
+    case Nil() => l2
+  }
+
+  def associative_append_lemma[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = {
+    append(append(l1, l2), l3) == append(l1, append(l2, l3))
+  }
+
+  def associative_append_lemma_induct[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = {
+    l1 match {
+      case Nil() => associative_append_lemma(l1, l2, l3)
+      case Cons(head, tail) => associative_append_lemma(l1, l2, l3) because associative_append_lemma_induct(tail, l2, l3)
+    }
+  }.holds
+
+  def flatMap[T,U](list: List[T], f: T => List[U]): List[U] = list match {
+    case Cons(head, tail) => append(f(head), flatMap(tail, f))
+    case Nil() => Nil()
+  }
+
+  def associative_lemma[T,U,V](list: List[T], f: T => List[U], g: U => List[V]): Boolean = {
+    flatMap(flatMap(list, f), g) == flatMap(list, (x: T) => flatMap(f(x), g))
+  }
+
+  def associative_lemma_induct[T,U,V](list: List[T], flist: List[U], glist: List[V], f: T => List[U], g: U => List[V]): Boolean = {
+    associative_lemma(list, f, g) because {
+      append(glist, flatMap(append(flist, flatMap(list, f)), g)) == append(append(glist, flatMap(flist, g)), flatMap(list, (x: T) => flatMap(f(x), g))) because
+      (glist match {
+        case Cons(ghead, gtail) =>
+          associative_lemma_induct(list, flist, gtail, f, g)
+        case Nil() => flist match {
+          case Cons(fhead, ftail) =>
+            associative_lemma_induct(list, ftail, g(fhead), f, g)
+          case Nil() => list match {
+            case Cons(head, tail) => associative_lemma_induct(tail, f(head), Nil(), f, g)
+            case Nil() => true
+          }
+        }
+      })
+    }
+  }.holds
+
+}
+
                  +

                  back

                  diff --git a/static/valid/FlatMap.scala b/static/valid/FlatMap.scala new file mode 100644 index 0000000000..cb7c3f132b --- /dev/null +++ b/static/valid/FlatMap.scala @@ -0,0 +1,52 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.proof._ +import stainless.collection._ + +object FlatMap { + + def append[T](l1: List[T], l2: List[T]): List[T] = l1 match { + case Cons(head, tail) => Cons(head, append(tail, l2)) + case Nil() => l2 + } + + def associative_append_lemma[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = { + append(append(l1, l2), l3) == append(l1, append(l2, l3)) + } + + def associative_append_lemma_induct[T](l1: List[T], l2: List[T], l3: List[T]): Boolean = { + l1 match { + case Nil() => associative_append_lemma(l1, l2, l3) + case Cons(head, tail) => associative_append_lemma(l1, l2, l3) because associative_append_lemma_induct(tail, l2, l3) + } + }.holds + + def flatMap[T,U](list: List[T], f: T => List[U]): List[U] = list match { + case Cons(head, tail) => append(f(head), flatMap(tail, f)) + case Nil() => Nil() + } + + def associative_lemma[T,U,V](list: List[T], f: T => List[U], g: U => List[V]): Boolean = { + flatMap(flatMap(list, f), g) == flatMap(list, (x: T) => flatMap(f(x), g)) + } + + def associative_lemma_induct[T,U,V](list: List[T], flist: List[U], glist: List[V], f: T => List[U], g: U => List[V]): Boolean = { + associative_lemma(list, f, g) because { + append(glist, flatMap(append(flist, flatMap(list, f)), g)) == append(append(glist, flatMap(flist, g)), flatMap(list, (x: T) => flatMap(f(x), g))) because + (glist match { + case Cons(ghead, gtail) => + associative_lemma_induct(list, flist, gtail, f, g) + case Nil() => flist match { + case Cons(fhead, ftail) => + associative_lemma_induct(list, ftail, g(fhead), f, g) + case Nil() => list match { + case Cons(head, tail) => associative_lemma_induct(tail, f(head), Nil(), f, g) + case Nil() => true + } + } + }) + } + }.holds + +} diff --git a/static/valid/FoldAssociative.html b/static/valid/FoldAssociative.html new file mode 100644 index 0000000000..81f7fba43f --- /dev/null +++ b/static/valid/FoldAssociative.html @@ -0,0 +1,113 @@ + + + +valid/FoldAssociative.scala + + +

                  FoldAssociative.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless._
+import stainless.lang._
+import stainless.proof._
+
+object FoldAssociative {
+
+  sealed abstract class List
+  case class Cons(head: Int, tail: List) extends List
+  case class Nil() extends List
+
+  sealed abstract class Option
+  case class Some(x: Int) extends Option
+  case class None() extends Option
+
+  def foldRight[A](list: List, state: A, f: (Int, A) => A): A = list match {
+    case Cons(head, tail) =>
+      val tailState = foldRight(tail, state, f)
+      f(head, tailState)
+    case Nil() => state
+  }
+
+  def take(list: List, count: Int): List = {
+    require(count >= 0)
+    list match {
+      case Cons(head, tail) if count > 0 => Cons(head, take(tail, count - 1))
+      case _ => Nil()
+    }
+  }
+
+  def drop(list: List, count: Int): List = {
+    require(count >= 0)
+    list match {
+      case Cons(head, tail) if count > 0 => drop(tail, count - 1)
+      case _ => list
+    }
+  }
+
+  def append(l1: List, l2: List): List = {
+    l1 match {
+      case Cons(head, tail) => Cons(head, append(tail, l2))
+      case Nil() => l2
+    }
+  }
+
+  def lemma_split(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    foldRight(list, 0, f) == foldRight(l1, foldRight(l2, 0, f), f)
+  }
+
+  def lemma_split_induct(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    lemma_split(list, x) because (list match {
+      case Cons(head, tail) if x > 0 =>
+        lemma_split_induct(tail, x - 1)
+      case _ => true
+    })
+  }.holds
+
+  def lemma_reassociative(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+
+    foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f)
+  }
+
+  def lemma_reassociative_induct(list: List, x: Int): Boolean = {
+    require(x >= 0)
+    val f = (x: Int, s: Int) => x + s
+    val l1 = take(list, x)
+    val l2 = drop(list, x)
+    lemma_reassociative(list, x) because (list match {
+      case Cons(head, tail) if x > 0 =>
+        lemma_reassociative_induct(tail, x - 1)
+      case _ => true
+    })
+  }.holds
+
+  def lemma_reassociative_presplit(l1: List, l2: List): Boolean = {
+    val f = (x: Int, s: Int) => x + s
+    val list = append(l1, l2)
+    foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f)
+  }
+
+  def lemma_reassociative_presplit_induct(l1: List, l2: List): Boolean = {
+    val f = (x: Int, s: Int) => x + s
+    val list = append(l1, l2)
+    lemma_reassociative_presplit(l1, l2) because (l1 match {
+      case Cons(head, tail) =>
+        lemma_reassociative_presplit_induct(tail, l2)
+      case Nil() => true
+    })
+  }.holds
+
+}
+
                  +

                  back

                  diff --git a/static/valid/FoldAssociative.scala b/static/valid/FoldAssociative.scala new file mode 100644 index 0000000000..4c80b4ad98 --- /dev/null +++ b/static/valid/FoldAssociative.scala @@ -0,0 +1,104 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless._ +import stainless.lang._ +import stainless.proof._ + +object FoldAssociative { + + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class Option + case class Some(x: Int) extends Option + case class None() extends Option + + def foldRight[A](list: List, state: A, f: (Int, A) => A): A = list match { + case Cons(head, tail) => + val tailState = foldRight(tail, state, f) + f(head, tailState) + case Nil() => state + } + + def take(list: List, count: Int): List = { + require(count >= 0) + list match { + case Cons(head, tail) if count > 0 => Cons(head, take(tail, count - 1)) + case _ => Nil() + } + } + + def drop(list: List, count: Int): List = { + require(count >= 0) + list match { + case Cons(head, tail) if count > 0 => drop(tail, count - 1) + case _ => list + } + } + + def append(l1: List, l2: List): List = { + l1 match { + case Cons(head, tail) => Cons(head, append(tail, l2)) + case Nil() => l2 + } + } + + def lemma_split(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + foldRight(list, 0, f) == foldRight(l1, foldRight(l2, 0, f), f) + } + + def lemma_split_induct(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + lemma_split(list, x) because (list match { + case Cons(head, tail) if x > 0 => + lemma_split_induct(tail, x - 1) + case _ => true + }) + }.holds + + def lemma_reassociative(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + + foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f) + } + + def lemma_reassociative_induct(list: List, x: Int): Boolean = { + require(x >= 0) + val f = (x: Int, s: Int) => x + s + val l1 = take(list, x) + val l2 = drop(list, x) + lemma_reassociative(list, x) because (list match { + case Cons(head, tail) if x > 0 => + lemma_reassociative_induct(tail, x - 1) + case _ => true + }) + }.holds + + def lemma_reassociative_presplit(l1: List, l2: List): Boolean = { + val f = (x: Int, s: Int) => x + s + val list = append(l1, l2) + foldRight(list, 0, f) == foldRight(l1, 0, f) + foldRight(l2, 0, f) + } + + def lemma_reassociative_presplit_induct(l1: List, l2: List): Boolean = { + val f = (x: Int, s: Int) => x + s + val list = append(l1, l2) + lemma_reassociative_presplit(l1, l2) because (l1 match { + case Cons(head, tail) => + lemma_reassociative_presplit_induct(tail, l2) + case Nil() => true + }) + }.holds + +} diff --git a/static/valid/Formulas.html b/static/valid/Formulas.html new file mode 100644 index 0000000000..236168fdcc --- /dev/null +++ b/static/valid/Formulas.html @@ -0,0 +1,61 @@ + + + +valid/Formulas.scala + + +

                  Formulas.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless._
+
+object Formulas {
+  abstract class Expr
+  case class And(lhs: Expr, rhs: Expr) extends Expr
+  case class Or(lhs: Expr, rhs: Expr) extends Expr
+  case class Implies(lhs: Expr, rhs: Expr) extends Expr
+  case class Not(e : Expr) extends Expr
+  case class BoolLiteral(i: BigInt) extends Expr
+
+  def exists(e: Expr, f: Expr => Boolean): Boolean = {
+    f(e) || (e match {
+      case And(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Or(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Implies(lhs, rhs) => exists(lhs, f) || exists(rhs, f)
+      case Not(e) => exists(e, f)
+      case _ => false
+    })
+  }
+
+  def existsImplies(e: Expr): Boolean = {
+    e.isInstanceOf[Implies] || (e match {
+      case And(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Or(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Implies(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs)
+      case Not(e) => existsImplies(e)
+      case _ => false
+    })
+  }
+
+  abstract class Value
+  case class BoolValue(b: Boolean) extends Value
+  case class IntValue(i: BigInt) extends Value
+  case object Error extends Value
+
+  def desugar(e: Expr): Expr = {
+    e match {
+      case And(lhs, rhs) => And(desugar(lhs), desugar(rhs))
+      case Or(lhs, rhs) => Or(desugar(lhs), desugar(rhs))
+      case Implies(lhs, rhs) =>
+        Or(Not(desugar(lhs)), desugar(rhs))
+      case Not(e) => Not(desugar(e))
+      case e => e
+    }
+  } ensuring { out =>
+    !existsImplies(out) &&
+    !exists(out, f => f.isInstanceOf[Implies])
+  }
+}
+
                  +

                  back

                  diff --git a/static/valid/Formulas.scala b/static/valid/Formulas.scala new file mode 100644 index 0000000000..a5a350d827 --- /dev/null +++ b/static/valid/Formulas.scala @@ -0,0 +1,52 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless._ + +object Formulas { + abstract class Expr + case class And(lhs: Expr, rhs: Expr) extends Expr + case class Or(lhs: Expr, rhs: Expr) extends Expr + case class Implies(lhs: Expr, rhs: Expr) extends Expr + case class Not(e : Expr) extends Expr + case class BoolLiteral(i: BigInt) extends Expr + + def exists(e: Expr, f: Expr => Boolean): Boolean = { + f(e) || (e match { + case And(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Or(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Implies(lhs, rhs) => exists(lhs, f) || exists(rhs, f) + case Not(e) => exists(e, f) + case _ => false + }) + } + + def existsImplies(e: Expr): Boolean = { + e.isInstanceOf[Implies] || (e match { + case And(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Or(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Implies(lhs, rhs) => existsImplies(lhs) || existsImplies(rhs) + case Not(e) => existsImplies(e) + case _ => false + }) + } + + abstract class Value + case class BoolValue(b: Boolean) extends Value + case class IntValue(i: BigInt) extends Value + case object Error extends Value + + def desugar(e: Expr): Expr = { + e match { + case And(lhs, rhs) => And(desugar(lhs), desugar(rhs)) + case Or(lhs, rhs) => Or(desugar(lhs), desugar(rhs)) + case Implies(lhs, rhs) => + Or(Not(desugar(lhs)), desugar(rhs)) + case Not(e) => Not(desugar(e)) + case e => e + } + } ensuring { out => + !existsImplies(out) && + !exists(out, f => f.isInstanceOf[Implies]) + } +} diff --git a/static/valid/FunctionCaching.html b/static/valid/FunctionCaching.html new file mode 100644 index 0000000000..e6bfc480c3 --- /dev/null +++ b/static/valid/FunctionCaching.html @@ -0,0 +1,49 @@ + + + +valid/FunctionCaching.scala + + +

                  FunctionCaching.scala [raw]


