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Using inverse functions to encode predicate function injectivity #545

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Using inverse functions to encode predicate function injectivity #545

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29 changes: 15 additions & 14 deletions src/main/scala/viper/carbon/modules/impls/DefaultHeapModule.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -451,6 +451,8 @@ class DefaultHeapModule(val verifier: Verifier)
val f0 = FuncApp(predicate, vars, t)
val f1 = predicateMaskField(f0)
val f2 = FuncApp(pmField, vars, pmT)
val inverseFunctionInfo = varDecls map (vd => (Identifier(s"${p.name}_inv_${vd.name.name}"), vd.typ))
val inversePMaskFunctionInfo = varDecls map (vd => (Identifier(s"${p.name}_pmask_inv_${vd.name.name}"), vd.typ))
TypeDecl(predicateMetaTypeOf(p)) ++
Func(predicate, varDecls, t) ++
Func(pmField, varDecls, pmT) ++
Expand All @@ -459,23 +461,22 @@ class DefaultHeapModule(val verifier: Verifier)
Axiom(MaybeForall(varDecls, Trigger(f0), getPredicateOrWandId(f0) === IntLit(predId))) ++
Func(predicateTriggerIdentifier(p), Seq(LocalVarDecl(heapName, heapTyp), LocalVarDecl(Identifier("pred"), predicateVersionFieldType())), Bool) ++
Func(predicateTriggerAnyStateIdentifier(p), Seq(LocalVarDecl(Identifier("pred"), predicateVersionFieldType())), Bool) ++
(inverseFunctionInfo map (ifi => {
Func(ifi._1, Seq(LocalVarDecl(Identifier("p"), t)),ifi._2)
})) ++
(inversePMaskFunctionInfo map (ifi => {
Func(ifi._1, Seq(LocalVarDecl(Identifier("pm"), pmT)), ifi._2)
})) ++
{
// axiom that two predicate identifiers can only be the same, if all arguments
// are the same (e.g., we immediatly know that valid(1) != valid(2))
if (vars.size == 0) Nil
// are the same (e.g., we immediately know that valid(1) != valid(2))
if (vars.isEmpty) Nil
else {
val varDecls2 = varDecls map (
v => LocalVarDecl(Identifier(v.name.name + "2")(v.name.namespace), v.typ))
val vars2 = varDecls2 map (_.l)
var varsEqual = All((vars zip vars2) map {
case (v1, v2) => v1 === v2
})
val f0_2 = FuncApp(predicate, vars2, t)
val f2_2 = FuncApp(pmField, vars2, t)
Axiom(Forall(varDecls ++ varDecls2, Trigger(Seq(f0, f0_2)),
(f0 === f0_2) ==> varsEqual)) ++
Axiom(Forall(varDecls ++ varDecls2, Trigger(Seq(f2, f2_2)),
(f2 === f2_2) ==> varsEqual))
val inverseAppEqs = inverseFunctionInfo.zip(vars) map (ifiv => FuncApp(ifiv._1._1, Seq(f0), ifiv._1._2) === ifiv._2)
val injectiveAxiom = Axiom(Forall(varDecls, Trigger(f0), All(inverseAppEqs)))
val inversePMaskAppEqs = inversePMaskFunctionInfo.zip(vars) map (ifiv => FuncApp(ifiv._1._1, Seq(f2), ifiv._1._2) === ifiv._2)
val injectivePMaskAxiom = Axiom(Forall(varDecls, Trigger(f2), All(inversePMaskAppEqs)))
injectiveAxiom ++ injectivePMaskAxiom
}
}
}
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