snapshot of testcases as used in evaluation for sas2011 submission.

sas2011-testcases/AssociativeList.scala

+import scala.collection.immutable.Set
+import funcheck.Utils._
+import funcheck.Annotations._
+
+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 update(l1: List, l2: List): List = (l2 match {
+    case Nil() => l1
+    case Cons(x, xs) => update(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
+}

sas2011-testcases/InsertionSort.scala

+import scala.collection.immutable.Set
+import funcheck.Annotations._
+import funcheck.Utils._
+
+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) : Int = (l match {
+    case Nil() => 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
+            )
+
+  /* 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
+            )
+
+  /* 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)
+             )
+
+  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))
+  }
+}

sas2011-testcases/ListOperations.scala

+import scala.collection.immutable.Set
+import funcheck.Annotations._
+import funcheck.Utils._
+
+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) : Int = (l match {
+        case Nil() => 0
+        case Cons(_, t) => 1 + size(t)
+    }) ensuring(res => res >= 0)
+
+    def iplSize(l: IntPairList) : Int = (l match {
+      case IPNil() => 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) : Int = sizeTailRecAcc(l, 0)
+    def sizeTailRecAcc(l: List, acc: Int) : Int = {
+     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) == 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))
+}

sas2011-testcases/PropositionalLogic.scala

+import scala.collection.immutable.Set
+import funcheck.Utils._
+import funcheck.Annotations._
+
+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 wrongCommutative(f: Formula) : Boolean = {
+    nnf(simplify(f)) == simplify(nnf(f))
+  } holds
+
+  @induct
+  def simplifyBreaksNNF(f: Formula) : Boolean = {
+    require(isNNF(f))
+    isNNF(simplify(f))
+  } holds
+
+  @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
+}

sas2011-testcases/RedBlackTree.scala

+import scala.collection.immutable.Set
+import funcheck.Annotations._
+import funcheck.Utils._
+
+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: 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) : Int = t match {
+    case Empty() => 0
+    case Node(_, l, v, r) => size(l) + 1 + size(r)
+  }
+
+  /* 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) : Int = 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: 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 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: Int, 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 buggyAdd(x: Int, t: Tree): Tree = {
+    require(redNodesHaveBlackChildren(t))
+    ins(x, t)
+  } ensuring (res => content(res) == content(t) ++ Set(x) && redNodesHaveBlackChildren(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 buggyBalance(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))
+}