                  +
                  import stainless.lang._
+import stainless.collection._
+
+object FunctionCaching {
+
+  case class FunCache(var cached: Map[BigInt, BigInt])
+
+  def fun(x: BigInt)(implicit funCache: FunCache): BigInt = {
+    funCache.cached.get(x) match {
+      case None() => 
+        val res = 2*x + 42
+        funCache.cached = funCache.cached.updated(x, res)
+        res
+      case Some(cached) =>
+        cached
+    }
+  } ensuring(res => old(funCache).cached.get(x) match {
+    case None() => true
+    case Some(v) => v == res
+  })
+
+  def funProperlyCached(x: BigInt, trash: List[BigInt]): Boolean = {
+    implicit val cache = FunCache(Map())
+    val res1 = fun(x)
+    multipleCalls(trash, x)
+    val res2 = fun(x)
+    res1 == res2
+  } holds
+
+  def multipleCalls(args: List[BigInt], x: BigInt)(implicit funCache: FunCache): Unit = {
+    require(funCache.cached.get(x).forall(_ == 2*x + 42))
+    args match {
+      case Nil() => ()
+      case y::ys => 
+        fun(y)
+        multipleCalls(ys, x)
+    }
+  } ensuring(_ => funCache.cached.get(x).forall(_ == 2*x + 42))
+
+}
+
                  +

                  back

                  diff --git a/static/valid/FunctionCaching.scala b/static/valid/FunctionCaching.scala new file mode 100644 index 0000000000..5e0984b3aa --- /dev/null +++ b/static/valid/FunctionCaching.scala @@ -0,0 +1,40 @@ +import stainless.lang._ +import stainless.collection._ + +object FunctionCaching { + + case class FunCache(var cached: Map[BigInt, BigInt]) + + def fun(x: BigInt)(implicit funCache: FunCache): BigInt = { + funCache.cached.get(x) match { + case None() => + val res = 2*x + 42 + funCache.cached = funCache.cached.updated(x, res) + res + case Some(cached) => + cached + } + } ensuring(res => old(funCache).cached.get(x) match { + case None() => true + case Some(v) => v == res + }) + + def funProperlyCached(x: BigInt, trash: List[BigInt]): Boolean = { + implicit val cache = FunCache(Map()) + val res1 = fun(x) + multipleCalls(trash, x) + val res2 = fun(x) + res1 == res2 + } holds + + def multipleCalls(args: List[BigInt], x: BigInt)(implicit funCache: FunCache): Unit = { + require(funCache.cached.get(x).forall(_ == 2*x + 42)) + args match { + case Nil() => () + case y::ys => + fun(y) + multipleCalls(ys, x) + } + } ensuring(_ => funCache.cached.get(x).forall(_ == 2*x + 42)) + +} diff --git a/static/valid/GuessNumber.html b/static/valid/GuessNumber.html new file mode 100644 index 0000000000..4ace4ee467 --- /dev/null +++ b/static/valid/GuessNumber.html @@ -0,0 +1,51 @@ + + + +valid/GuessNumber.scala + + +

                  GuessNumber.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+
+object GuessNumber {
+
+  case class State(var seed: BigInt)
+
+  def between(a: Int, x: Int, b: Int): Boolean = a <= x && x <= b
+
+  def random(min: Int, max: Int)(implicit state: State): Int = {
+    require(min <= max)
+    state.seed += 1
+    assert(between(min, min, max))
+    choose((x: Int) => between(min, x, max))
+  }
+  
+  def main()(implicit state: State): Unit = {
+    val choice = random(0, 10)
+
+    var guess = random(0, 10)
+    var top = 10
+    var bot = 0
+
+    (while(bot < top) {
+      if(isGreater(guess, choice)) {
+        top = guess-1
+        guess = random(bot, top)
+      } else if(isSmaller(guess, choice)) {
+        bot = guess+1
+        guess = random(bot, top)
+      }
+    }) invariant(guess >= bot && guess <= top && bot >= 0 && top <= 10 && bot <= top && choice >= bot && choice <= top &&
+                 true)
+    val answer = bot
+    assert(answer == choice)
+  }
+
+  def isGreater(guess: Int, choice: Int): Boolean = guess > choice
+  def isSmaller(guess: Int, choice: Int): Boolean = guess < choice
+
+}
+
                  +

                  back

                  diff --git a/static/valid/GuessNumber.scala b/static/valid/GuessNumber.scala new file mode 100644 index 0000000000..c0ceca6696 --- /dev/null +++ b/static/valid/GuessNumber.scala @@ -0,0 +1,42 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ + +object GuessNumber { + + case class State(var seed: BigInt) + + def between(a: Int, x: Int, b: Int): Boolean = a <= x && x <= b + + def random(min: Int, max: Int)(implicit state: State): Int = { + require(min <= max) + state.seed += 1 + assert(between(min, min, max)) + choose((x: Int) => between(min, x, max)) + } + + def main()(implicit state: State): Unit = { + val choice = random(0, 10) + + var guess = random(0, 10) + var top = 10 + var bot = 0 + + (while(bot < top) { + if(isGreater(guess, choice)) { + top = guess-1 + guess = random(bot, top) + } else if(isSmaller(guess, choice)) { + bot = guess+1 + guess = random(bot, top) + } + }) invariant(guess >= bot && guess <= top && bot >= 0 && top <= 10 && bot <= top && choice >= bot && choice <= top && + true) + val answer = bot + assert(answer == choice) + } + + def isGreater(guess: Int, choice: Int): Boolean = guess > choice + def isSmaller(guess: Int, choice: Int): Boolean = guess < choice + +} diff --git a/static/valid/Heaps.html b/static/valid/Heaps.html new file mode 100644 index 0000000000..6e21ff6d9c --- /dev/null +++ b/static/valid/Heaps.html @@ -0,0 +1,156 @@ + + + +valid/Heaps.scala + + +

                  Heaps.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Heaps {
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Data type definitions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  case class Node(rank : BigInt, elem : Int, nodes : Heap)
+  
+  sealed abstract class Heap
+  private case class  Nodes(head : Node, tail : Heap) extends Heap
+  private case object Empty extends Heap
+  
+  sealed abstract class OptInt
+  case class Some(value : Int) extends OptInt
+  case object None extends OptInt
+  
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Abstraction functions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~*/
+  def heapContent(h : Heap) : Set[Int] = h match {
+    case Empty => Set.empty[Int]
+    case Nodes(n, ns) => nodeContent(n) ++ heapContent(ns)
+  }
+  
+  def nodeContent(n : Node) : Set[Int] = n match {
+    case Node(_, e, h) => Set(e) ++ heapContent(h)
+  }
+  
+  /*~~~~~~~~~~~~~~~~~~~~~~~~*/
+  /* Helper/local functions */
+  /*~~~~~~~~~~~~~~~~~~~~~~~~*/
+  private def reverse(h : Heap) : Heap = reverse0(h, Empty)
+  private def reverse0(h : Heap, acc : Heap) : Heap = (h match {
+    case Empty => acc
+    case Nodes(n, ns) => reverse0(ns, Nodes(n, acc))
+  }) ensuring(res => heapContent(res) == heapContent(h) ++ heapContent(acc))
+  
+  private def link(t1 : Node, t2 : Node) = (t1, t2) match {
+    case (Node(r, e1, ns1), Node(_, e2, ns2)) =>
+      if(e1 <= e2) {
+        Node(r + 1, e1, Nodes(t2, ns1))
+      } else {
+        Node(r + 1, e2, Nodes(t1, ns2))
+      }
+  }
+  
+  private def insertNode(t : Node, h : Heap) : Heap = (h match {
+    case Empty => Nodes(t, Empty)
+    case Nodes(t2, h2) =>
+      if(t.rank < t2.rank) {
+        Nodes(t, h)
+      } else {
+        insertNode(link(t, t2), h2)
+      }
+  }) ensuring(res => heapContent(res) == nodeContent(t) ++ heapContent(h))
+  
+  private def getMin(h : Heap) : (Node, Heap) = {
+    require(h != Empty)
+    h match {
+      case Nodes(t, Empty) => (t, Empty)
+      case Nodes(t, ts) =>
+        val (t0, ts0) = getMin(ts)
+        if(t.elem < t0.elem) {
+          (t, ts)
+        } else {
+          (t0, Nodes(t, ts0))
+        }
+    }
+  } ensuring(_ match {
+    case (n,h2) => nodeContent(n) ++ heapContent(h2) == heapContent(h)
+  })
+  
+  /*~~~~~~~~~~~~~~~~*/
+  /* Heap interface */
+  /*~~~~~~~~~~~~~~~~*/
+  def empty() : Heap = {
+    Empty
+  } ensuring(res => heapContent(res) == Set.empty[Int])
+  
+  def isEmpty(h : Heap) : Boolean = {
+    (h == Empty)
+  } ensuring(res => res == (heapContent(h) == Set.empty[Int]))
+  
+  def insert(e : Int, h : Heap) : Heap = {
+    insertNode(Node(0, e, Empty), h)
+  } ensuring(res => heapContent(res) == heapContent(h) ++ Set(e))
+  
+  def merge(h1 : Heap, h2 : Heap) : Heap = ((h1,h2) match {
+    case (_, Empty) => h1
+    case (Empty, _) => h2
+    case (Nodes(t1, ts1), Nodes(t2, ts2)) =>
+      if(t1.rank < t2.rank) {
+        Nodes(t1, merge(ts1, h2))
+      } else if(t2.rank < t1.rank) {
+        Nodes(t2, merge(h1, ts2))
+      } else {
+        insertNode(link(t1, t2), merge(ts1, ts2))
+      }
+  }) ensuring(res => heapContent(res) == heapContent(h1) ++ heapContent(h2))
+  
+  def findMin(h : Heap) : OptInt = (h match {
+    case Empty => None
+    case Nodes(Node(_, e, _), ns) =>
+      findMin(ns) match {
+        case None => Some(e)
+        case Some(e2) => Some(if(e < e2) e else e2)
+      }
+  }) ensuring(_ match {
+    case None => isEmpty(h)
+    case Some(v) => heapContent(h).contains(v)
+  })
+  
+  def deleteMin(h : Heap) : Heap = (h match {
+    case Empty => Empty
+    case ts : Nodes =>
+      val (Node(_, e, ns1), ns2) = getMin(ts)
+      merge(reverse(ns1), ns2)
+  }) ensuring(res => heapContent(res).subsetOf(heapContent(h)))
+  
+  def sanity0() : Boolean = {
+    val h0 : Heap = Empty
+    val h1 = insert(42, h0)
+    val h2 = insert(72, h1)
+    val h3 = insert(0, h2)
+    findMin(h0) == None &&
+    findMin(h1) == Some(42) &&
+    findMin(h2) == Some(42) &&
+    findMin(h3) == Some(0)
+  }.holds
+  
+  def sanity1() : Boolean = {
+    val h0 = insert(42, Empty)
+    val h1 = insert(0, Empty)
+    val h2 = merge(h0, h1)
+    findMin(h2) == Some(0)
+  }.holds
+  
+  def sanity3() : Boolean = {
+    val h0 = insert(42, insert(0, insert(12, Empty)))
+    val h1 = deleteMin(h0)
+    findMin(h1) == Some(12)
+  }.holds
+}
+
+
                  +

                  back

                  diff --git a/static/valid/Heaps.scala b/static/valid/Heaps.scala new file mode 100644 index 0000000000..b16418adb3 --- /dev/null +++ b/static/valid/Heaps.scala @@ -0,0 +1,147 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Heaps { + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Data type definitions */ + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + case class Node(rank : BigInt, elem : Int, nodes : Heap) + + sealed abstract class Heap + private case class Nodes(head : Node, tail : Heap) extends Heap + private case object Empty extends Heap + + sealed abstract class OptInt + case class Some(value : Int) extends OptInt + case object None extends OptInt + + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Abstraction functions */ + /*~~~~~~~~~~~~~~~~~~~~~~~*/ + def heapContent(h : Heap) : Set[Int] = h match { + case Empty => Set.empty[Int] + case Nodes(n, ns) => nodeContent(n) ++ heapContent(ns) + } + + def nodeContent(n : Node) : Set[Int] = n match { + case Node(_, e, h) => Set(e) ++ heapContent(h) + } + + /*~~~~~~~~~~~~~~~~~~~~~~~~*/ + /* Helper/local functions */ + /*~~~~~~~~~~~~~~~~~~~~~~~~*/ + private def reverse(h : Heap) : Heap = reverse0(h, Empty) + private def reverse0(h : Heap, acc : Heap) : Heap = (h match { + case Empty => acc + case Nodes(n, ns) => reverse0(ns, Nodes(n, acc)) + }) ensuring(res => heapContent(res) == heapContent(h) ++ heapContent(acc)) + + private def link(t1 : Node, t2 : Node) = (t1, t2) match { + case (Node(r, e1, ns1), Node(_, e2, ns2)) => + if(e1 <= e2) { + Node(r + 1, e1, Nodes(t2, ns1)) + } else { + Node(r + 1, e2, Nodes(t1, ns2)) + } + } + + private def insertNode(t : Node, h : Heap) : Heap = (h match { + case Empty => Nodes(t, Empty) + case Nodes(t2, h2) => + if(t.rank < t2.rank) { + Nodes(t, h) + } else { + insertNode(link(t, t2), h2) + } + }) ensuring(res => heapContent(res) == nodeContent(t) ++ heapContent(h)) + + private def getMin(h : Heap) : (Node, Heap) = { + require(h != Empty) + h match { + case Nodes(t, Empty) => (t, Empty) + case Nodes(t, ts) => + val (t0, ts0) = getMin(ts) + if(t.elem < t0.elem) { + (t, ts) + } else { + (t0, Nodes(t, ts0)) + } + } + } ensuring(_ match { + case (n,h2) => nodeContent(n) ++ heapContent(h2) == heapContent(h) + }) + + /*~~~~~~~~~~~~~~~~*/ + /* Heap interface */ + /*~~~~~~~~~~~~~~~~*/ + def empty() : Heap = { + Empty + } ensuring(res => heapContent(res) == Set.empty[Int]) + + def isEmpty(h : Heap) : Boolean = { + (h == Empty) + } ensuring(res => res == (heapContent(h) == Set.empty[Int])) + + def insert(e : Int, h : Heap) : Heap = { + insertNode(Node(0, e, Empty), h) + } ensuring(res => heapContent(res) == heapContent(h) ++ Set(e)) + + def merge(h1 : Heap, h2 : Heap) : Heap = ((h1,h2) match { + case (_, Empty) => h1 + case (Empty, _) => h2 + case (Nodes(t1, ts1), Nodes(t2, ts2)) => + if(t1.rank < t2.rank) { + Nodes(t1, merge(ts1, h2)) + } else if(t2.rank < t1.rank) { + Nodes(t2, merge(h1, ts2)) + } else { + insertNode(link(t1, t2), merge(ts1, ts2)) + } + }) ensuring(res => heapContent(res) == heapContent(h1) ++ heapContent(h2)) + + def findMin(h : Heap) : OptInt = (h match { + case Empty => None + case Nodes(Node(_, e, _), ns) => + findMin(ns) match { + case None => Some(e) + case Some(e2) => Some(if(e < e2) e else e2) + } + }) ensuring(_ match { + case None => isEmpty(h) + case Some(v) => heapContent(h).contains(v) + }) + + def deleteMin(h : Heap) : Heap = (h match { + case Empty => Empty + case ts : Nodes => + val (Node(_, e, ns1), ns2) = getMin(ts) + merge(reverse(ns1), ns2) + }) ensuring(res => heapContent(res).subsetOf(heapContent(h))) + + def sanity0() : Boolean = { + val h0 : Heap = Empty + val h1 = insert(42, h0) + val h2 = insert(72, h1) + val h3 = insert(0, h2) + findMin(h0) == None && + findMin(h1) == Some(42) && + findMin(h2) == Some(42) && + findMin(h3) == Some(0) + }.holds + + def sanity1() : Boolean = { + val h0 = insert(42, Empty) + val h1 = insert(0, Empty) + val h2 = merge(h0, h1) + findMin(h2) == Some(0) + }.holds + + def sanity3() : Boolean = { + val h0 = insert(42, insert(0, insert(12, Empty))) + val h1 = deleteMin(h0) + findMin(h1) == Some(12) + }.holds +} + diff --git a/static/valid/InsertionSort.html b/static/valid/InsertionSort.html new file mode 100644 index 0000000000..79cc64a131 --- /dev/null +++ b/static/valid/InsertionSort.html @@ -0,0 +1,78 @@ + + + +valid/InsertionSort.scala + + +

