From 1ad0810ce091378ef8616ec305750363bf446d3a Mon Sep 17 00:00:00 2001
From: Philippe Suter <philippe.suter@gmail.com>
Date: Wed, 4 Aug 2010 18:49:17 +0000
Subject: [PATCH]

---
 demo-munch                      |   2 +-
 lib-bin/libz3.so                | Bin 8783743 -> 8884287 bytes
 lib/z3.jar                      | Bin 133387 -> 136483 bytes
 src/purescala/Analysis.scala    | 237 ++++++++++++--------------
 src/purescala/Common.scala      |   4 +
 src/purescala/Definitions.scala |  21 +--
 src/purescala/Trees.scala       | 293 +++++++++++++++++++++++++-------
 src/purescala/Z3Solver.scala    |  11 +-
 8 files changed, 369 insertions(+), 199 deletions(-)

diff --git a/demo-munch b/demo-munch
index d52320836..9b1b6a7de 100644
--- a/demo-munch
+++ b/demo-munch
@@ -1 +1 @@
-./scalac-funcheck -P:funcheck:extensions=multisets.Main testcases/MultiExample.scala
+./scalac-funcheck -P:funcheck:nodefaults -P:funcheck:extensions=multisets.Main testcases/MultiExample.scala
diff --git a/lib-bin/libz3.so b/lib-bin/libz3.so
index bb6fcf57d8f85161e3e14738aae7a3c090b8cdb5..a6ea716dd3c70164f2308536703537ae61663166 100755
GIT binary patch
delta 3662991
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diff --git a/lib/z3.jar b/lib/z3.jar
index c9534e6d12ab40fd170b1b06ebafced18cf16689..33340bcc3861619181a3b03d4b43770713ef8c57 100644
GIT binary patch
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diff --git a/src/purescala/Analysis.scala b/src/purescala/Analysis.scala
index af93704e3..b989ce0fd 100644
--- a/src/purescala/Analysis.scala
+++ b/src/purescala/Analysis.scala
@@ -136,155 +136,142 @@ class Analysis(val program: Program) {
       }
 
       import Analysis._
-      // reporter.info("Before unrolling:")
-      // reporter.info(expandLets(withPrec))
-      val expr0 = unrollRecursiveFunctions(program, withPrec, Settings.unrollingLevel)
-      // reporter.info("Before inlining:")
-      // reporter.info(expandLets(expr0))
-      val expr1 = inlineFunctionsAndContracts(program, expr0)
-      // reporter.info("Before PM-rewriting:")
-      // reporter.info(expandLets(expr1))
-      val expr2 = rewriteSimplePatternMatching(expr1)
-      // reporter.info("After PM-rewriting:")
-      // reporter.info(expandLets(expr2))
-      assert(wellOrderedLets(expr2))
-      expr2
+    
+      if(Settings.experimental) {
+        reporter.info("Raw:")
+        reporter.info(withPrec)
+        reporter.info("Raw, expanded:")
+        reporter.info(expandLets(withPrec))
+      }
+      reporter.info(" - inlining...")
+      val expr0 = inlineNonRecursiveFunctions(program, withPrec)
+      if(Settings.experimental) {
+        reporter.info("Inlined:")
+        reporter.info(expr0)
+        reporter.info("Inlined, expanded:")
+        reporter.info(expandLets(expr0))
+      }
+      reporter.info(" - unrolling...")
+      val expr1 = unrollRecursiveFunctions(program, expr0, Settings.unrollingLevel)
+      if(Settings.experimental) {
+        reporter.info("Unrolled:")
+        reporter.info(expr1)
+        reporter.info("Unrolled, expanded:")
+        reporter.info(expandLets(expr1))
+      }
+      reporter.info(" - inlining contracts...")
+      val expr2 = inlineContracts(expr1)
+      if(Settings.experimental) {
+        reporter.info("Contract'ed:")
+        reporter.info(expr2)
+        reporter.info("Contract'ed, expanded:")
+        reporter.info(expandLets(expr2))
+      }
+      reporter.info(" - converting pattern-matching...")
+      val expr3 = rewriteSimplePatternMatching(expr2)
+      if(Settings.experimental) {
+        reporter.info("Pattern'ed:")
+        reporter.info(expr3)
+        reporter.info("Pattern'ed, expanded:")
+        reporter.info(expandLets(expr3))
+      }
+      expr3
     }
   }
-
 }
 
 object Analysis {
-  // Warning: this should only be called on a top-level formula ! It will add
-  // new variables and implications in a way that preserves the validity of the
-  // formula.
-  def inlineFunctionsAndContracts(program: Program, expr: Expr) : Expr = {
-    var extras : List[Expr] = Nil
+  private def inlineFunctionCall(f : FunctionInvocation) : Expr = {
+    val FunctionInvocation(fd, args) = f
+    val newLetIDs = fd.args.map(a => FreshIdentifier("arg_" + a.id.name, true).setType(a.tpe)).toList
+    val substMap = Map[Expr,Expr]((fd.args.map(_.toVariable) zip newLetIDs.map(Variable(_))) : _*)
+    val newBody = replace(substMap, fd.body.get)
+    simplifyLets((newLetIDs zip args).foldRight(newBody)((iap, e) => Let(iap._1, iap._2, e)))
+  }
 
