updated tests and docs to use polymorphic lambda to create FunctionK

build.sbt

@@ -62,7 +62,7 @@ lazy val commonSettings = Seq(
     "com.github.mpilquist" %%% "simulacrum" % "0.8.0",
     "org.typelevel" %%% "machinist" % "0.4.1",
     compilerPlugin("org.scalamacros" %% "paradise" % "2.1.0" cross CrossVersion.full),
-    compilerPlugin("org.spire-math" %% "kind-projector" % "0.6.3")
+    compilerPlugin("org.spire-math" %% "kind-projector" % "0.9.0")
   ),
   fork in test := true,
   parallelExecution in Test := false,

core/src/main/scala/cats/arrow/FunctionK.scala

@@ -9,6 +9,11 @@ import cats.macros.MacroCompat
   * `FunctionK[F[_], G[_]]` is a functor transformation from `F` to `G`
   * in the same manner that function `A => B` is a morphism from values
   * of type `A` to `B`.
+  * An easy way to create a FunctionK instance is to use the Polymorphic
+  * lambdas provided by non/kind-projector v0.9+. E.g.
+  * {{{
+  *   val listToOption = λ[FunctionK[List, Option]](_.headOption)
+  * }}}
   */
 trait FunctionK[F[_], G[_]] extends Serializable { self =>
 

core/src/main/scala/cats/data/Coproduct.scala

@@ -67,10 +67,7 @@ final case class Coproduct[F[_], G[_], A](run: Either[F[A], G[A]]) {
    * {{{
    * scala> import cats.arrow.FunctionK
    * scala> import cats.data.Coproduct
-   * scala> val listToOption =
-   *      |   new FunctionK[List, Option] {
-   *      |     def apply[A](fa: List[A]): Option[A] = fa.headOption
-   *      |   }
+   * scala> val listToOption = λ[FunctionK[List, Option]](_.headOption)
    * scala> val optionToOption = FunctionK.id[Option]
    * scala> val cp1: Coproduct[List, Option, Int] = Coproduct.leftc(List(1,2,3))
    * scala> val cp2: Coproduct[List, Option, Int] = Coproduct.rightc(Some(4))

docs/src/main/tut/freeapplicative.md

@@ -61,14 +61,13 @@ import cats.implicits._
 type FromString[A] = String => A
 
 val compiler =
-  new FunctionK[ValidationOp, FromString] {
-    def apply[A](fa: ValidationOp[A]): String => A =
+   λ[FunctionK[ValidationOp, FromString]] { fa =>
       str =>
         fa match {
           case Size(size) => str.size >= size
           case HasNumber  => str.exists(c => "0123456789".contains(c))
         }
-  }
+   }
 ```
 
 ```tut:book
@@ -103,14 +102,13 @@ import scala.concurrent.ExecutionContext.Implicits.global
 type ParValidator[A] = Kleisli[Future, String, A]
 
 val parCompiler =
-  new FunctionK[ValidationOp, ParValidator] {
-    def apply[A](fa: ValidationOp[A]): ParValidator[A] =
-      Kleisli { str =>
-        fa match {
-          case Size(size) => Future { str.size >= size }
-          case HasNumber  => Future { str.exists(c => "0123456789".contains(c)) }
-        }
+  λ[FunctionK[ValidationOp, ParValidator]] { fa =>
+    Kleisli { str =>
+      fa match {
+        case Size(size) => Future { str.size >= size }
+        case HasNumber  => Future { str.exists(c => "0123456789".contains(c)) }
       }
+    }
   }
 
 val parValidation = prog.foldMap[ParValidator](parCompiler)
@@ -130,12 +128,9 @@ import cats.implicits._
 type Log[A] = Const[List[String], A]
 
 val logCompiler =
-  new FunctionK[ValidationOp, Log] {
-    def apply[A](fa: ValidationOp[A]): Log[A] =
-      fa match {
-        case Size(size) => Const(List(s"size >= $size"))
-        case HasNumber  => Const(List("has number"))
-      }
+  λ[FunctionK[ValidationOp, Log]] {
+    case Size(size) => Const(List(s"size >= $size"))
+    case HasNumber  => Const(List("has number"))
   }
 