                  InsertionSort.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object InsertionSort {
+  sealed abstract class List
+  case class Cons(head:Int,tail:List) extends List
+  case class Nil() extends List
+
+  sealed abstract class OptInt
+  case class Some(value: Int) extends OptInt
+  case class None() extends OptInt
+
+  def size(l : List) : BigInt = (l match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def contents(l: List): Set[Int] = l match {
+    case Nil() => Set.empty
+    case Cons(x,xs) => contents(xs) ++ Set(x)
+  }
+
+  def min(l : List) : OptInt = l match {
+    case Nil() => None()
+    case Cons(x, xs) => min(xs) match {
+      case None() => Some(x)
+      case Some(x2) => if(x < x2) Some(x) else Some(x2)
+    }
+  }
+
+  def isSorted(l: List): Boolean = l match {
+    case Nil() => true
+    case Cons(x, Nil()) => true
+    case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys))
+  }
+
+  /* Inserting element 'e' into a sorted list 'l' produces a sorted list with
+   * the expected content and size */
+  def sortedIns(e: Int, l: List): List = {
+    require(isSorted(l))
+    l match {
+      case Nil() => Cons(e,Nil())
+      case Cons(x,xs) => if (x <= e) Cons(x,sortedIns(e, xs)) else Cons(e, l)
+    }
+  } ensuring(res => contents(res) == contents(l) ++ Set(e)
+                    && isSorted(res)
+                    && size(res) == size(l) + 1
+            )
+
+  /* Insertion sort yields a sorted list of same size and content as the input
+   * list */
+  def sort(l: List): List = (l match {
+    case Nil() => Nil()
+    case Cons(x,xs) => sortedIns(x, sort(xs))
+  }) ensuring(res => contents(res) == contents(l)
+                     && isSorted(res)
+                     && size(res) == size(l)
+             )
+
+  @ignore
+  def main(args: Array[String]): Unit = {
+    val ls: List = Cons(5, Cons(2, Cons(4, Cons(5, Cons(1, Cons(8,Nil()))))))
+
+    println(ls)
+    println(sort(ls))
+  }
+}
+
                  +

                  back

                  diff --git a/static/valid/InsertionSort.scala b/static/valid/InsertionSort.scala new file mode 100644 index 0000000000..0acab72588 --- /dev/null +++ b/static/valid/InsertionSort.scala @@ -0,0 +1,69 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object InsertionSort { + sealed abstract class List + case class Cons(head:Int,tail:List) extends List + case class Nil() extends List + + sealed abstract class OptInt + case class Some(value: Int) extends OptInt + case class None() extends OptInt + + def size(l : List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def contents(l: List): Set[Int] = l match { + case Nil() => Set.empty + case Cons(x,xs) => contents(xs) ++ Set(x) + } + + def min(l : List) : OptInt = l match { + case Nil() => None() + case Cons(x, xs) => min(xs) match { + case None() => Some(x) + case Some(x2) => if(x < x2) Some(x) else Some(x2) + } + } + + def isSorted(l: List): Boolean = l match { + case Nil() => true + case Cons(x, Nil()) => true + case Cons(x, Cons(y, ys)) => x <= y && isSorted(Cons(y, ys)) + } + + /* Inserting element 'e' into a sorted list 'l' produces a sorted list with + * the expected content and size */ + def sortedIns(e: Int, l: List): List = { + require(isSorted(l)) + l match { + case Nil() => Cons(e,Nil()) + case Cons(x,xs) => if (x <= e) Cons(x,sortedIns(e, xs)) else Cons(e, l) + } + } ensuring(res => contents(res) == contents(l) ++ Set(e) + && isSorted(res) + && size(res) == size(l) + 1 + ) + + /* Insertion sort yields a sorted list of same size and content as the input + * list */ + def sort(l: List): List = (l match { + case Nil() => Nil() + case Cons(x,xs) => sortedIns(x, sort(xs)) + }) ensuring(res => contents(res) == contents(l) + && isSorted(res) + && size(res) == size(l) + ) + + @ignore + def main(args: Array[String]): Unit = { + val ls: List = Cons(5, Cons(2, Cons(4, Cons(5, Cons(1, Cons(8,Nil())))))) + + println(ls) + println(sort(ls)) + } +} diff --git a/static/valid/ListOperations.html b/static/valid/ListOperations.html new file mode 100644 index 0000000000..b643302da6 --- /dev/null +++ b/static/valid/ListOperations.html @@ -0,0 +1,113 @@ + + + +valid/ListOperations.scala + + +

                  ListOperations.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object ListOperations {
+    sealed abstract class List
+    case class Cons(head: Int, tail: List) extends List
+    case class Nil() extends List
+
+    sealed abstract class IntPairList
+    case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList
+    case class IPNil() extends IntPairList
+
+    sealed abstract class IntPair
+    case class IP(fst: Int, snd: Int) extends IntPair
+
+    def size(l: List) : BigInt = (l match {
+        case Nil() => BigInt(0)
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def iplSize(l: IntPairList) : BigInt = (l match {
+      case IPNil() => BigInt(0)
+      case IPCons(_, xs) => 1 + iplSize(xs)
+    }) ensuring(_ >= 0)
+
+    def zip(l1: List, l2: List) : IntPairList = {
+      // try to comment this and see how pattern-matching becomes
+      // non-exhaustive and post-condition fails
+      require(size(l1) == size(l2))
+
+      l1 match {
+        case Nil() => IPNil()
+        case Cons(x, xs) => l2 match {
+          case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys))
+        }
+      }
+    } ensuring(iplSize(_) == size(l1))
+
+    def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0)
+    def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = {
+     require(acc >= 0)
+     l match {
+       case Nil() => acc
+       case Cons(_, xs) => sizeTailRecAcc(xs, acc+1)
+     }
+    } ensuring(res => res == size(l) + acc)
+
+    def sizesAreEquiv(l: List) : Boolean = {
+      size(l) == sizeTailRec(l)
+    }.holds
+
+    def content(l: List) : Set[Int] = l match {
+      case Nil() => Set.empty[Int]
+      case Cons(x, xs) => Set(x) ++ content(xs)
+    }
+
+    def sizeAndContent(l: List) : Boolean = {
+      size(l) == BigInt(0) || content(l) != Set.empty[Int]
+    }.holds
+    
+    def drunk(l : List) : List = (l match {
+      case Nil() => Nil()
+      case Cons(x,l1) => Cons(x,Cons(x,drunk(l1)))
+    }) ensuring (size(_) == 2 * size(l))
+
+    def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l))
+    def reverse0(l1: List, l2: List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => reverse0(xs, Cons(x, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    def append(l1 : List, l2 : List) : List = (l1 match {
+      case Nil() => l2
+      case Cons(x,xs) => Cons(x, append(xs, l2))
+    }) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds
+
+    @induct
+    def appendAssoc(xs : List, ys : List, zs : List) : Boolean =
+      (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds
+
+    @induct
+    def sizeAppend(l1 : List, l2 : List) : Boolean =
+      (size(append(l1, l2)) == size(l1) + size(l2)).holds
+
+    @induct
+    def concat(l1: List, l2: List) : List = 
+      concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2))
+
+    @induct
+    def concat0(l1: List, l2: List, l3: List) : List = (l1 match {
+      case Nil() => l2 match {
+        case Nil() => reverse(l3)
+        case Cons(y, ys) => {
+          concat0(Nil(), ys, Cons(y, l3))
+        }
+      }
+      case Cons(x, xs) => concat0(xs, l2, Cons(x, l3))
+    }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3))
+}
+
                  +

                  back

                  diff --git a/static/valid/ListOperations.scala b/static/valid/ListOperations.scala new file mode 100644 index 0000000000..3a4383cc9b --- /dev/null +++ b/static/valid/ListOperations.scala @@ -0,0 +1,104 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object ListOperations { + sealed abstract class List + case class Cons(head: Int, tail: List) extends List + case class Nil() extends List + + sealed abstract class IntPairList + case class IPCons(head: IntPair, tail: IntPairList) extends IntPairList + case class IPNil() extends IntPairList + + sealed abstract class IntPair + case class IP(fst: Int, snd: Int) extends IntPair + + def size(l: List) : BigInt = (l match { + case Nil() => BigInt(0) + case Cons(_, t) => 1 + size(t) + }) ensuring(res => res >= 0) + + def iplSize(l: IntPairList) : BigInt = (l match { + case IPNil() => BigInt(0) + case IPCons(_, xs) => 1 + iplSize(xs) + }) ensuring(_ >= 0) + + def zip(l1: List, l2: List) : IntPairList = { + // try to comment this and see how pattern-matching becomes + // non-exhaustive and post-condition fails + require(size(l1) == size(l2)) + + l1 match { + case Nil() => IPNil() + case Cons(x, xs) => l2 match { + case Cons(y, ys) => IPCons(IP(x, y), zip(xs, ys)) + } + } + } ensuring(iplSize(_) == size(l1)) + + def sizeTailRec(l: List) : BigInt = sizeTailRecAcc(l, 0) + def sizeTailRecAcc(l: List, acc: BigInt) : BigInt = { + require(acc >= 0) + l match { + case Nil() => acc + case Cons(_, xs) => sizeTailRecAcc(xs, acc+1) + } + } ensuring(res => res == size(l) + acc) + + def sizesAreEquiv(l: List) : Boolean = { + size(l) == sizeTailRec(l) + }.holds + + def content(l: List) : Set[Int] = l match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def sizeAndContent(l: List) : Boolean = { + size(l) == BigInt(0) || content(l) != Set.empty[Int] + }.holds + + def drunk(l : List) : List = (l match { + case Nil() => Nil() + case Cons(x,l1) => Cons(x,Cons(x,drunk(l1))) + }) ensuring (size(_) == 2 * size(l)) + + def reverse(l: List) : List = reverse0(l, Nil()) ensuring(content(_) == content(l)) + def reverse0(l1: List, l2: List) : List = (l1 match { + case Nil() => l2 + case Cons(x, xs) => reverse0(xs, Cons(x, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + def append(l1 : List, l2 : List) : List = (l1 match { + case Nil() => l2 + case Cons(x,xs) => Cons(x, append(xs, l2)) + }) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def nilAppend(l : List) : Boolean = (append(l, Nil()) == l).holds + + @induct + def appendAssoc(xs : List, ys : List, zs : List) : Boolean = + (append(append(xs, ys), zs) == append(xs, append(ys, zs))).holds + + @induct + def sizeAppend(l1 : List, l2 : List) : Boolean = + (size(append(l1, l2)) == size(l1) + size(l2)).holds + + @induct + def concat(l1: List, l2: List) : List = + concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2)) + + @induct + def concat0(l1: List, l2: List, l3: List) : List = (l1 match { + case Nil() => l2 match { + case Nil() => reverse(l3) + case Cons(y, ys) => { + concat0(Nil(), ys, Cons(y, l3)) + } + } + case Cons(x, xs) => concat0(xs, l2, Cons(x, l3)) + }) ensuring(content(_) == content(l1) ++ content(l2) ++ content(l3)) +} diff --git a/static/valid/Mean.html b/static/valid/Mean.html new file mode 100644 index 0000000000..7aeb602c83 --- /dev/null +++ b/static/valid/Mean.html @@ -0,0 +1,22 @@ + + + +valid/Mean.scala + + +

