Finding an absolute value term from example-works!

testcases/SimpInterpret.scala

+//import scala.collection.immutable.Set
+//import leon.Annotations._
+import leon.Utils._
+
+object Interpret {
+  abstract class BoolTree 
+  case class Eq(t1 : IntTree, t2 : IntTree) extends BoolTree
+  case class And(t1 : BoolTree, t2 : BoolTree) extends BoolTree
+  case class Not(t : BoolTree) extends BoolTree
+
+  abstract class IntTree 
+  case class Const(c:Int) extends IntTree
+  case class Var() extends IntTree
+  case class Plus(t1 : IntTree, t2 : IntTree) extends IntTree
+  case class Minus(t1 : IntTree, t2 : IntTree) extends IntTree
+  case class Less(t1 : IntTree, t2 : IntTree) extends BoolTree
+  case class If(cond : BoolTree, t : IntTree, e : IntTree) extends IntTree
+
+  def repOk(t : IntTree) : Boolean = {
+    true
+  }
+
+  def beval(t:BoolTree, x0 : Int) : Boolean = {
+    t match {   
+      case Less(t1, t2) => ieval(t1,x0) < ieval(t2,x0)
+      case Eq(t1, t2) => ieval(t1,x0) == ieval(t2,x0)
+      case And(t1, t2) => beval(t1,x0) && beval(t2,x0)
+      case Not(t1) => !beval(t1,x0)
+    }
+  }
+
+  def ieval(t:IntTree, x0 : Int) : Int = {
+    t match {
+      case Const(c) => c
+      case Var() => x0
+      case Plus(t1,t2) => ieval(t1,x0) + ieval(t2,x0)
+      case Minus(t1, t2) => ieval(t1,x0) - ieval(t2,x0)
+      case If(c,t1,t2) => if (beval(c,x0)) ieval(t1,x0) else ieval(t2,x0)
+    }
+  }
+  def computesPositive(t : IntTree) : Boolean = {
+    ieval(t,0) >= 0 &&
+    ieval(t,1) >= 0 &&
+    ieval(t,-1) >= 0 &&
+    ieval(t,-2) >= 0 &&
+    ieval(t,2) >= 0
+  }
+  def identityForPositive(t : IntTree) : Boolean = {
+    ieval(t, 5) == 5 &&
+    ieval(t, 33) == 33 &&
+    ieval(t, 0) == 0 &&
+    ieval(t, -1) == 1 &&
+    ieval(t, -2) == 2
+  }
+
+  def treeBad(t : IntTree) : Boolean = {
+    !(repOk(t) && computesPositive(t) && identityForPositive(t))
+  } holds
+
+  def thereIsGoodTree() : Boolean = {
+    !treeBad(If(Less(Const(0),Var()), Var(), Minus(Const(0),Var())))
+  } holds
+
+  def main(args : Array[String]) {
+    thereIsGoodTree()
+  }
+}