+  def inlineNonRecursiveFunctions(program: Program, expression: Expr) : Expr = {
     def applyToCall(e: Expr) : Option[Expr] = e match {
-      case f @ FunctionInvocation(fd, args) => {
-        val fArgsAsVars: List[Variable] = fd.args.map(_.toVariable).toList
-        val fParamsAsLetVars: List[Identifier] = fd.args.map(a => FreshIdentifier("arg", true).setType(a.tpe)).toList
-        val fParamsAsLetVarVars = fParamsAsLetVars.map(Variable(_))
-  
-        def mkBigLet(ex: Expr) : Expr = (fParamsAsLetVars zip args).foldRight(ex)((iap, e) => {
-          Let(iap._1, iap._2, e)
-        })
-
-        val substMap = Map[Expr,Expr]((fArgsAsVars zip fParamsAsLetVarVars) : _*)
-        if(fd.hasPostcondition) {
-          val newVar = Variable(FreshIdentifier("call", true)).setType(fd.returnType)
-          extras = And(
-            replace(substMap + (ResultVariable() -> newVar), fd.postcondition.get),
-            Equals(newVar, FunctionInvocation(fd, fParamsAsLetVarVars).setType(fd.returnType))
-          ) :: extras
-          Some(mkBigLet(newVar))
-          /* END CHANGE */
-        } else if(fd.hasImplementation && !program.isRecursive(fd)) { // means we can inline at least one level...
-          Some(mkBigLet(replace(substMap, fd.body.get)))
-        } else { // we can't do much for calls to recursive functions or to functions with no bodies
-          None
-        }
-      }
-      case o => None
+      case f @ FunctionInvocation(fd, args) if fd.hasImplementation && !program.isRecursive(fd) => Some(inlineFunctionCall(f))
+      case _ => None
     }
 
-    val finalE = searchAndReplace(applyToCall)(expr)
-    val toReturn = pulloutLets(Implies(And(extras.reverse), finalE))
+    var change: Boolean = true
+    var toReturn: Expr = expression
+    while(change) {
+      val (t,c) = searchAndReplaceDFSandTrackChanges(applyToCall)(toReturn)
+      change = c
+      toReturn = t
+    }
     toReturn
   }
 
-  // Warning: this should only be called on a top-level formula ! It will add
-  // new variables and implications in a way that preserves the validity of the
-  // formula.
   def unrollRecursiveFunctions(program: Program, expression: Expr, times: Int) : Expr = {
-    def unroll(exx: Expr) : (Expr,Seq[Expr]) = {
-      var extras : List[Expr] = Nil
+    def applyToCall(e: Expr) : Option[Expr] = e match {
+      case f @ FunctionInvocation(fd, args) if fd.hasImplementation && program.isRecursive(fd) => Some(inlineFunctionCall(f))
+      case _ => None
+    }
 
-      def urf(expr: Expr, left: Int) : Expr = {
-        def unrollCall(t: Int)(e: Expr) : Option[Expr] = e match {
-          case f @ FunctionInvocation(fd, args) if fd.hasImplementation && program.isRecursive(fd) => {
-            val newLetIDs = fd.args.map(a => FreshIdentifier(a.id.name, true).setType(a.tpe))
-            val newLetVars = newLetIDs.map(Variable(_))
-            val substs: Map[Expr,Expr] = Map((fd.args.map(_.toVariable) zip newLetVars) :_*)
-            val bodyWithLetVars: Expr = replace(substs, fd.body.get)
-            if(fd.hasPostcondition) {
-              val post = fd.postcondition.get
-              val newVar = Variable(FreshIdentifier("call", true)).setType(fd.returnType)
-              val newExtra1 = Equals(newVar, bodyWithLetVars)
-              val newExtra2 = replace(substs + (ResultVariable() -> newVar), post)
-              val bigLet = (newLetIDs zip args).foldLeft(And(newExtra1, newExtra2))((e,p) => Let(p._1, p._2, e))
-              extras = urf(bigLet, t-1) :: extras
-              // println("*********************************")
-              // println(bigLet)
-              // println(" --- from -----------------------")
-              // println(f)
-              // println(" --- newVar is ------------------")
-              // println(newVar)
-              // println("*********************************")
-              Some(newVar)
-            } else {
-              val bigLet = (newLetIDs zip args).foldLeft(bodyWithLetVars)((e,p) => Let(p._1, p._2, e))
-              Some(urf(bigLet, t-1))
-            }
-          }
-          case o => None
-        }
+    var remaining = if(times < 0) 0 else times
+    var change: Boolean = true
+    var toReturn: Expr = expression
+    while(remaining > 0 && change) {
+      val (t,c) = searchAndReplaceDFSandTrackChanges(applyToCall)(toReturn)
+      change = c
+      toReturn = inlineNonRecursiveFunctions(program, t)
+      remaining = remaining - 1
+    }
+    toReturn
+  }
 
