From f7399f63292f0e3a5db16c747f895ed2fa9d60fc Mon Sep 17 00:00:00 2001
From: Philippe Suter <philippe.suter@gmail.com>
Date: Mon, 16 Aug 2010 08:39:42 +0000
Subject: [PATCH] more examples in here
---
testcases/ListWithSize.scala | 33 +++++++++++++++++++++++++++++++++
1 file changed, 33 insertions(+)
diff --git a/testcases/ListWithSize.scala b/testcases/ListWithSize.scala
index be9a7e234..31f315e6a 100644
--- a/testcases/ListWithSize.scala
+++ b/testcases/ListWithSize.scala
@@ -1,15 +1,48 @@
+import scala.collection.immutable.Set
+
object ListWithSize {
sealed abstract class List
case class Cons(head: Int, tail: List) extends List
case class Nil() extends List
+ // proved with unrolling=0
def size(l: List) : Int = (l match {
case Nil() => 0
case Cons(_, t) => 1 + size(t)
}) ensuring(_ >= 0)
+ def content(l: List) : Set[Int] = l match {
+ case Nil() => Set.empty[Int]
+ case Cons(x, xs) => Set(x) ++ content(xs)
+ }
+
+ // proved with unrolling=1
def append(x: Int, l: List) : List = (l match {
case Nil() => Cons(x, Nil())
case c @ Cons(_,_) => Cons(x, c)
}) ensuring(size(_) > 0)
+
+ // proved with unrolling=2
+ 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))
+ }
+
+ // proved with unrolling=4
+ def concat(l1: List, l2: List) : List = concat0(l1, l2, Nil()) ensuring(content(_) == content(l1) ++ content(l2))
+ 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))
+
+ // proved with unrolling=2 ???
+ def property1(l1: List, l2: List) : Boolean = {
+ reverse(concat(l1, l2)) == concat(reverse(l2), reverse(l1))
+ } ensuring(_ == true)
}
--
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