                  Mean.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object Mean {
+
+  def mean(x: Int, y: Int): Int = {
+    require(x <= y && x >= 0 && y >= 0)
+    x + (y - x)/2
+  } ensuring(m => m >= x && m <= y)
+
+}
+
                  +

                  back

                  diff --git a/static/valid/Mean.scala b/static/valid/Mean.scala new file mode 100644 index 0000000000..ec1108f4e5 --- /dev/null +++ b/static/valid/Mean.scala @@ -0,0 +1,13 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object Mean { + + def mean(x: Int, y: Int): Int = { + require(x <= y && x >= 0 && y >= 0) + x + (y - x)/2 + } ensuring(m => m >= x && m <= y) + +} diff --git a/static/valid/MergeSort.html b/static/valid/MergeSort.html new file mode 100644 index 0000000000..2e3c792880 --- /dev/null +++ b/static/valid/MergeSort.html @@ -0,0 +1,136 @@ + + + +valid/MergeSort.scala + + +

                  MergeSort.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object MergeSort {
+  // Data types
+  sealed abstract class List
+  case class Cons(head : Int, tail : List) extends List
+  case class Nil() extends List
+
+  sealed abstract class LList
+  case class LCons(head : List, tail : LList) extends LList
+  case class LNil() extends LList
+
+  def content(list : List) : Set[Int] = list match {
+    case Nil() => Set.empty[Int]
+    case Cons(x, xs) => Set(x) ++ content(xs)
+  }
+
+  def lContent(llist : LList) : Set[Int] = llist match {
+    case LNil() => Set.empty[Int]
+    case LCons(x, xs) => content(x) ++ lContent(xs)
+  }
+
+  def size(list : List) : BigInt = (list match {
+    case Nil() => BigInt(0)
+    case Cons(_, xs) => 1 + size(xs)
+  }) ensuring(_ >= 0)
+
+  def isSorted(list : List) : Boolean = list match {
+    case Nil() => true
+    case Cons(_, Nil()) => true
+    case Cons(x1, Cons(x2, _)) if(x1 > x2) => false
+    case Cons(_, xs) => isSorted(xs)
+  }
+
+  def lIsSorted(llist : LList) : Boolean = llist match {
+    case LNil() => true
+    case LCons(x, xs) => isSorted(x) && lIsSorted(xs)
+  }
+
+  def abs(i : BigInt) : BigInt = {
+    if(i < 0) -i else i
+  } ensuring(_ >= 0)
+
+  def mergeSpec(list1 : List, list2 : List, res : List) : Boolean = {
+    isSorted(res) && content(res) == content(list1) ++ content(list2)
+  }
+
+  def mergeFast(list1 : List, list2 : List) : List = {
+    require(isSorted(list1) && isSorted(list2))
+
+    (list1, list2) match {
+      case (_, Nil()) => list1
+      case (Nil(), _) => list2
+      case (Cons(x, xs), Cons(y, ys)) =>
+        if(x <= y) {
+          Cons(x, mergeFast(xs, list2)) 
+        } else {
+          Cons(y, mergeFast(list1, ys))
+        }
+    }
+  } ensuring(res => mergeSpec(list1, list2, res))
+
+  def splitSpec(list : List, res : (List,List)) : Boolean = {
+    val s1 = size(res._1)
+    val s2 = size(res._2)
+    abs(s1 - s2) <= 1 && s1 + s2 == size(list) &&
+    content(res._1) ++ content(res._2) == content(list) 
+  }
+
+  def split(list : List) : (List,List) = (list match {
+    case Nil() => (Nil(), Nil())
+    case Cons(x, Nil()) => (Cons(x, Nil()), Nil())
+    case Cons(x1, Cons(x2, xs)) =>
+      val (s1,s2) = split(xs)
+      (Cons(x1, s1), Cons(x2, s2))
+  }) ensuring(res => splitSpec(list, res))
+
+  def sortSpec(in : List, out : List) : Boolean = {
+    content(out) == content(in) && isSorted(out)
+  }
+
+  // Not really quicksort, neither mergesort.
+  // Note: the `s` argument is just a witness for termination (always decreases),
+  // and not needed for functionality. Any decent optimizer will remove it ;-)
+  def weirdSort(s: BigInt, in : List) : List = {
+    require(s == size(in))
+    in match {
+      case Nil() => Nil()
+      case Cons(x, Nil()) => Cons(x, Nil())
+      case _ =>
+        val (s1,s2) = split(in)
+        mergeFast(weirdSort(size(s1), s1), weirdSort(size(s2), s2))
+    }
+  } ensuring(res => sortSpec(in, res))
+
+  def toLList(list : List) : LList = (list match {
+    case Nil() => LNil()
+    case Cons(x, xs) => LCons(Cons(x, Nil()), toLList(xs))
+  }) ensuring(res => lContent(res) == content(list) && lIsSorted(res))
+
+  def mergeMap(llist : LList) : LList = {
+    require(lIsSorted(llist))
+
+    llist match {
+      case LNil() => LNil()
+      case o @ LCons(x, LNil()) => o
+      case LCons(x, LCons(y, ys)) => LCons(mergeFast(x, y), mergeMap(ys))
+    }
+  } ensuring(res => lContent(res) == lContent(llist) && lIsSorted(res))
+
+  def mergeReduce(llist : LList) : List = {
+    require(lIsSorted(llist))
+
+    llist match {
+      case LNil() => Nil()
+      case LCons(x, LNil()) => x
+      case _ => mergeReduce(mergeMap(llist))
+    }
+  } ensuring(res => content(res) == lContent(llist) && isSorted(res))
+
+  def mergeSort(in : List) : List = {
+    mergeReduce(toLList(in))
+  } ensuring(res => sortSpec(in, res))
+}
+
                  +

                  back

                  diff --git a/static/valid/MergeSort.scala b/static/valid/MergeSort.scala new file mode 100644 index 0000000000..b4cd205689 --- /dev/null +++ b/static/valid/MergeSort.scala @@ -0,0 +1,127 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object MergeSort { + // Data types + sealed abstract class List + case class Cons(head : Int, tail : List) extends List + case class Nil() extends List + + sealed abstract class LList + case class LCons(head : List, tail : LList) extends LList + case class LNil() extends LList + + def content(list : List) : Set[Int] = list match { + case Nil() => Set.empty[Int] + case Cons(x, xs) => Set(x) ++ content(xs) + } + + def lContent(llist : LList) : Set[Int] = llist match { + case LNil() => Set.empty[Int] + case LCons(x, xs) => content(x) ++ lContent(xs) + } + + def size(list : List) : BigInt = (list match { + case Nil() => BigInt(0) + case Cons(_, xs) => 1 + size(xs) + }) ensuring(_ >= 0) + + def isSorted(list : List) : Boolean = list match { + case Nil() => true + case Cons(_, Nil()) => true + case Cons(x1, Cons(x2, _)) if(x1 > x2) => false + case Cons(_, xs) => isSorted(xs) + } + + def lIsSorted(llist : LList) : Boolean = llist match { + case LNil() => true + case LCons(x, xs) => isSorted(x) && lIsSorted(xs) + } + + def abs(i : BigInt) : BigInt = { + if(i < 0) -i else i + } ensuring(_ >= 0) + + def mergeSpec(list1 : List, list2 : List, res : List) : Boolean = { + isSorted(res) && content(res) == content(list1) ++ content(list2) + } + + def mergeFast(list1 : List, list2 : List) : List = { + require(isSorted(list1) && isSorted(list2)) + + (list1, list2) match { + case (_, Nil()) => list1 + case (Nil(), _) => list2 + case (Cons(x, xs), Cons(y, ys)) => + if(x <= y) { + Cons(x, mergeFast(xs, list2)) + } else { + Cons(y, mergeFast(list1, ys)) + } + } + } ensuring(res => mergeSpec(list1, list2, res)) + + def splitSpec(list : List, res : (List,List)) : Boolean = { + val s1 = size(res._1) + val s2 = size(res._2) + abs(s1 - s2) <= 1 && s1 + s2 == size(list) && + content(res._1) ++ content(res._2) == content(list) + } + + def split(list : List) : (List,List) = (list match { + case Nil() => (Nil(), Nil()) + case Cons(x, Nil()) => (Cons(x, Nil()), Nil()) + case Cons(x1, Cons(x2, xs)) => + val (s1,s2) = split(xs) + (Cons(x1, s1), Cons(x2, s2)) + }) ensuring(res => splitSpec(list, res)) + + def sortSpec(in : List, out : List) : Boolean = { + content(out) == content(in) && isSorted(out) + } + + // Not really quicksort, neither mergesort. + // Note: the `s` argument is just a witness for termination (always decreases), + // and not needed for functionality. Any decent optimizer will remove it ;-) + def weirdSort(s: BigInt, in : List) : List = { + require(s == size(in)) + in match { + case Nil() => Nil() + case Cons(x, Nil()) => Cons(x, Nil()) + case _ => + val (s1,s2) = split(in) + mergeFast(weirdSort(size(s1), s1), weirdSort(size(s2), s2)) + } + } ensuring(res => sortSpec(in, res)) + + def toLList(list : List) : LList = (list match { + case Nil() => LNil() + case Cons(x, xs) => LCons(Cons(x, Nil()), toLList(xs)) + }) ensuring(res => lContent(res) == content(list) && lIsSorted(res)) + + def mergeMap(llist : LList) : LList = { + require(lIsSorted(llist)) + + llist match { + case LNil() => LNil() + case o @ LCons(x, LNil()) => o + case LCons(x, LCons(y, ys)) => LCons(mergeFast(x, y), mergeMap(ys)) + } + } ensuring(res => lContent(res) == lContent(llist) && lIsSorted(res)) + + def mergeReduce(llist : LList) : List = { + require(lIsSorted(llist)) + + llist match { + case LNil() => Nil() + case LCons(x, LNil()) => x + case _ => mergeReduce(mergeMap(llist)) + } + } ensuring(res => content(res) == lContent(llist) && isSorted(res)) + + def mergeSort(in : List) : List = { + mergeReduce(toLList(in)) + } ensuring(res => sortSpec(in, res)) +} diff --git a/static/valid/PropositionalLogic.html b/static/valid/PropositionalLogic.html new file mode 100644 index 0000000000..265a202cc6 --- /dev/null +++ b/static/valid/PropositionalLogic.html @@ -0,0 +1,85 @@ + + + +valid/PropositionalLogic.scala + + +

                  PropositionalLogic.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.lang._
+import stainless.annotation._
+
+object PropositionalLogic { 
+
+  sealed abstract class Formula
+  case class And(lhs: Formula, rhs: Formula) extends Formula
+  case class Or(lhs: Formula, rhs: Formula) extends Formula
+  case class Implies(lhs: Formula, rhs: Formula) extends Formula
+  case class Not(f: Formula) extends Formula
+  case class Literal(id: Int) extends Formula
+
+  def simplify(f: Formula): Formula = (f match {
+    case And(lhs, rhs) => And(simplify(lhs), simplify(rhs))
+    case Or(lhs, rhs) => Or(simplify(lhs), simplify(rhs))
+    case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs))
+    case Not(f) => Not(simplify(f))
+    case Literal(_) => f
+  }) ensuring(isSimplified(_))
+
+  def isSimplified(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs)
+    case Implies(_,_) => false
+    case Not(f) => isSimplified(f)
+    case Literal(_) => true
+  }
+
+  def nnf(formula: Formula): Formula = (formula match {
+    case And(lhs, rhs) => And(nnf(lhs), nnf(rhs))
+    case Or(lhs, rhs) => Or(nnf(lhs), nnf(rhs))
+    case Implies(lhs, rhs) => Implies(nnf(lhs), nnf(rhs))
+    case Not(And(lhs, rhs)) => Or(nnf(Not(lhs)), nnf(Not(rhs)))
+    case Not(Or(lhs, rhs)) => And(nnf(Not(lhs)), nnf(Not(rhs)))
+    case Not(Implies(lhs, rhs)) => And(nnf(lhs), nnf(Not(rhs)))
+    case Not(Not(f)) => nnf(f)
+    case Not(Literal(_)) => formula
+    case Literal(_) => formula
+  }) ensuring(isNNF(_))
+
+  def isNNF(f: Formula): Boolean = f match {
+    case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs)
+    case Not(Literal(_)) => true
+    case Not(_) => false
+    case Literal(_) => true
+  }
+
+  def vars(f: Formula): Set[Int] = {
+    require(isNNF(f))
+    f match {
+      case And(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Or(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Implies(lhs, rhs) => vars(lhs) ++ vars(rhs)
+      case Not(Literal(i)) => Set[Int](i)
+      case Literal(i) => Set[Int](i)
+    }
+  }
+
+  def fv(f : Formula) = { vars(nnf(f)) }
+
+  @induct
+  def nnfIsStable(f: Formula) : Boolean = {
+    require(isNNF(f))
+    nnf(f) == f
+  }.holds
+  
+  @induct
+  def simplifyIsStable(f: Formula) : Boolean = {
+    require(isSimplified(f))
+    simplify(f) == f
+  }.holds
+}
+
                  +