-        if(left > 0)
-          searchAndReplace(unrollCall(left), false)(expr)
-        else
-          expr
+  def inlineContracts(expression: Expr) : Expr = {
+    var trueThings: List[Expr] = Nil
+
+    def applyToCall(e: Expr) : Option[Expr] = e match {
+      case f @ FunctionInvocation(fd, args) if fd.hasPostcondition => {
+        val argsAsLet   = fd.args.map(a => FreshIdentifier("parg_" + a.id.name, true).setType(a.tpe)).toList
+        val argsAsLetVars = argsAsLet.map(Variable(_))
+        val resultAsLet = FreshIdentifier("call_" + fd.id.name, true).setType(f.getType)
+        val newFunCall = FunctionInvocation(fd, argsAsLetVars)
+        val substMap = Map[Expr,Expr]((fd.args.map(_.toVariable) zip argsAsLetVars) : _*) + (ResultVariable() -> Variable(resultAsLet))
+        // this thing is full of let variables! We will need to lift the let
+        // defs. later to make sure they capture this
+        val trueFact = replace(substMap, fd.postcondition.get)
+        val defList: Seq[(Identifier,Expr)] = ((argsAsLet :+ resultAsLet) zip (args :+ newFunCall))
+        trueThings = trueFact :: trueThings
+        // again: these let defs. need eventually to capture the "true thing"
+        Some(defList.foldRight[Expr](Variable(resultAsLet))((iap, e) => Let(iap._1, iap._2, e)))
       }
-      val finalE = urf(exx, times)
-      (finalE, extras)
+      case _ => None
     }
-
-    val (savedLets, naked) = pulloutAndKeepLets(expression)
-    val infoFromLets: Seq[(Expr,Seq[Expr])] = savedLets.map(_._2).map(unroll(_))
-    val extrasFromLets: Seq[Expr] = infoFromLets.map(_._2).flatten
-    val newLetBodies: Seq[Expr] = infoFromLets.map(_._1)
-    val newSavedLets: Seq[(Identifier,Expr)] = savedLets.map(_._1) zip newLetBodies
-    val (cleaned, extras) = unroll(naked)
-    val toReturn = rebuildLets(newSavedLets, Implies(And(extrasFromLets ++ extras), cleaned))
-    toReturn
+    val result = searchAndReplaceDFS(applyToCall)(expression)
+    liftLets(Implies(And(trueThings.reverse), result))
   }
 
   // Rewrites pattern matching expressions where the cases simply correspond to
   // the list of constructors
   def rewriteSimplePatternMatching(expression: Expr) : Expr = {
-    def rspm(expr: Expr) : (Expr,Seq[Expr]) = {
-      var extras : List[Expr] = Nil
+    var extras : List[Expr] = Nil
 