 def logValidation[A](validation: Validation[A]): List[String] =
@@ -166,19 +161,15 @@ import cats.data.Prod
 type ValidateAndLog[A] = Prod[ParValidator, Log, A]
 
 val prodCompiler =
-  new FunctionK[ValidationOp, ValidateAndLog] {
-    def apply[A](fa: ValidationOp[A]): ValidateAndLog[A] = {
-      fa match {
-        case Size(size) =>
-          val f: ParValidator[Boolean] = Kleisli(str => Future { str.size >= size })
-          val l: Log[Boolean] = Const(List(s"size > $size"))
-          Prod[ParValidator, Log, Boolean](f, l)
-        case HasNumber  =>
-          val f: ParValidator[Boolean] = Kleisli(str => Future(str.exists(c => "0123456789".contains(c))))
-          val l: Log[Boolean] = Const(List("has number"))
-          Prod[ParValidator, Log, Boolean](f, l)
-      }
-    }
+  λ[FunctionK[ValidationOp, ValidateAndLog]] {
+    case Size(size) =>
+      val f: ParValidator[Boolean] = Kleisli(str => Future { str.size >= size })
+      val l: Log[Boolean] = Const(List(s"size > $size"))
+      Prod[ParValidator, Log, Boolean](f, l)
+    case HasNumber  =>
+      val f: ParValidator[Boolean] = Kleisli(str => Future(str.exists(c => "0123456789".contains(c))))
+      val l: Log[Boolean] = Const(List("has number"))
+      Prod[ParValidator, Log, Boolean](f, l)
   }
 
 val prodValidation = prog.foldMap[ValidateAndLog](prodCompiler)

free/src/test/scala/cats/free/CoyonedaTests.scala

@@ -26,10 +26,7 @@ class CoyonedaTests extends CatsSuite {
   }
 
   test("transform and run is same as applying natural trans") {
-      val nt =
-        new FunctionK[Option, List] {
-          def apply[A](fa: Option[A]): List[A] = fa.toList
-        }
+      val nt = λ[FunctionK[Option, List]](_.toList)
       val o = Option("hello")
       val c = Coyoneda.lift(o)
       c.transform(nt).run should === (nt(o))

free/src/test/scala/cats/free/FreeApplicativeTests.scala

@@ -62,10 +62,7 @@ class FreeApplicativeTests extends CatsSuite {
     val f = x.map(i => (j: Int) => i + j)
     val r1 = y.ap(f)
     val r2 = r1.monad
-    val nt =
-      new FunctionK[Id, Id] {
-        def apply[A](fa: Id[A]): Id[A] = fa
-      }
+    val nt = FunctionK.id[Id]
     r1.foldMap(nt) should === (r2.foldMap(nt))
   }
 
@@ -81,9 +78,7 @@ class FreeApplicativeTests extends CatsSuite {
 
   test("FreeApplicative#analyze") {
     type G[A] = List[Int]
-    val countingNT = new FunctionK[List, G] {
-      def apply[A](la: List[A]): G[A] = List(la.length)
-    }
+    val countingNT = λ[FunctionK[List, G]](la => List(la.length))
 
     val fli1 = FreeApplicative.lift[List, Int](List(1, 3, 5, 7))
     fli1.analyze[G[Int]](countingNT) should === (List(4))
@@ -103,8 +98,8 @@ class FreeApplicativeTests extends CatsSuite {
 
     type Tracked[A] = State[String, A]
 
-    val f: FunctionK[Foo,Tracked] = new FunctionK[Foo,Tracked] {
-      def apply[A](fa: Foo[A]): Tracked[A] = State[String, A]{ s0 =>
+    val f = λ[FunctionK[Foo,Tracked]] { fa =>
+      State { s0 =>
         (s0 + fa.toString + ";", fa.getA)
       }
     }
@@ -126,9 +121,7 @@ class FreeApplicativeTests extends CatsSuite {
 
     val z = Apply[Dsl].map2(x, y)((_, _) => ())
 