                  back

                  diff --git a/static/valid/PropositionalLogic.scala b/static/valid/PropositionalLogic.scala new file mode 100644 index 0000000000..d1a4a4a460 --- /dev/null +++ b/static/valid/PropositionalLogic.scala @@ -0,0 +1,76 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.lang._ +import stainless.annotation._ + +object PropositionalLogic { + + sealed abstract class Formula + case class And(lhs: Formula, rhs: Formula) extends Formula + case class Or(lhs: Formula, rhs: Formula) extends Formula + case class Implies(lhs: Formula, rhs: Formula) extends Formula + case class Not(f: Formula) extends Formula + case class Literal(id: Int) extends Formula + + def simplify(f: Formula): Formula = (f match { + case And(lhs, rhs) => And(simplify(lhs), simplify(rhs)) + case Or(lhs, rhs) => Or(simplify(lhs), simplify(rhs)) + case Implies(lhs, rhs) => Or(Not(simplify(lhs)), simplify(rhs)) + case Not(f) => Not(simplify(f)) + case Literal(_) => f + }) ensuring(isSimplified(_)) + + def isSimplified(f: Formula): Boolean = f match { + case And(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Or(lhs, rhs) => isSimplified(lhs) && isSimplified(rhs) + case Implies(_,_) => false + case Not(f) => isSimplified(f) + case Literal(_) => true + } + + def nnf(formula: Formula): Formula = (formula match { + case And(lhs, rhs) => And(nnf(lhs), nnf(rhs)) + case Or(lhs, rhs) => Or(nnf(lhs), nnf(rhs)) + case Implies(lhs, rhs) => Implies(nnf(lhs), nnf(rhs)) + case Not(And(lhs, rhs)) => Or(nnf(Not(lhs)), nnf(Not(rhs))) + case Not(Or(lhs, rhs)) => And(nnf(Not(lhs)), nnf(Not(rhs))) + case Not(Implies(lhs, rhs)) => And(nnf(lhs), nnf(Not(rhs))) + case Not(Not(f)) => nnf(f) + case Not(Literal(_)) => formula + case Literal(_) => formula + }) ensuring(isNNF(_)) + + def isNNF(f: Formula): Boolean = f match { + case And(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Or(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Implies(lhs, rhs) => isNNF(lhs) && isNNF(rhs) + case Not(Literal(_)) => true + case Not(_) => false + case Literal(_) => true + } + + def vars(f: Formula): Set[Int] = { + require(isNNF(f)) + f match { + case And(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Or(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Implies(lhs, rhs) => vars(lhs) ++ vars(rhs) + case Not(Literal(i)) => Set[Int](i) + case Literal(i) => Set[Int](i) + } + } + + def fv(f : Formula) = { vars(nnf(f)) } + + @induct + def nnfIsStable(f: Formula) : Boolean = { + require(isNNF(f)) + nnf(f) == f + }.holds + + @induct + def simplifyIsStable(f: Formula) : Boolean = { + require(isSimplified(f)) + simplify(f) == f + }.holds +} diff --git a/static/valid/QuickSort.html b/static/valid/QuickSort.html new file mode 100644 index 0000000000..5fb43443e8 --- /dev/null +++ b/static/valid/QuickSort.html @@ -0,0 +1,60 @@ + + + +valid/QuickSort.scala + + +

                  QuickSort.scala [raw]


                  +
                  import stainless.proof._
+import stainless.lang._
+import stainless.collection._
+
+object QuickSort {
+
+  def isSorted(list: List[BigInt]): Boolean = {
+    list match {
+      case Cons(x, xs @ Cons(y, _)) => x <= y && isSorted(xs)
+      case _ => true
+    }
+  }
+
+  def appendSorted(l1: List[BigInt], l2: List[BigInt]): List[BigInt] = {
+    require(isSorted(l1) && isSorted(l2) && (l1.isEmpty || l2.isEmpty || l1.last <= l2.head))
+    l1 match {
+      case Nil() => l2
+      case Cons(x, xs) => Cons(x, appendSorted(xs, l2))
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == l1.content ++ l2.content
+  }
+
+  def quickSort(list: List[BigInt]): List[BigInt] = {
+    decreases(list.size, BigInt(0))
+    list match {
+      case Nil() => Nil[BigInt]()
+      case Cons(x, xs) => par(x, Nil(), Nil(), xs)
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == list.content
+  }
+
+  def par(x: BigInt, l: List[BigInt], r: List[BigInt], ls: List[BigInt]): List[BigInt] = {
+    require(
+      forall((a: BigInt) => l.contains(a) ==> a <= x) &&
+      forall((a: BigInt) => r.contains(a) ==> x < a)
+    )
+    decreases(l.size + r.size + ls.size, ls.size + 1)
+
+    ls match {
+      case Nil() => appendSorted(quickSort(l), Cons(x, quickSort(r)))
+      case Cons(x2, xs2) => if (x2 <= x) par(x, Cons(x2, l), r, xs2) else par(x, l, Cons(x2, r), xs2)
+    }
+  } ensuring { res =>
+    isSorted(res) &&
+    res.content == l.content ++ r.content ++ ls.content + x
+  }
+}
+
                  +

                  back

                  diff --git a/static/valid/QuickSort.scala b/static/valid/QuickSort.scala new file mode 100644 index 0000000000..9cd49876e8 --- /dev/null +++ b/static/valid/QuickSort.scala @@ -0,0 +1,51 @@ +import stainless.proof._ +import stainless.lang._ +import stainless.collection._ + +object QuickSort { + + def isSorted(list: List[BigInt]): Boolean = { + list match { + case Cons(x, xs @ Cons(y, _)) => x <= y && isSorted(xs) + case _ => true + } + } + + def appendSorted(l1: List[BigInt], l2: List[BigInt]): List[BigInt] = { + require(isSorted(l1) && isSorted(l2) && (l1.isEmpty || l2.isEmpty || l1.last <= l2.head)) + l1 match { + case Nil() => l2 + case Cons(x, xs) => Cons(x, appendSorted(xs, l2)) + } + } ensuring { res => + isSorted(res) && + res.content == l1.content ++ l2.content + } + + def quickSort(list: List[BigInt]): List[BigInt] = { + decreases(list.size, BigInt(0)) + list match { + case Nil() => Nil[BigInt]() + case Cons(x, xs) => par(x, Nil(), Nil(), xs) + } + } ensuring { res => + isSorted(res) && + res.content == list.content + } + + def par(x: BigInt, l: List[BigInt], r: List[BigInt], ls: List[BigInt]): List[BigInt] = { + require( + forall((a: BigInt) => l.contains(a) ==> a <= x) && + forall((a: BigInt) => r.contains(a) ==> x < a) + ) + decreases(l.size + r.size + ls.size, ls.size + 1) + + ls match { + case Nil() => appendSorted(quickSort(l), Cons(x, quickSort(r))) + case Cons(x2, xs2) => if (x2 <= x) par(x, Cons(x2, l), r, xs2) else par(x, l, Cons(x2, r), xs2) + } + } ensuring { res => + isSorted(res) && + res.content == l.content ++ r.content ++ ls.content + x + } +} diff --git a/static/valid/RedBlackTree.html b/static/valid/RedBlackTree.html new file mode 100644 index 0000000000..308c69ad22 --- /dev/null +++ b/static/valid/RedBlackTree.html @@ -0,0 +1,108 @@ + + + +valid/RedBlackTree.scala + + +

                  RedBlackTree.scala [raw]


                  +
                  /* Copyright 2009-2016 EPFL, Lausanne */
+
+import stainless.annotation._
+import stainless.lang._
+
+object RedBlackTree { 
+  sealed abstract class Color
+  case class Red() extends Color
+  case class Black() extends Color
+ 
+  sealed abstract class Tree
+  case class Empty() extends Tree
+  case class Node(color: Color, left: Tree, value: BigInt, right: Tree) extends Tree
+
+  sealed abstract class OptionInt
+  case class Some(v : BigInt) extends OptionInt
+  case class None() extends OptionInt
+
+  def content(t: Tree) : Set[BigInt] = t match {
+    case Empty() => Set.empty
+    case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r)
+  }
+
+  def size(t: Tree) : BigInt = (t match {
+    case Empty() => BigInt(0)
+    case Node(_, l, v, r) => size(l) + 1 + size(r)
+  }) ensuring(_ >= 0)
+
+  /* We consider leaves to be black by definition */
+  def isBlack(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(),_,_,_) => true
+    case _ => false
+  }
+
+  def redNodesHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+    case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def redDescHaveBlackChildren(t: Tree) : Boolean = t match {
+    case Empty() => true
+    case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r)
+  }
+
+  def blackBalanced(t : Tree) : Boolean = t match {
+    case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r)
+    case Empty() => true
+  }
+
+  def blackHeight(t : Tree) : BigInt = t match {
+    case Empty() => 1
+    case Node(Black(), l, _, _) => blackHeight(l) + 1
+    case Node(Red(), l, _, _) => blackHeight(l)
+  }
+
+  // <<insert element x into the tree t>>
+  def ins(x: BigInt, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    t match {
+      case Empty() => Node(Red(),Empty(),x,Empty())
+      case Node(c,a,y,b) =>
+        if      (x < y)  balance(c, ins(x, a), y, b)
+        else if (x == y) Node(c,a,y,b)
+        else             balance(c,a,y,ins(x, b))
+    }
+  } ensuring (res => content(res) == content(t) ++ Set(x) 
+                   && size(t) <= size(res) && size(res) <= size(t) + 1
+                   && redDescHaveBlackChildren(res)
+                   && blackBalanced(res))
+
+  def makeBlack(n: Tree): Tree = {
+    require(redDescHaveBlackChildren(n) && blackBalanced(n))
+    n match {
+      case Node(Red(),l,v,r) => Node(Black(),l,v,r)
+      case _ => n
+    }
+  } ensuring(res => redNodesHaveBlackChildren(res) && blackBalanced(res))
+
+  def add(x: BigInt, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t) && blackBalanced(t))
+    makeBlack(ins(x, t))
+  } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res) && blackBalanced(res))
+
+  def balance(c: Color, a: Tree, x: BigInt, b: Tree): Tree = {
+    Node(c,a,x,b) match {
+      case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => 
+        Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d))
+      case Node(c,a,xV,b) => Node(c,a,xV,b)
+    }
+  } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res))
+}
+
                  +

                  back

                  diff --git a/static/valid/RedBlackTree.scala b/static/valid/RedBlackTree.scala new file mode 100644 index 0000000000..94577704d6 --- /dev/null +++ b/static/valid/RedBlackTree.scala @@ -0,0 +1,99 @@ +/* Copyright 2009-2016 EPFL, Lausanne */ + +import stainless.annotation._ +import stainless.lang._ + +object RedBlackTree { + sealed abstract class Color + case class Red() extends Color + case class Black() extends Color + + sealed abstract class Tree + case class Empty() extends Tree + case class Node(color: Color, left: Tree, value: BigInt, right: Tree) extends Tree + + sealed abstract class OptionInt + case class Some(v : BigInt) extends OptionInt + case class None() extends OptionInt + + def content(t: Tree) : Set[BigInt] = t match { + case Empty() => Set.empty + case Node(_, l, v, r) => content(l) ++ Set(v) ++ content(r) + } + + def size(t: Tree) : BigInt = (t match { + case Empty() => BigInt(0) + case Node(_, l, v, r) => size(l) + 1 + size(r) + }) ensuring(_ >= 0) + + /* We consider leaves to be black by definition */ + def isBlack(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(),_,_,_) => true + case _ => false + } + + def redNodesHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(Black(), l, _, r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + case Node(Red(), l, _, r) => isBlack(l) && isBlack(r) && redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def redDescHaveBlackChildren(t: Tree) : Boolean = t match { + case Empty() => true + case Node(_,l,_,r) => redNodesHaveBlackChildren(l) && redNodesHaveBlackChildren(r) + } + + def blackBalanced(t : Tree) : Boolean = t match { + case Node(_,l,_,r) => blackBalanced(l) && blackBalanced(r) && blackHeight(l) == blackHeight(r) + case Empty() => true + } + + def blackHeight(t : Tree) : BigInt = t match { + case Empty() => 1 + case Node(Black(), l, _, _) => blackHeight(l) + 1 + case Node(Red(), l, _, _) => blackHeight(l) + } + + // <> + def ins(x: BigInt, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + t match { + case Empty() => Node(Red(),Empty(),x,Empty()) + case Node(c,a,y,b) => + if (x < y) balance(c, ins(x, a), y, b) + else if (x == y) Node(c,a,y,b) + else balance(c,a,y,ins(x, b)) + } + } ensuring (res => content(res) == content(t) ++ Set(x) + && size(t) <= size(res) && size(res) <= size(t) + 1 + && redDescHaveBlackChildren(res) + && blackBalanced(res)) + + def makeBlack(n: Tree): Tree = { + require(redDescHaveBlackChildren(n) && blackBalanced(n)) + n match { + case Node(Red(),l,v,r) => Node(Black(),l,v,r) + case _ => n + } + } ensuring(res => redNodesHaveBlackChildren(res) && blackBalanced(res)) + + def add(x: BigInt, t: Tree): Tree = { + require(redNodesHaveBlackChildren(t) && blackBalanced(t)) + makeBlack(ins(x, t)) + } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(res) && blackBalanced(res)) + + def balance(c: Color, a: Tree, x: BigInt, b: Tree): Tree = { + Node(c,a,x,b) match { + case Node(Black(),Node(Red(),Node(Red(),a,xV,b),yV,c),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),Node(Red(),a,xV,Node(Red(),b,yV,c)),zV,d) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),Node(Red(),b,yV,c),zV,d)) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(Black(),a,xV,Node(Red(),b,yV,Node(Red(),c,zV,d))) => + Node(Red(),Node(Black(),a,xV,b),yV,Node(Black(),c,zV,d)) + case Node(c,a,xV,b) => Node(c,a,xV,b) + } + } ensuring (res => content(res) == content(Node(c,a,x,b)))// && redDescHaveBlackChildren(res)) +} diff --git a/static/valid/StableSorter.html b/static/valid/StableSorter.html new file mode 100644 index 0000000000..bc8e1d335a --- /dev/null +++ b/static/valid/StableSorter.html @@ -0,0 +1,124 @@ + + + +valid/StableSorter.scala + + +

                  StableSorter.scala [raw]