-      def rewritePM(e: Expr) : Option[Expr] = e match {
-        // case NotSoSimplePatternMatching(_) => None
-        case SimplePatternMatching(scrutinee, classType, casesInfo) => Some({
-          val newVar = Variable(FreshIdentifier("pm", true)).setType(e.getType)
-          val scrutAsLetID = FreshIdentifier("scrut", true).setType(scrutinee.getType)
-          val lle : List[(Variable,List[Expr])] = casesInfo.map(cseInfo => {
-            val (ccd, newPID, argIDs, rhs) = cseInfo
-            val newPVar = Variable(newPID)
-            val argVars = argIDs.map(Variable(_))
-            val (rewrittenRHS, moreExtras) = rspm(rhs)
-            (newPVar, List(Equals(newPVar, CaseClass(ccd, argVars)), Implies(Equals(Variable(scrutAsLetID), newPVar), Equals(newVar, rewrittenRHS))) ::: moreExtras.toList)
-          }).toList
-          val (newPVars, newExtras) = lle.unzip
-          extras = Let(scrutAsLetID, scrutinee, And(Or(newPVars.map(Equals(Variable(scrutAsLetID), _))), And(newExtras.flatten))) :: extras
-          newVar
-        })
-        case _ => None
+    def rewritePM(e: Expr) : Option[Expr] = e match {
+      // case NotSoSimplePatternMatching(_) => None
+      case SimplePatternMatching(scrutinee, classType, casesInfo) => {
+        val newVar = Variable(FreshIdentifier("pm", true)).setType(e.getType)
+        val scrutAsLetID = FreshIdentifier("scrut", true).setType(scrutinee.getType)
+        val lle : List[(Variable,List[Expr])] = casesInfo.map(cseInfo => {
+          val (ccd, newPID, argIDs, rhs) = cseInfo
+          val newPVar = Variable(newPID)
+          val argVars = argIDs.map(Variable(_))
+          (newPVar, List(Equals(newPVar, CaseClass(ccd, argVars)), Implies(Equals(Variable(scrutAsLetID), newPVar), Equals(newVar, rhs))))
+        }).toList
+        val (newPVars, newExtras) = lle.unzip
+        extras = Let(scrutAsLetID, scrutinee, And(Or(newPVars.map(Equals(Variable(scrutAsLetID), _))), And(newExtras.flatten))) :: extras 
+        Some(newVar)
       }
-      
-      val cleanerTree = searchAndReplace(rewritePM)(expr) 
-      (cleanerTree, extras.reverse)
+      case m @ MatchExpr(s,_) => Settings.reporter.error("Untranslatable PM expression on type " + s.getType + " : " + m); None
+      case _ => None
     }
-    val (savedLets, naked) = pulloutAndKeepLets(expression)
-    val infoFromLets: Seq[(Expr,Seq[Expr])] = savedLets.map(_._2).map(rspm(_))
-    val extrasFromLets: Seq[Expr] = infoFromLets.map(_._2).flatten
-    val newLetBodies: Seq[Expr] = infoFromLets.map(_._1)
-    val newSavedLets: Seq[(Identifier,Expr)] = savedLets.map(_._1) zip newLetBodies
-    val (cleaned, extras) = rspm(naked)
-    val toReturn = rebuildLets(newSavedLets, Implies(And(extrasFromLets ++ extras), cleaned))
-    toReturn
+
+    val newExpr = searchAndReplaceDFS(rewritePM)(expression)
+    liftLets(Implies(And(extras), newExpr))
   }
 }
diff --git a/src/purescala/Common.scala b/src/purescala/Common.scala
index bd99628e7..7e326ca3c 100644
--- a/src/purescala/Common.scala
+++ b/src/purescala/Common.scala
@@ -26,6 +26,10 @@ object Common {
     }
 
     def uniqueName : String = name + id
+
+    private var _islb: Boolean = false
+    def markAsLetBinder : Identifier = { _islb = true; this }
+    def isLetBinder : Boolean = _islb
   }
 
   private object UniqueCounter {
diff --git a/src/purescala/Definitions.scala b/src/purescala/Definitions.scala
index 90d418bb7..67fe9fd5b 100644
--- a/src/purescala/Definitions.scala
+++ b/src/purescala/Definitions.scala
@@ -48,19 +48,20 @@ object Definitions {
     lazy val classHierarchyRoots : Seq[ClassTypeDef] = defs.filter(_.isInstanceOf[ClassTypeDef]).map(_.asInstanceOf[ClassTypeDef]).filter(!_.hasParent)
 
     lazy val (callGraph, callers, callees) = {
-      var resSet: Set[(FunDef,FunDef)] =
-        new scala.collection.immutable.HashSet[(FunDef,FunDef)]()
+      type CallGraph = Set[(FunDef,FunDef)]
 
-      def applyToFunCall(f1: FunDef)(e: Expr) : Option[Expr] = e match {
-        case f @ FunctionInvocation(f2, _) => { resSet = resSet + ((f1,f2)); Some(f) }
-        case _ => None
+      val convert: Expr=>CallGraph = (_ => Set.empty)
+      val combine: (CallGraph,CallGraph)=>CallGraph = (s1,s2) => s1 ++ s2
+      def compute(fd: FunDef)(e: Expr, g: CallGraph) : CallGraph = e match {
+        case f @ FunctionInvocation(f2, _) => g + ((fd, f2))
+        case _ => g
       }
 
-      for(funDef <- definedFunctions) {
-        funDef.precondition.map(searchAndReplace(applyToFunCall(funDef))(_))
-        funDef.body.map(searchAndReplace(applyToFunCall(funDef))(_))
-        funDef.postcondition.map(searchAndReplace(applyToFunCall(funDef))(_))
-      }
+      val resSet: CallGraph = (for(funDef <- definedFunctions) yield {
+        funDef.precondition.map(treeCatamorphism[CallGraph](convert, combine, compute(funDef)_, _)).getOrElse(Set.empty) ++
+        funDef.body.map(treeCatamorphism[CallGraph](convert, combine, compute(funDef)_, _)).getOrElse(Set.empty) ++
+        funDef.postcondition.map(treeCatamorphism[CallGraph](convert, combine, compute(funDef)_, _)).getOrElse(Set.empty)
+      }).reduceLeft(_ ++ _)
 
       var callers: Map[FunDef,Set[FunDef]] =
         new scala.collection.immutable.HashMap[FunDef,Set[FunDef]]
diff --git a/src/purescala/Trees.scala b/src/purescala/Trees.scala
index fbe596910..2b0d54130 100644
--- a/src/purescala/Trees.scala
+++ b/src/purescala/Trees.scala
@@ -16,6 +16,7 @@ object Trees {
 