-    val asString: FunctionK[Id, λ[α => String]] = new FunctionK[Id, λ[α => String]] {
-      def apply[A](a: A): String = a.toString
-    }
+    val asString = λ[FunctionK[Id, λ[α => String]]](_.toString)
 
     z.analyze(asString) should === ("xy")
   }

free/src/test/scala/cats/free/FreeInvariantMonoidalTests.scala

@@ -59,9 +59,7 @@ class FreeInvariantMonoidalTests extends CatsSuite {
 
   test("FreeInvariantMonoidal#analyze") {
     type G[A] = List[Int]
-    val countingNT = new FunctionK[List, G] {
-      def apply[A](la: List[A]): G[A] = List(la.length)
-    }
+    val countingNT = λ[FunctionK[List, G]](la => List(la.length))
 
     val fli1 = FreeInvariantMonoidal.lift[List, Int](List(1, 3, 5, 7))
     fli1.analyze[G[Int]](countingNT) should === (List(4))

free/src/test/scala/cats/free/FreeTests.scala

@@ -69,10 +69,8 @@ class FreeTests extends CatsSuite {
       z <- if (j<10000) a(j) else Free.pure[FTestApi, Int](j)
     } yield z
 
-    def runner: FunctionK[FTestApi,Id] = new FunctionK[FTestApi,Id] {
-      def apply[A](fa: FTestApi[A]): Id[A] = fa match {
-        case TB(i) => i+1
-      }
+    def runner: FunctionK[FTestApi,Id] = λ[FunctionK[FTestApi,Id]] {
+      case TB(i) => i+1
     }
 
     assert(10000 == a(0).foldMap(runner))
@@ -117,9 +115,7 @@ object FreeTests extends FreeTestsInstances {
 }
 
 sealed trait FreeTestsInstances {
-  val headOptionU: FunctionK[List,Option] = new FunctionK[List,Option] {
-    def apply[A](fa: List[A]): Option[A] = fa.headOption
-  }
+  val headOptionU = λ[FunctionK[List,Option]](_.headOption)
 
   private def freeGen[F[_], A](maxDepth: Int)(implicit F: Arbitrary[F[A]], A: Arbitrary[A]): Gen[Free[F, A]] = {
     val noFlatMapped = Gen.oneOf(

tests/src/test/scala/cats/tests/FunctionKTests.scala

@@ -7,15 +7,11 @@ import cats.data.NonEmptyList
 import cats.laws.discipline.arbitrary._
 
 class FunctionKTests extends CatsSuite {
-  val listToOption =
-    new FunctionK[List, Option] {
-      def apply[A](fa: List[A]): Option[A] = fa.headOption
-    }
 
-  val optionToList =
-    new FunctionK[Option, List] {
-      def apply[A](fa: Option[A]): List[A] = fa.toList
-    }
+  val listToOption = λ[FunctionK[List, Option]](_.headOption)
+
+  val optionToList = λ[FunctionK[Option, List]](_.toList)
+
 
   sealed trait Test1Algebra[A] {
     def v : A
@@ -29,13 +25,9 @@ class FunctionKTests extends CatsSuite {
 
   case class Test2[A](v : A) extends Test2Algebra[A]
 
-  object Test1NT extends FunctionK[Test1Algebra,Id] {
-    override def apply[A](fa: Test1Algebra[A]): Id[A] = fa.v
-  }
+  val Test1NT = λ[FunctionK[Test1Algebra,Id]](_.v)
 
-  object Test2NT extends FunctionK[Test2Algebra,Id] {
-    override def apply[A](fa: Test2Algebra[A]): Id[A] = fa.v
-  }
+  val Test2NT = λ[FunctionK[Test2Algebra,Id]](_.v)
 
   type T[A] = Coproduct[Test1Algebra, Test2Algebra, A]
 

tests/src/test/scala/cats/tests/KleisliTests.scala

@@ -126,7 +126,7 @@ class KleisliTests extends CatsSuite {
 
   test("transform") {
     val opt = Kleisli { (x: Int) => Option(x.toDouble) }
-    val optToList = new FunctionK[Option,List] { def apply[A](fa: Option[A]): List[A] = fa.toList }
+    val optToList = λ[FunctionK[Option,List]](_.toList)
     val list = opt.transform(optToList)
 
     val is = 0.to(10).toList