                  +
                  import stainless.annotation._
+import stainless.collection._
+import stainless.lang._
+import stainless.proof._
+
+object StableSorter {
+
+  // Inserting into a stable list adds to the content and increases the length
+  def insert[T](t: T, l: List[T], key: T => BigInt): List[T] = {
+    l match {
+      case Nil() => t :: l
+      case Cons(hd, tl) if key(t) <= key(hd) => t :: l
+      case Cons(hd, tl) => hd :: insert(t, tl, key)
+    }
+  } ensuring { res => res.content == Set(t) ++ l.content && res.length == 1 + l.length }
+
+  // Sorting a list preserves the content and preserves the length
+  def sort[T](l: List[T], key: T => BigInt): List[T] = { l match {
+    case Nil() => l
+    case Cons(hd, tl) => {
+      val tlSorted = sort(tl, key)
+      insert(hd, tlSorted, key)
+    }
+  }} ensuring { res => res.content == l.content && res.length == l.length }
+
+  // To define stability, we first annotate the input list with the initial indices...
+  def annotateList[T](l: List[T], n: BigInt): List[(T, BigInt)] = {
+    l match {
+      case Nil() => Nil[(T, BigInt)]()
+      case Cons(hd, tl) => {
+        val tlAnn = annotateList(tl, n + 1)
+        hint((hd, n) :: tlAnn, trivProp2(annotateList(tl, n + 1), n))
+      }
+    }
+  } ensuring { res => l2AtLeast(res, n) }
+
+  // ... where:
+  def l2AtLeast[T](l: List[(T, BigInt)], n: BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => n <= hdIndex && l2AtLeast(tl, n)
+  }
+
+  // ... and the following trivial property holds:
+  @induct
+  def trivProp2[T](l: List[(T, BigInt)], n: BigInt): Boolean = {
+    require(l2AtLeast(l, n + 1))
+    l2AtLeast(l, n)
+  }.holds
+
+  // Next, we identify an appropriate value which is increasing in a stably sorted list:
+  def isStableSorted[T](l: List[(T, BigInt)], key: T => BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => isStableSortedAndAtLeast(tl, key, key(hd), hdIndex)
+  }
+
+  def isStableSortedAndAtLeast[T](
+    l: List[(T, BigInt)],
+    key: T => BigInt,
+    x: BigInt,
+    minIndex: BigInt): Boolean = l match {
+    case Nil() => true
+    case Cons((hd, hdIndex), tl) => {
+      val hdSmall = x < key(hd) || x == key(hd) && minIndex <= hdIndex
+      val tlSorted = isStableSortedAndAtLeast(tl, key, key(hd), hdIndex)
+      hdSmall && tlSorted
+    }
+  }
+
+  // The insertion sort we initially defined is stable:
+  def sortStableProp[T](l: List[T], key: T => BigInt): Boolean = {
+    require(sortStablePropInt(l, 0, key))
+    val lAnn = annotateList(l, 0)
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val lAnnSorted = sort(lAnn, keyAnn)
+    isStableSorted(lAnnSorted, key)
+  }.holds
+
+  // To prove that insertion sort is stable, we first show that insertion is stable:
+  @induct
+  def insertStableProp[T](t: T, n: BigInt, l: List[(T, BigInt)], key: T => BigInt): Boolean = {
+    require(isStableSorted(l, key) && l2AtLeast(l, n))
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val res = insert((t, n), l, keyAnn)
+    isStableSorted(res, key) && l2AtLeast(res, n)
+  }.holds
+
+  // ... and complete the proof of stability.
+  def sortStablePropInt[T](l: List[T], n: BigInt, key: T => BigInt): Boolean = {
+    val lAnn = annotateList(l, n)
+    val keyAnn = (tn: (T, BigInt)) => key(tn._1)
+    val lAnnSorted = sort(lAnn, keyAnn)
+    lAnn match {
+      case Nil() => isStableSorted(lAnnSorted, key)
+      case Cons((hd, hdIndex), tlAnn) => {
+        val Cons(_, xs) = l
+        val tlAnnSorted = sort(tlAnn, keyAnn)
+        sortStablePropInt(xs, n + 1, key) &&
+        n == hdIndex &&
+        l2AtLeast(tlAnn, n) &&
+        l2AtLeast(tlAnnSorted, n + 1) &&
+        trivProp2(tlAnnSorted, n) &&
+        l2AtLeast(tlAnnSorted, n) &&
+        insertStableProp(hd, hdIndex, tlAnnSorted, key) &&
+        isStableSorted(lAnnSorted, key) &&
+        l2AtLeast(lAnnSorted, n)
+      }
+    }
+  }.holds
+
+  def hint[T](t: T, lemma: Boolean): T = {
+    require(lemma)
+    t
+  }
+
+}
+
                  +

                  back

                  diff --git a/static/valid/StableSorter.scala b/static/valid/StableSorter.scala new file mode 100644 index 0000000000..699b853cf3 --- /dev/null +++ b/static/valid/StableSorter.scala @@ -0,0 +1,115 @@ +import stainless.annotation._ +import stainless.collection._ +import stainless.lang._ +import stainless.proof._ + +object StableSorter { + + // Inserting into a stable list adds to the content and increases the length + def insert[T](t: T, l: List[T], key: T => BigInt): List[T] = { + l match { + case Nil() => t :: l + case Cons(hd, tl) if key(t) <= key(hd) => t :: l + case Cons(hd, tl) => hd :: insert(t, tl, key) + } + } ensuring { res => res.content == Set(t) ++ l.content && res.length == 1 + l.length } + + // Sorting a list preserves the content and preserves the length + def sort[T](l: List[T], key: T => BigInt): List[T] = { l match { + case Nil() => l + case Cons(hd, tl) => { + val tlSorted = sort(tl, key) + insert(hd, tlSorted, key) + } + }} ensuring { res => res.content == l.content && res.length == l.length } + + // To define stability, we first annotate the input list with the initial indices... + def annotateList[T](l: List[T], n: BigInt): List[(T, BigInt)] = { + l match { + case Nil() => Nil[(T, BigInt)]() + case Cons(hd, tl) => { + val tlAnn = annotateList(tl, n + 1) + hint((hd, n) :: tlAnn, trivProp2(annotateList(tl, n + 1), n)) + } + } + } ensuring { res => l2AtLeast(res, n) } + + // ... where: + def l2AtLeast[T](l: List[(T, BigInt)], n: BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => n <= hdIndex && l2AtLeast(tl, n) + } + + // ... and the following trivial property holds: + @induct + def trivProp2[T](l: List[(T, BigInt)], n: BigInt): Boolean = { + require(l2AtLeast(l, n + 1)) + l2AtLeast(l, n) + }.holds + + // Next, we identify an appropriate value which is increasing in a stably sorted list: + def isStableSorted[T](l: List[(T, BigInt)], key: T => BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => isStableSortedAndAtLeast(tl, key, key(hd), hdIndex) + } + + def isStableSortedAndAtLeast[T]( + l: List[(T, BigInt)], + key: T => BigInt, + x: BigInt, + minIndex: BigInt): Boolean = l match { + case Nil() => true + case Cons((hd, hdIndex), tl) => { + val hdSmall = x < key(hd) || x == key(hd) && minIndex <= hdIndex + val tlSorted = isStableSortedAndAtLeast(tl, key, key(hd), hdIndex) + hdSmall && tlSorted + } + } + + // The insertion sort we initially defined is stable: + def sortStableProp[T](l: List[T], key: T => BigInt): Boolean = { + require(sortStablePropInt(l, 0, key)) + val lAnn = annotateList(l, 0) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val lAnnSorted = sort(lAnn, keyAnn) + isStableSorted(lAnnSorted, key) + }.holds + + // To prove that insertion sort is stable, we first show that insertion is stable: + @induct + def insertStableProp[T](t: T, n: BigInt, l: List[(T, BigInt)], key: T => BigInt): Boolean = { + require(isStableSorted(l, key) && l2AtLeast(l, n)) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val res = insert((t, n), l, keyAnn) + isStableSorted(res, key) && l2AtLeast(res, n) + }.holds + + // ... and complete the proof of stability. + def sortStablePropInt[T](l: List[T], n: BigInt, key: T => BigInt): Boolean = { + val lAnn = annotateList(l, n) + val keyAnn = (tn: (T, BigInt)) => key(tn._1) + val lAnnSorted = sort(lAnn, keyAnn) + lAnn match { + case Nil() => isStableSorted(lAnnSorted, key) + case Cons((hd, hdIndex), tlAnn) => { + val Cons(_, xs) = l + val tlAnnSorted = sort(tlAnn, keyAnn) + sortStablePropInt(xs, n + 1, key) && + n == hdIndex && + l2AtLeast(tlAnn, n) && + l2AtLeast(tlAnnSorted, n + 1) && + trivProp2(tlAnnSorted, n) && + l2AtLeast(tlAnnSorted, n) && + insertStableProp(hd, hdIndex, tlAnnSorted, key) && + isStableSorted(lAnnSorted, key) && + l2AtLeast(lAnnSorted, n) + } + } + }.holds + + def hint[T](t: T, lemma: Boolean): T = { + require(lemma) + t + } + +} diff --git a/tutorial.html b/tutorial.html new file mode 100644 index 0000000000..8d22ac420f --- /dev/null +++ b/tutorial.html @@ -0,0 +1,523 @@ + + + + + + + Tutorial: Sorting — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
                  + + +
                  + + +
                  +
                  + + +
                  + +
                  +
                  +
                  +
                  + +
                  +

                  Tutorial: Sorting

                  +

                  This tutorial shows how to:

                  +
                  +
                    +

                  • use ensuring, require, and holds constructs

                    • +

                  • learn the difference between Int and BigInt

                    • +

                  • define lists as algebraic data types

                    • +

                  • use sets and recursive function to specify data structures

                    • +
                  +
                  +

                  See Verifying and Compiling Examples about how to setup the command line +tool.

                  +
                  +

                  Warm-up: Max

                  +

                  As a warm-up illustrating verification, we define and debug a max function +and specify its properties. Stainless uses Scala constructs +require and ensuring to document preconditions and +postconditions of functions. Note that, in addition to +checking these conditions at run-time (which standard Scala +does), Stainless can analyze the specifications statically and +prove them for all executions, or, if they are wrong, automatically find +inputs for which the conditions fail.

                  +

                  Consider the following definition inside of an object TestMax.

                  +
                  object TestMax {
+  def max(x: Int, y: Int): Int = {
+    val d = x - y
+    if (d > 0) x
+    else y
+  } ensuring(res =>
+    x <= res && y <= res && (res == x || res == y))
+}
+
                  +
                  +

                  A Stainless program consists of one or more modules delimited by +object and class declarations. +The code of max attempts to compute the maximum of two given arguments +by subtracting them. If the result is positive, it returns +the first one, otherwise, it returns the second one.

                  +

                  To specify the correctness of the computed result, we use +the ensuring clause. In this case, the clause specifies +that the result is larger than x and than y, and that it +equals to one of them. The construct ensuring(res => P) +denotes that, if we denote by res the return value of the +function, then res satisfies the boolean-valued expression +P. The name res we chose is an arbitrary bound variable +(even though we often tend to use res).

                  +

                  We can evaluate this code on some values by writing +parameterless functions and inspecting what they evaluate +to. The web interface will display these results for us.

                  +
                  def test1 = max(10, 5)
+def test2 = max(-5, 5)
+def test3 = max(-5, -7)
+
                  +
                  +

                  The code seems to work correctly on the example values. +However, Stainless automatically finds that it is not correct:

                  +
                  [  Info  ]  - Now solving 'postcondition' VC for max @6:16...
+[  Info  ]  - Result for 'postcondition' VC for max @6:16:
+[Warning ]  => INVALID
+[Warning ] Found counter-example:
+[Warning ]   y: Int -> 2147483647
+[Warning ]   x: Int -> -2147483648
+
+[  Info  ]  - Now solving 'postcondition' VC for max @7:10...
+[  Info  ]  - Result for 'postcondition' VC for max @7:10:
+[Warning ]  => INVALID
+[Warning ] Found counter-example:
+[Warning ]   y: Int -> -2147483648
+[Warning ]   x: Int -> 1
+
+[  Info  ]  - Now solving 'body assertion: Subtraction overflow' VC for max @5:13...
+[  Info  ]  - Result for 'body assertion: Subtraction overflow' VC for max @5:13:
+[Warning ]  => INVALID
+[Warning ] Found counter-example:
+[Warning ]   y: Int -> -2147483648
+[Warning ]   x: Int -> 0
+
                  +
                  +

                  Here, Stainless emits three distinct verification conditions:

                  +
                    +

                  • One which corresponds to the postcondition of max when we take the then branch +of the if statement, on line 6.

                    • +

                  • Another one for the postcondition of max when we take the else branch +of the if statement, on line 7.

                    • +

                  • A last one with an overflow check for the subtraction on line 5.

                    • +
                  +

                  Let us look at the first verification condition:

                  +
                   - Now solving 'postcondition' VC for max @6:16...
+ - Result for 'postcondition' VC for max @6:16:
+ => INVALID
+Found counter-example:
+  y: Int -> 2147483647
+  x: Int -> -2147483648
+
                  +
                  +

                  Stainless tells us that it found two input for which the ensuring clause of the +max function evaluates to false. The second verification is similar.

                  +

                  We may wish to define a test method

                  +
                  def test4 = max(-1639624704, 1879048192)
+
                  +
                  +

                  whose evaluation indeed results in ensuring condition being violated. +The problem is due to overflow of 32-bit integers, due to which +the value d becomes positive, even though x is negative and thus smaller than +the large positive value y.

                  +

                  In fact, Stainless alerts us of this very problem in the third verification condition, +to help us pin point the place where the overflow occured.

                  +
                  +

                  Note

                  +

                  As in Scala, the Int type denotes 32-bit integers with the usual signed arithmetic +operations from computer architecture and the JVM specification.