   /* Like vals */
   case class Let(binder: Identifier, value: Expr, body: Expr) extends Expr {
+    binder.markAsLetBinder
     val et = body.getType
     if(et != NoType)
       setType(et)
@@ -26,7 +27,23 @@ object Trees {
     val fixedType = funDef.returnType
   }
   case class IfExpr(cond: Expr, then: Expr, elze: Expr) extends Expr 
-  case class MatchExpr(scrutinee: Expr, cases: Seq[MatchCase]) extends Expr {
+
+  object MatchExpr {
+    def apply(scrutinee: Expr, cases: Seq[MatchCase]) : MatchExpr = {
+      scrutinee.getType match {
+        case a: AbstractClassType => new MatchExpr(scrutinee, cases)
+        case c: CaseClassType => new MatchExpr(scrutinee, cases.filter(_.pattern match {
+          case CaseClassPattern(_, ccd, _) if ccd != c.classDef => false
+          case _ => true
+        }))
+        case _ => scala.Predef.error("Constructing match expression on non-class type.")
+      }
+    }
+
+    def unapply(me: MatchExpr) : Option[(Expr,Seq[MatchCase])] = if (me == null) None else Some((me.scrutinee, me.cases))
+  }
+
+  class MatchExpr(val scrutinee: Expr, val cases: Seq[MatchCase]) extends Expr {
     def scrutineeClassType: ClassType = scrutinee.getType.asInstanceOf[ClassType]
   }
 
@@ -35,13 +52,16 @@ object Trees {
     val rhs: Expr
     val theGuard: Option[Expr]
     def hasGuard = theGuard.isDefined
+    def expressions: Seq[Expr]
   }
 
   case class SimpleCase(pattern: Pattern, rhs: Expr) extends MatchCase {
     val theGuard = None
+    def expressions = List(rhs)
   }
   case class GuardedCase(pattern: Pattern, guard: Expr, rhs: Expr) extends MatchCase {
     val theGuard = Some(guard)
+    def expressions = List(guard, rhs)
   }
 
   sealed abstract class Pattern
@@ -338,14 +358,14 @@ object Trees {
   // Warning ! This may loop forever if the substitutions are not
   // well-formed!
   def replace(substs: Map[Expr,Expr], expr: Expr) : Expr = {
-    searchAndReplace(substs.get)(expr)
+    searchAndReplaceDFS(substs.get)(expr)
   }
 
   def searchAndReplace(subst: Expr=>Option[Expr], recursive: Boolean=true)(expr: Expr) : Expr = {
     def rec(ex: Expr, skip: Expr = null) : Expr = (if (ex == skip) None else subst(ex)) match {
       case Some(newExpr) => {
         if(newExpr.getType == NoType) {
-          Settings.reporter.warning("REPLACING IN EXPRESSION WITH AN UNTYPED TREE ! " + ex + " --to--> " + newExpr)
+          Settings.reporter.error("REPLACING IN EXPRESSION WITH AN UNTYPED TREE ! " + ex + " --to--> " + newExpr)
         }
         if(ex == newExpr)
           if(recursive) rec(ex, ex) else ex
@@ -415,29 +435,153 @@ object Trees {
     rec(expr)
   }
 