                  +
                  +

                  To use unbounded integers, we simply change the types to +BigInt, obtaining a program that verifies (and, as +expected, passes all the test cases).

                  +
                  def max(x: BigInt, y: BigInt): BigInt = {
+  val d = x - y
+  if (d > 0) x
+  else y
+} ensuring(res =>
+  x <= res && y <= res && (res == x || res == y))
+
                  +
                  +

                  As a possibly simpler specification, we could have also +defined the reference implementation

                  +
                  def rmax(x: BigInt, y: BigInt) = {
+  if (x <= y) y else x
+}
+
                  +
                  +

                  and then used as the postcondition of max simply

                  +
                  ensuring (res =>  res == rmax(x,y))
+
                  +
                  +

                  In general, Stainless uses both function body and function +specification when reasoning about the function and its +uses. Thus, we need not repeat in the postcondition those +aspects of function body that follow directly through +inlining the function, but we may wish to state those +that require induction to prove.

                  +

                  The fact that we can use functions in preconditions +and postconditions allows us to state fairly general +properties. For example, the following lemma verifies +a number of algebraic properties of max.

                  +
                  def max_lemma(x: BigInt, y: BigInt, z: BigInt): Boolean = {
+  max(x,x) == x &&
+  max(x,y) == max(y,x) &&
+  max(x,max(y,z)) == max(max(x,y), z) &&
+  max(x,y) + z == max(x + z, y + z)
+} holds
+
                  +
                  +

                  Here holds operator on the function body is an +abbreviation for the postcondition stating that the returned +result is always true, that is, for

                  +
                  ensuring(res => res==true)
+
                  +
                  +

                  As a guideline, we typically use holds to express such +algebraic properties that relate multiple invocations of +functions, whereas we use ensuring to document property of +an arbitrary single invocation of a function. Stainless is more likely to automatically +use the property of a function if it is associated with it using +ensuring than using an external lemma.

                  +

                  Going back to our buggy implementation of max on Int-s, +an alternative to using BigInt-s is to decide that +the method should only be used under certain conditions, +such as x and y being non-negative. To specify the +conditions on input, we use the require clause.

                  +
                  def max(x: Int, y: Int): Int = {
+  require(0 <= x && 0 <= y)
+  val d = x - y
+  if (d > 0) x
+  else y
+} ensuring (res =>
+  x <= res && y <= res && (res == x || res == y))
+
                  +
                  +

                  This program verifies and indeed works correctly on +non-negative 32-bit integers as inputs.

                  +

                  Question: What if we restrict the inputs to max to be +a) non-positive, or b) strictly negative? Modify the +require clause for each case accordingly and explain the +behavior of Stainless. See the note below, as well.

                  +
                  +

                  Note

                  +

                  By default, Stainless will emit verification conditions to +check that arithmetic operations on sized integers such as +Int cannot overflow. To opt-out of this behavior, eg. when +such wrapping semantics are desired, one can wrap the offending +expression in a call to stainless.math.wrapping:

                  +
                  import stainless.math.wrapping
+
+def doubleOverflow(x: Int): Int = {
+   wrapping { x + x }
+}
+
                  +
                  +
                  +

                  In the sequel, we will mostly use BigInt types.

                  +
                  +
                  +

                  Defining Lists and Their Properties

                  +

                  We next consider sorting an unbounded number of elements. +For this purpose, we define a data structure for lists of +integers. Stainless has a built-in data type of parametric +lists, see Stainless Library, but here we define +our own variant instead.

                  +
                  +

                  Lists

                  +

                  We use a recursive algebraic data type +definition, expressed using Scala’s case classes.

                  +
                  sealed abstract class List
+case object Nil extends List
+case class Cons(head: BigInt, tail: List) extends List
+
                  +
                  +

                  We can read the definition as follows: the set of lists is +defined as the least set that satisfies them:

                  +
                  +
                    +

                  • empty list Nil is a list

                    • +

                  • if head is an integer and tail is a List, then +Cons(head,tail) is a List.

                    • +
                  +
                  +

                  Each list is constructed by applying the above two rules +finitely many times. A concrete list containing elements 5, +2, and 7, in that order, is denoted

                  +
                  Cons(5, Cons(2, Cons(7, Nil)))
+
                  +
                  +

                  Having defined the structure of lists, we can move on to +define some semantic properties of lists that are of +interests. For this purpose, we use recursive functions +defined on lists.

                  +
                  +
                  +

                  Size of a List

                  +

                  As the starting point, we define the size of a list.

                  +
                  def size(l: List) : BigInt = (l match {
+    case Nil => 0
+    case Cons(x, rest) => 1 + size(rest)
+})
+
                  +
                  +

                  The definition uses pattern matching to define size of the +list in the case it is empty (where it is zero) and when it +is non-empty, or, if it’s non-empty, then it has a head x +and the rest of the list rest, so the size is one plus the +size of the rest. Thus size is a recursive function. A +strength of Stainless is that it allows using such recursive +functions in specifications.

                  +

                  It makes little sense to try to write a complete +specification of size, given that its recursive definition +is already a pretty clear description of its +meaning. However, it is useful to add a consequence of this +definition, namely that the size is non-negative. The reason +is that Stainless most of the time reasons by unfolding size, +and the property of size being non-negative is not revealed +by such unfolding. Once specified, the non-negativity is +easily proven and Stainless will make use of it.

                  +
                  def isize(l: List) : Int = (l match {
+  case Nil => 0
+  case Cons(x, rest) => {
+    val rSize = isize(rest)
+    if (rSize == Int.MaxValue) rSize
+    else 1 + rSize
+  }
+}).ensuring(res => res >= 0)
+
                  +
                  +

                  In some cases, it may be helpful to define a size function +that returns a bounded integer type, such as the 32-bit signed integer `Int. +One useful way to do this is to define function as follows:

                  +
                  def isize(l: List) : Int = (l match {
+    case Nil => 0
+    case Cons(x, rest) => {
+      val rSize = isize(rest)
+      if (rSize == Int.Max) rSize
+      else 1 + rSize
+    }
+}) ensuring(res => res >= 0)
+
                  +
                  +

                  The above isize function satisfies the usual recursive definition for all but a huge +lists, returns a non-negative integer, and ensures that if isize returns a small +number, then the list is indeed small.

                  +
                  +
                  +

                  Sorted Lists

                  +

                  We define properties of values simply as executable +predicates that check if the property holds. The following +is a property that a list is sorted in a strictly ascending +order.

                  +
                  def isSorted(l : List) : Boolean = l match {
+  case Nil => true
+  case Cons(_,Nil) => true
+  case Cons(x1, Cons(x2, rest)) =>
+    x1 < x2 && isSorted(Cons(x2,rest))
+}
+
                  +
                  +
                  +
                  +
                  +

                  Insertion into Sorted List

                  +

                  Consider the following specification of insertion into a sorted list. It’s a +building block for an insertion sort.

                  +
                  def sInsert(x : BigInt, l : List) : List = {
+  require(isSorted(l))
+  l match {
+    case Nil => Cons(x, Nil)
+    case Cons(e, rest) if (x == e) => l
+    case Cons(e, rest) if (x < e) => Cons(x, Cons(e,rest))
+    case Cons(e, rest) if (x > e) => Cons(e, sInsert(x,rest))
+  }
+} ensuring {(res:List) => isSorted(res)}
+
                  +
                  +

                  Stainless verifies that the returned list is indeed sorted. Note +how we are again using a recursively defined function to +specify another function. We can introduce a bug into the +definition above and examine the counterexamples that Stainless +finds.

                  +
                  +
                  +

                  Being Sorted is Not Enough

                  +

                  Note, however, that a function such as this one is also correct.

                  +
                  def fsInsert(x : BigInt, l : List) : List = {
+  require(isSorted(l))
+  Nil
+} ensuring {(res:List) => isSorted(res)}
+
                  +
                  +

                  So, our specification may be considered weak, because it does +not say anything about the elements.

                  +
                  +
                  +

                  Using Size in Specification

                  +

                  Consider a stronger additional postcondition property:

                  +
                  size(res) == size(l) + 1
+
                  +
                  +

                  Does it hold? If we try to add it, we obtain a counterexample. +A correct strengthening, taking into account that the element +may or may not already be in the list, is the following.

                  +
                  size(l) <= size(res) && size(res) <= size(l) + 1
+
                  +
                  +
                  +
                  +

                  Using Content in Specification

                  +

                  A stronger specification needs to talk about the content +of the list.

                  +
                  def sInsert(x : BigInt, l : List) : List = {
+  require(isSorted(l))
+  l match {
+    case Nil => Cons(x, Nil)
+    case Cons(e, rest) if (x == e) => l
+    case Cons(e, rest) if (x < e) => Cons(x, Cons(e,rest))
+    case Cons(e, rest) if (x > e) => Cons(e, sInsert(x,rest))
+  }
+} ensuring {(res:List) =>
+   isSorted(res) && content(res) == content(l) ++ Set(x)}
+
                  +
                  +

                  To compute content, in this example we use sets (even +though in general, it might be better to use bags +i.e. multisets).

                  +
                  def content(l: List): Set[BigInt] = l match {
+  case Nil => Set()
+  case Cons(i, t) => Set(i) ++ content(t)
+}
+
                  +
                  +

                  This completes the tutorial. To learn more, check the rest of this +documentation and browse the examples provided with Stainless.

                  +
                  +
                  + + +
                  +
                  +
                  + + +
                  + +
                  +

                  © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

                  +
                  + + + +
                  +
                  +
                  +
                  +
                  + + + + \ No newline at end of file diff --git a/verification.html b/verification.html new file mode 100644 index 0000000000..83c37db34f --- /dev/null +++ b/verification.html @@ -0,0 +1,371 @@ + + + + + + + Verification conditions — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + + +
                  + + +
                  + + +
                  +
                  + + +
                  + +
                  +
                  +
                  +
                  + +
                  +

                  Verification conditions

                  +

                  Software verification aims at making software safer. In its typical use case, +it is a tool that takes as input the source code of a program with +specifications as annotations and attempt to prove — or disprove — their +validity.

                  +

                  One of the core modules of Stainless is a verifier for the subset of Scala described +in the sections Pure Scala and Imperative. In this +section, we describe the specification language that can be used to declare +properties of programs, as well as the safety properties automatically checked +by Stainless. We also discuss how Stainless can be used to prove mathematical theorems.

                  +

                  Given an input program, Stainless generates individual verification conditions +corresponding to different properties of the program. A program is correct if +all of the generated verification conditions are valid. The validity of some +conditions depends on the validity of other conditions — typically a +postcondition is valid assuming the precondition is valid.

                  +

                  For each function, Stainless attempts to verify its contract, if there is one. A +contract is the combination of a precondition and a postcondition. A +function meets its contract if, for any input parameter that passes the +precondition, the postcondition holds after executing the function. +Preconditions and postconditions are annotations given by the user — they are +the specifications and hence cannot be inferred by a tool and must be provided.

                  +

                  In addition to user-provided contracts, Stainless will also generate a few safety +verification conditions of its own. It will check that all of the array +accesses are within proper bounds, and that pattern matching always covers all +possible cases, even given complex precondition. The latter is different from +the Scala compiler checks on pattern matching exhaustiveness, as Stainless considers +information provided by (explicit or implicit) preconditions to the match +expression.

                  +
                  +

                  Postconditions

                  +

                  One core concept in verification is to check the contract of functions. The most +important part of a contract is the postcondition. The postcondition specifies +the behavior of the function. It takes into account the precondition and only +asserts the property of the output when the input satisfies the precondition.

                  +

                  Formally, we consider a function with a single parameter (one can generalize +the following for any number of parameters):

                  +
                  def f(x: A): B = {
+  require(prec)
+  body
+} ensuring(r => post)
+
                  +
                  +

                  where, \(\mbox{prec}(x)\) is a Boolean expression with free variables +contained in \(\{ x \}\), \(\mbox{body}(x)\) is an expression with +free variables contained in \(\{ x \}\) and \(\mbox{post}(x, r)\) is a +Boolean expression with free variables contained in \(\{ x, r \}\). The +types of \(x\) and \(r\) are respectively A and B. We write +\(\mbox{expr}(a)\) to mean the substitution in \(\mbox{expr}\) of its +free variable by \(a\).

                  +

                  Stainless attempts to prove the following theorem:

                  +
                  +\[\forall x. \mbox{prec}(x) \implies \mbox{post}(x, \mbox{body}(x))\]
                  +

                  If Stainless is able to prove the above theorem, it returns valid for the +function f. This gives you a guarantee that the function f is correct +with respect to its contract.

                  +

                  However, if the theorem is not valid, Stainless will return a counterexample to the +theorem. The negation of the theorem is:

                  +
                  +\[\exists x. \mbox{prec}(x) \land \neg \mbox{post}(x, \mbox{body}(x))\]
                  +

                  and to prove the validity of the negation, Stainless finds a witness \(x\) — a +counterexample — such that the precondition is verified and the postcondition +is not.

                  +

                  The general problem of verification is undecidable for a Turing-complete +language, and the Stainless language is Turing-complete. So Stainless has to be +incomplete in some sense. Generally, Stainless will eventually find a counterexample +if one exists. However, in practice, some program structures require too many +unrollings and Stainless is likely to timeout (or being out of memory) before +finding the counterexample. When the postcondition is valid, it could also +happen that Stainless keeps unrolling the program forever, without being able to +prove the correctness. We discuss the exact conditions for this in the +chapter on Stainless’s algorithms.

                  +
                  +
                  +

                  Preconditions

                  +

                  Preconditions are used as part of the contract of functions. They are a way to +restrict the input to only relevant inputs, without having to implement guards +and error handling in the functions themselves.