-  def variablesOf(expr: Expr) : Set[Identifier] = {
-    def rec(ex: Expr, lets: Set[Identifier]) : Set[Identifier] = ex match {
+  def searchAndReplaceDFS(subst: Expr=>Option[Expr])(expr: Expr) : Expr = {
+    val (res,_) = searchAndReplaceDFSandTrackChanges(subst)(expr)
+    res
+  }
+
+  def searchAndReplaceDFSandTrackChanges(subst: Expr=>Option[Expr])(expr: Expr) : (Expr,Boolean) = {
+    var somethingChanged: Boolean = false
+    def applySubst(ex: Expr) : Expr = subst(ex) match {
+      case None => ex
+      case Some(newEx) => {
+        somethingChanged = true
+        if(newEx.getType == NoType) {
+          Settings.reporter.warning("REPLACING WITH AN UNTYPED EXPRESSION !")
+        }
+        newEx
+      }
+    }
+
+    def rec(ex: Expr) : Expr = ex match {
       case l @ Let(i,e,b) => {
-        val newLets = lets + i
-        rec(e, newLets) ++ rec(b, newLets)
+        val re = rec(e)
+        val rb = rec(b)
+        applySubst(if(re != e || rb != b) {
+          Let(i, re, rb).setType(l.getType)
+        } else {
+          l
+        })
       }
-      case Variable(i) => if(lets(i)) Set.empty[Identifier] else Set(i)
-      case n @ NAryOperator(args, _) => if(args.isEmpty) Set.empty[Identifier] else args.map(rec(_, lets)).reduceLeft(_ ++ _)
-      case b @ BinaryOperator(t1,t2,_) => rec(t1,lets) ++ rec(t2,lets)
-      case u @ UnaryOperator(t,_) => rec(t, lets)
-      case i @ IfExpr(t1,t2,t3) => rec(t1,lets) ++ rec(t2,lets) ++ rec(t3,lets)
-      case m @ MatchExpr(scrut,cses) => rec(scrut, lets) ++ cses.map(inCase(_, lets)).reduceLeft(_ ++ _)
-      case t if t.isInstanceOf[Terminal] => Set.empty[Identifier]
-      case unhandled => scala.Predef.error("Non-terminal case should be handled in searchAndReplace: " + unhandled)
+      case n @ NAryOperator(args, recons) => {
+        var change = false
+        val rargs = args.map(a => {
+          val ra = rec(a)
+          if(ra != a) {
+            change = true  
+            ra
+          } else {
+            a
+          }            
+        })
+        applySubst(if(change) {
+          recons(rargs).setType(n.getType)
+        } else {
+          n
+        })
+      }
+      case b @ BinaryOperator(t1,t2,recons) => {
+        val r1 = rec(t1)
+        val r2 = rec(t2)
+        applySubst(if(r1 != t1 || r2 != t2) {
+          recons(r1,r2).setType(b.getType)
+        } else {
+          b
+        })
+      }
+      case u @ UnaryOperator(t,recons) => {
+        val r = rec(t)
+        applySubst(if(r != t) {
+          recons(r).setType(u.getType)
+        } else {
+          u
+        })
+      }
+      case i @ IfExpr(t1,t2,t3) => {
+        val r1 = rec(t1)
+        val r2 = rec(t2)
+        val r3 = rec(t3)
+        applySubst(if(r1 != t1 || r2 != t2 || r3 != t3) {
+          IfExpr(rec(t1),rec(t2),rec(t3)).setType(i.getType)
+        } else {
+          i
+        })
+      }
+      case m @ MatchExpr(scrut,cses) => {
+        val rscrut = rec(scrut)
+        val (newCses,changes) = cses.map(inCase(_)).unzip
+        applySubst(if(rscrut != scrut || changes.exists(res=>res)) {
+          MatchExpr(rscrut, newCses).setType(m.getType)
+        } else {
+          m
+        })
+      }
+      case t if t.isInstanceOf[Terminal] => applySubst(t)
+      case unhandled => scala.Predef.error("Non-terminal case should be handled in searchAndReplaceDFS: " + unhandled)
     }
 
-    // note that the identifiers in the patterns are not included if they don't show up on the rhs.
-    def inCase(cse: MatchCase, lets: Set[Identifier]) : Set[Identifier] = cse match {
-      case SimpleCase(pat, rhs) => rec(rhs, lets)
-      case GuardedCase(pat, guard, rhs) => rec(guard, lets) ++ rec(rhs, lets)
+    def inCase(cse: MatchCase) : (MatchCase,Boolean) = cse match {
+      case s @ SimpleCase(pat, rhs) => {
+        val rrhs = rec(rhs)
+        if(rrhs != rhs) {
+          (SimpleCase(pat, rrhs), true)
+        } else {
+          (s, false)
+        }
+      }
+      case g @ GuardedCase(pat, guard, rhs) => {
+        val rguard = rec(guard)
+        val rrhs = rec(rhs)
+        if(rguard != guard || rrhs != rhs) {
+          (GuardedCase(pat, rguard, rrhs), true)
+        } else {
+          (g, false)
+        }
+      }
+    }
+
+    val res = rec(expr)
+    (res, somethingChanged)
+  }
+
+  // convert describes how to compute a value for the leaves (that includes
+  // functions with no args.)
+  // combine descriess how to combine two values
+  def treeCatamorphism[A](convert: Expr=>A, combine: (A,A)=>A, expression: Expr) : A = {
+    treeCatamorphism(convert, combine, (e:Expr,a:A)=>a, expression)
+  }
+  // compute allows the catamorphism to change the combined value depending on the tree
+  def treeCatamorphism[A](convert: Expr=>A, combine: (A,A)=>A, compute: (Expr,A)=>A, expression: Expr) : A = {
+    def rec(expr: Expr) : A = expr match {
+      case l @ Let(_, e, b) => compute(l, combine(rec(e), rec(b)))
+      case n @ NAryOperator(args, _) => {
+        if(args.size == 0)
+          compute(n, convert(n))
+        else
+          compute(n, args.map(rec(_)).reduceLeft(combine))
+      }
+      case b @ BinaryOperator(a1,a2,_) => compute(b, combine(rec(a1),rec(a2)))
+      case u @ UnaryOperator(a,_) => compute(u, rec(a))
+      case i @ IfExpr(a1,a2,a3) => compute(i, combine(combine(rec(a1), rec(a2)), rec(a3)))
+      case m @ MatchExpr(scrut, cses) => compute(m, (scrut +: cses.flatMap(_.expressions)).map(rec(_)).reduceLeft(combine))
+      case t: Terminal => compute(t, convert(t))
+      case unhandled => scala.Predef.error("Non-terminal case should be handled in treeCatamorphism: " + unhandled)
     }
 