                  +

                  Preconditions are contracts that the call sites should respect, and thus are +not checked as part of verifying the function. Given the following definition:

                  +
                  def f(x: A): B = {
+  require(prec)
+  body
+}
+
                  +
                  +

                  For each call site in the whole program (including in f itself):

                  +
                  ...
+f(e)
+...
+
                  +
                  +

                  where the expression \(\mbox{e}(x)\) is an expression of type A with +free variables among \(\{ x \}\). Let us define the path condition on \(x\) +at that program point as \(\mbox{pc}(x)\). The path condition is a formula that +summarizes the facts known about \(x\) at that call site. A typical example is +when the call site is inside an if expression:

                  +
                  if(x > 0)
+  f(x)
+
                  +
                  +

                  The path condition on \(x\) would include the fact that \(x > 0\). This +path condition is then used as a precondition of proving the validity of the +call to \(\mbox{f}\). Formally, for each such call site, Stainless will attempt +to prove the following theorem:

                  +
                  +\[\forall x. \mbox{pc}(x) \implies \mbox{prec}(\mbox{e}(x))\]
                  +

                  Stainless will generate one such theorem for each static call site of a function with +a precondition.

                  +
                  +

                  Note

                  +

                  Stainless only assumes an open program model, where any function could be called from +outside of the given program. In particular, Stainless will not derive a precondition +to a function based on known information in the context of the calls, such as +knowing that the function is always given positive parameters. Any information needed +to prove the postcondition will have to be provided as part of the precondition +of a function.

                  +
                  +
                  +
                  +

                  Sharing bindings between specifications and function body

                  +

                  The example ValEnsuring +shows that Stainless supports multiple require’s (in functions, but not for ADT invariants), and +shows how to share a val binding between precondition, postcondition, and function body.

                  +
                  +
                  +

                  Loop invariants

                  +

                  Stainless supports annotations for loop invariants in Imperative. To +simplify the presentation we will assume a single variable \(x\) is in +scope, but the definitions generalize to any number of variables. Given the +following program:

                  +
                  (while(cond) {
+  body
+}) invariant(inv)
+
                  +
                  +

                  where the Boolean expression \(\mbox{cond}(x)\) is over the free variable +\(x\) and the expression \(\mbox{body}(x, x')\) relates the value of +\(x\) when entering the loop to its updated value \(x'\) on loop exit. +The expression \(\mbox{inv}(x)\) is a Boolean formula over the free +variable \(x\).

                  +
                  +
                  A loop invariant must hold:
                    +

                  1. when the program enters the loop initially

                    2. +

                  2. after each completion of the body

                    3. +

                  3. right after exiting the loop (when the condition turns false)

                    4. +
                  +
                  +
                  +

                  Stainless will prove the points (1) and (2) above. Together, and by induction, they imply +that point (3) holds as well.

                  +

                  Stainless also supports noReturnInvariant (see ReturnInWhile3) to describe loop invariants that are allowed to be broken +after a return (can be combined with invariant).

                  +
                  +
                  +

                  Decrease annotation in loops

                  +

                  One can also specify that the value of a given expression of numerical type decreases +at each loop iteration by adding a decreases measure within the loop body:

                  +
                  while(cond) {
+  decreases(expr)
+  body
+}
+
                  +
                  +

                  Stainless will then emit a verification condition that checks whether the expression +is strictly positive and decreases at each iteration.

                  +
                  +
                  +

                  Array access safety

                  +

                  Stainless generates verification conditions for the safety of array accesses. For +each array variable, Stainless carries along a symbolic information on its length. +This information is used to prove that each expression used as an index in the +array is strictly smaller than that length. The expression is also checked to +be positive.

                  +
                  +
                  +

                  ADT invariants

                  +

                  Stainless lets the user write ADT invariants with the require keyword. +Internally, such invariants are extracted as methods (named inv). Whenever, +an ADT is constructed, and to make sure that the invariant is true, a +verification condition is generated with a call to the corresponding inv +method.

                  +

                  The Stainless annotation @inlineInvariant used on an ADT or one of its +ancestors can be used to inline the call to inv in the verification +condition, as shown in the following example. This annotation is only +supported when --type-checker=true (which is the case by default).

                  +
                  import stainless.annotation._
+
+object InlineInvariant {
+  sealed abstract class A
+
+  case class B(x: BigInt) extends A {
+    require(x >= 50)
+  }
+
+  @inlineInvariant
+  case class C(x: BigInt) extends A {
+    require(x >= 50)
+  }
+
+  def f(): A = {
+    B(100) // VC: inv(B(100))
+    c(100) // VC: 100 >= 50 (call to `inv` was inlined)
+  }
+}
+
                  +
                  +
                  +
                  +

                  Pattern matching exhaustiveness

                  +

                  Stainless verifies that pattern matching is exhaustive. The regular Scala compiler +only considers the types of expression involved in pattern matching, but Stainless +will consider information such as precondition to formally prove the +exhaustiveness of pattern matching.

                  +

                  As an example, the following code should issue a warning with Scala:

                  +
                  abstract class List
+case class Cons(head: Int, tail: List) extends List
+case object Nil extends List
+
+def getHead(l: List): Int = {
+  require(!l.isInstanceOf[Nil])
+  l match {
+    case Cons(x, _) => x
+  }
+}
+
                  +
                  +

                  But Stainless will prove that the pattern matching is actually exhaustive, +relying on the given precondition.

                  +
                  +
                  + + +
                  +
                  +
                  + + +
                  + +
                  +

                  © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

                  +
                  + + + +
                  +
                  +
                  +
                  +
                  + + + + \ No newline at end of file diff --git a/wrap.html b/wrap.html new file mode 100644 index 0000000000..d3cafecb27 --- /dev/null +++ b/wrap.html @@ -0,0 +1,347 @@ + + + + + + + Working With Existing Code — Stainless 0.9.1 documentation + + + + + + + + + + + + + + + + + + +
                  + + +
                  + + +
                  +
                  + + +
                  + +
                  +
                  +
                  +
                  + +
                  +

                  Working With Existing Code

                  +

                  While the subset of Scala (namely, PureScala) that is currently supported by Stainless +is already expressive enough to implement a lot of different data structures and algorithms, +it is often the case that one would like to avoid re-implementing a piece of code from scratch +in this fragment, but rather re-use some existing code, whether it is part of the codebase or +pulled in from a Java or Scala library.

                  +
                  +

                  A wrapper for TrieMap

                  +

                  As a running example, let’s write a wrapper for the scala.collection.concurrent.TrieMap class. +A first attempt to wrap it in a regular Stainless datatype could look like the following:

                  +
                  import stainless.lang._
+import stainless.annotation._
+
+import scala.collection.concurrent.TrieMap
+
+case class TrieMapWrapper[K, V](theMap: TrieMap[K, V])
+
                  +
                  +

                  Unfortunately, this will not work as Stainless will complain that it does not +know about the TrieMap type. In order to work around this, one can annotate +the field with the @extern annotation, which tells Stainless that the type +should be treated as opaque.

                  +
                  import stainless.lang._
+import stainless.annotation._
+
+import scala.collection.concurrent.TrieMap
+import scala.collection.concurrent.TrieMap
+
+case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V])
+
                  +
                  +
                  +
                  +

                  Extern methods

                  +

                  Let’s now define a forwarding method for the contains method of TrieMap:

                  +
                  import stainless.lang._
+import stainless.annotation._
+
+import scala.collection.concurrent.TrieMap
+import scala.collection.concurrent.TrieMap
+
+case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) {
+
+  def contains(k: K): Boolean = {
+    theMap contains k
+  }
+}
+
                  +
                  +

                  Once again, this will fail because, from Stainless’ point of view, theMap has an opaque type +and thus has no contains method. By annotating the method itself with @extern, Stainless will +not attempt to extract the method’s body, and we can thus freely refer to any of TrieMap’s methods:

                  +
                  import stainless.lang._
+import stainless.annotation._
+
+import scala.collection.concurrent.TrieMap
+
+case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) {
+
+  @extern
+  def contains(k: K): Boolean = {
+    theMap contains k
+  }
+}
+
                  +
                  +
                  +

                  Note

                  +

                  Methods marked @extern are allowed to mention types which Stainless is not able to extract. +Such types will be replaced by the unknown type ? during the recovery phase. +One can inspect which types are replaced during recovery, by supplying the --debug=recovery flag.

                  +
                  +
                  +
                  +

                  Contracts

                  +

                  Let’s also define another extern function, which creates a new empty map:

                  +
                  object TrieMapWrapper {
+  @extern
+  def empty[K, V]: TrieMapWrapper[K, V] = {
+    TrieMapWrapper(TrieMap.empty[K, V])
+  }
+}
+
+def prop1 = {
+  val wrapper = TrieMapWrapper.empty[Int, String]
+  assert(!wrapper.contains(42)) // invalid
+}
+
                  +
                  +

                  Indeed, because Stainless does not know about TrieMap.empty, it cannot assume +by itself that the result of TrieMapWrapper.empty does not contain any entries.

                  +

                  We can remedy to that by adding a postcondition to the empty function which says that, +for any key k of type K, the result of TrieMapWrapper.empty does not contain the key k.

                  +
                  object TrieMapWrapper {
+  @extern
+  def empty[K, V]: TrieMapWrapper[K, V] = {
+    TrieMapWrapper(TrieMap.empty[K, V])
+  } ensuring { res =>
+    forall((k: K) => !res.contains(k))
+  }
+}
+
                  +
                  +

                  The assertion above now verifies successfully.

                  +
                  +
                  +

                  Purity annotations

                  +

                  Let’s now see what happens when we call contains twice:

                  +
                  def prop1 = {
+  val wrapper = TrieMapWrapper.empty[Int, String]
+  assert(!wrapper.contains(42))
+  assert(!wrapper.contains(42))
+}
+
                  +
                  +
                    ┌───────────────────┐
+╔═╡ stainless summary ╞═══════════════════════════════════════════════════╗
+║ └───────────────────┘                                                   ║
+║ prop1  body assertion  valid    U:smt-z3  ExternField.scala:46:5  0.018 ║
+║ prop1  body assertion  invalid  U:smt-z3  ExternField.scala:47:5  0.110 ║
+╚═════════════════════════════════════════════════════════════════════════╝
+
                  +
                  +

                  The second assertion (perhaps surprisingly) fails to verify. This stems from the fact that Stainless assumes +by default that extern functions and methods mutate their arguments. Indeed, because Stainless +does not know about the body of such methods, it cannot know whether such a function is pure or not. +It is thus up to the user to instruct Stainless otherwise, by annotating the function with @pure:

                  +
                  case class TrieMapWrapper[K, V](@extern theMap: TrieMap[K, V]) {
+
+  @extern @pure
+  def contains(k: K): Boolean = {
+    theMap contains k
+  }
+}
+
                  +
                  +

                  With the annotation, the two assertions above now verify:

                  +
                    ┌───────────────────┐
+╔═╡ stainless summary ╞═════════════════════════════════════════════════╗
+║ └───────────────────┘                                                 ║
+║ prop1  body assertion  valid  U:smt-z3  ExternField.scala:46:5  0.018 ║
+║ prop1  body assertion  valid  U:smt-z3  ExternField.scala:48:5  0.110 ║
+╚═══════════════════════════════════════════════════════════════════════╝
+
                  +
                  +

                  We can now define the other methods of interest, with their appropriate contract:

                  +
                  import stainless.lang._
+import stainless.annotation._
+import scala.annotation.meta.field
+
+import scala.collection.concurrent.TrieMap
+
+case class TrieMapWrapper[K, V](
+  @extern
+  theMap: TrieMap[K, V]
+) {
+
+  @extern @pure
+  def contains(k: K): Boolean = {
+    theMap contains k
+  }
+
+  @extern
+  def insert(k: K, v: V): Unit = {
+    theMap.update(k, v)
+  } ensuring {
+    this.contains(k) &&
+    this.apply(k) == v
+  }
+
+  @extern @pure
+  def apply(k: K): V = {
+    require(contains(k))
+    theMap(k)
+  }
+}
+
+object TrieMapWrapper {
+  @extern @pure
+  def empty[K, V]: TrieMapWrapper[K, V] = {
+    TrieMapWrapper(TrieMap.empty[K, V])
+  } ensuring { res =>
+    forall((k: K) => !res.contains(k))
+  }
+}
+
                  +
                  +

                  And we can now reason about our wrapper for TrieMap:

                  +
                  def prop2 = {
+  val wrapper = TrieMapWrapper.empty[BigInt, String]
+  assert(!wrapper.contains(42))
+  wrapper.insert(42, "Hello")
+  assert(wrapper.contains(42))
+  assert(wrapper(42) == "Hello")
+}
+
                  +
                  +
                    ┌───────────────────┐
+╔═╡ stainless summary ╞═════════════════════════════════════════════════════════════════════════════════╗
+║ └───────────────────┘                                                                                 ║
+║ prop2  body assertion                                 valid  U:smt-z3  ExternField.scala:56:5   0.023 ║
+║ prop2  body assertion                                 valid  U:smt-z3  ExternField.scala:58:5   0.095 ║
+║ prop2  body assertion                                 valid  U:smt-z3  ExternField.scala:59:5   0.080 ║
+║ prop2  precond. (apply[BigInt, String](wrapper, 42))  valid  U:smt-z3  ExternField.scala:59:12  0.200 ║
+╟-------------------------------------------------------------------------------------------------------╢
+║ total: 4    valid: 4    (0 from cache) invalid: 0    unknown: 0    time:   0.398                      ║
+╚═══════════════════════════════════════════════════════════════════════════════════════════════════════╝
+
                  +
                  +
                  +
                  + + +
                  +
                  +
                  + + +
                  + +
                  +

                  © Copyright 2009-2021 EPFL, Lausanne. + Last updated on Dec 17, 2023. +

                  +
                  + + + +
                  +
                  +
                  +
                  +
                  + + + + \ No newline at end of file