-    rec(expr, Set.empty)
+    rec(expression)
+  }
+
+  def variablesOf(expr: Expr) : Set[Identifier] = {
+    def convert(t: Expr) : Set[Identifier] = t match {
+      case Variable(i) => Set(i)
+      case _ => Set.empty
+    }
+    def combine(s1: Set[Identifier], s2: Set[Identifier]) = s1 ++ s2
+    def compute(t: Expr, s: Set[Identifier]) = t match {
+      case Let(i,_,_) => s -- Set(i)
+      case _ => s
+    }
+    treeCatamorphism(convert, combine, compute, expr)
   }
 
   /* Simplifies let expressions:
@@ -448,15 +592,12 @@ object Trees {
    */
   def simplifyLets(expr: Expr) : Expr = {
     def simplerLet(t: Expr) : Option[Expr] = t match {
-      case letExpr @ Let(i, Variable(v), b) => Some(replace(Map((Variable(i) -> Variable(v))), b))
-      case letExpr @ Let(i, l: Literal[_], b) => Some(replace(Map((Variable(i) -> l)), b))
+      case letExpr @ Let(i, t: Terminal, b) => Some(replace(Map((Variable(i) -> t)), b))
       case letExpr @ Let(i,e,b) => {
-        var occurences = 0
-        def incCount(tr: Expr) = tr match {
-          case Variable(x) if x == i => { occurences = occurences + 1; None } 
-          case _ => None
-        }
-        searchAndReplace(incCount, false)(b)
+        val occurences = treeCatamorphism[Int]((e:Expr) => e match {
+          case Variable(x) if x == i => 1
+          case _ => 0
+        }, (x:Int,y:Int)=>x+y, b)
         if(occurences == 0) {
           Some(b)
         } else if(occurences == 1) {
@@ -470,30 +611,72 @@ object Trees {
     searchAndReplace(simplerLet)(expr)
   }
 
-  /* Rewrites the expression so that all lets are at the top levels. */
-  def pulloutLets(expr: Expr) : Expr = {
-    val (storedLets, noLets) = pulloutAndKeepLets(expr)
-    rebuildLets(storedLets, noLets)
-  }
+  // Pulls out all let constructs to the top level, and makes sure they're
+  // properly ordered.
+  private type DefPair  = (Identifier,Expr)
+  private type DefPairs = List[DefPair]
+  private def allLetDefinitions(expr: Expr) : DefPairs = treeCatamorphism[DefPairs](
+    (e: Expr) => Nil,
+    (s1: DefPairs, s2: DefPairs) => s1 ::: s2,
+    (e: Expr, dps: DefPairs) => e match {
+      case Let(i, e, _) => (i,e) :: dps
+      case _ => dps
+    },
+    expr)
   
-  // new code (keep this if nested lets can appear in the value part, too)
-  def pulloutAndKeepLets(expr: Expr) : (List[(Identifier,Expr)], Expr) = {
-    var storedLets: List[(Identifier,Expr)] = Nil
-
-    def storeLet(t: Expr) : Option[Expr] = t match {
-      case l @ Let(i, e, b) =>
-        val (stored, value) = pulloutAndKeepLets(e)
-        storedLets :::= stored
-        storedLets ::= i -> value
-        Some(b)
-      case _ => None
+  private def killAllLets(expr: Expr) : Expr = searchAndReplaceDFS((e: Expr) => e match {
+    case Let(i,_,ex) => Some(ex)
+    case _ => None
+  })(expr)
+
+  def liftLets(expr: Expr) : Expr = {
+    val initialDefinitionPairs = allLetDefinitions(expr)
+    val definitionPairs = initialDefinitionPairs.map(p => (p._1, killAllLets(p._2)))
+    val occursLists : Map[Identifier,Set[Identifier]] = Map(definitionPairs.map((dp: DefPair) => (dp._1 -> variablesOf(dp._2).toSet.filter(_.isLetBinder))) : _*)
+    var newList : DefPairs = Nil
+    var placed  : Set[Identifier] = Set.empty
+    val toPlace = definitionPairs.size
+    var placedC = 0
+    var traversals = 0
+
+    while(placedC < toPlace) {
+      if(traversals > toPlace + 1) {
+        scala.Predef.error("Cycle in let definitions or multiple definition for the same identifier in liftLets : " + definitionPairs.mkString("\n"))
+      }
+      for((id,ex) <- definitionPairs) if (!placed(id)) {
+        if((occursLists(id) -- placed) == Set.empty) {
+          placed = placed + id
+          newList = (id,ex) :: newList
+          placedC = placedC + 1
+        }
+      }
+      traversals = traversals + 1
     }
-    val noLets = searchAndReplace(storeLet)(expr)
-    (storedLets, noLets)
+
+    val noLets = killAllLets(expr)
+
+    val res = (newList.foldLeft(noLets)((e,iap) => Let(iap._1, iap._2, e)))
+    simplifyLets(res)
   }
 
-  def rebuildLets(lets: Seq[(Identifier,Expr)], expr: Expr) : Expr = {
-    lets.foldLeft(expr)((e,p) => Let(p._1, p._2, e))
+  def wellOrderedLets(tree : Expr) : Boolean = {
+    val pairs = allLetDefinitions(tree)
+    val definitions: Set[Identifier] = Set(pairs.map(_._1) : _*)
+    val vars: Set[Identifier] = variablesOf(tree)
+    val intersection = vars intersect definitions
+    if(!intersection.isEmpty) {
+      intersection.foreach(id => {
+        Settings.reporter.error("Variable with identifier '" + id + "' has escaped its let-definition !")
+      })
+      false
+    } else {
+      vars.forall(id => if(id.isLetBinder) {
+        Settings.reporter.error("Variable with identifier '" + id + "' has lost its let-definition (it disappeared??)")
+        false
+      } else {
+        true
+      })
+    }
   }
 
   /* Fully expands all let expressions. */
@@ -666,18 +849,4 @@ object Trees {
     })
   }
 
-  // we use this when debugging our tree transformations...
-  def wellOrderedLets(tree : Expr) : Boolean = {
-    val (pairs, _) = pulloutAndKeepLets(tree)
-    val definitions: Set[Identifier] = Set(pairs.map(_._1) : _*)
-    val vars: Set[Identifier] = variablesOf(tree)
-    val intersection = vars intersect definitions
-    if(intersection.isEmpty) true
-    else {
-      intersection.foreach(id => {
-        Settings.reporter.error("Variable with identifier '" + id + "' has escaped its let-definition !")
-      })
-      false
-    }
-  }
 }
diff --git a/src/purescala/Z3Solver.scala b/src/purescala/Z3Solver.scala
index c828fcd5e..114e46b0d 100644
--- a/src/purescala/Z3Solver.scala
+++ b/src/purescala/Z3Solver.scala
@@ -282,6 +282,8 @@ class Z3Solver(reporter: Reporter) extends Solver(reporter) {
   private def toZ3Formula(z3: Z3Context, expr: Expr, initialMap: Map[String,Z3AST] = Map.empty) : Option[Z3AST] = {
     class CantTranslateException extends Exception
 
+    val varsInformula: Set[Identifier] = variablesOf(expr)
+
     var z3Vars: Map[String,Z3AST] = initialMap
 
     def rec(ex: Expr) : Z3AST = ex match {
@@ -295,6 +297,9 @@ class Z3Solver(reporter: Reporter) extends Solver(reporter) {
       case v @ Variable(id) => z3Vars.get(id.uniqueName) match {
         case Some(ast) => ast
         case None => {
+          if(id.isLetBinder) {
+            scala.Predef.error("Error in formula being translated to Z3: identifier " + id + " seems to have escaped its let-definition")
+          }
           val newAST = z3.mkFreshConst(id.name, typeToSort(v.getType))
           z3Vars = z3Vars + (id.uniqueName -> newAST)
           newAST
@@ -346,7 +351,11 @@ class Z3Solver(reporter: Reporter) extends Solver(reporter) {
     }
     
     try {
-      Some(rec(expr))
+      val res = Some(rec(expr))
+      val usedInZ3Form = z3Vars.keys.toSet
+      println("Variables in formula:   " + varsInformula.map(_.uniqueName))
+      println("Variables passed to Z3: " + usedInZ3Form)
+      res
     } catch {
       case e: CantTranslateException => None
     }
-- 
GitLab