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// In this example, additional unfold/fold pairs make the verification of the last three methods fail.
class Node {
var next : Node;
var val : int;
predicate list {
acc(next) && acc(val) && (next!=null ==> next.list)
}
function vals() : seq<int>
requires list
{
unfolding list in (next == null ? [val] : [val] ++ next.vals())
}
function reverse_vals() : seq<int>
requires list
{
unfolding list in (next == null ? [val] : next.reverse_vals() ++ [val])
}
method reverse_in_place() returns (r:Node)
requires list;
ensures true;
{
var l : Node := this;
r := null;
var rev : seq<int> := this.reverse_vals();
while (l != null)
invariant l!=null ==> l.list;
invariant r!=null ==> r.list;
invariant rev == (l==null ? nil<int> : l.reverse_vals()) ++ (r==null ? nil<int> : r.vals());
{
var y: Node;
// if (r != null) {
// unfold r.list; fold r.list;
// }
unfold l.list;
// if (l.next != null) {
// unfold l.next.list; fold l.next.list;
// }
y := l.next;
l.next := r;
r := l;
fold r.list;
l := y;
}
assert r.vals() == rev; // should be the post-condition
}
method reverse_in_place_01() returns (r:Node)
requires list;
ensures true;
{
var l : Node := this;
r := null;
var rev : seq<int> := this.reverse_vals();
while (l != null)
invariant l!=null ==> l.list;
invariant r!=null ==> r.list;
invariant rev == (l==null ? nil<int> : l.reverse_vals()) ++ (r==null ? nil<int> : r.vals());
{
var y: Node;
// if (r != null) {
// unfold r.list; fold r.list;
// }
unfold l.list;
if (l.next != null) {
unfold l.next.list; fold l.next.list;
}
y := l.next;
l.next := r;
r := l;
fold r.list;
l := y;
}
assert r.vals() == rev; // should be the post-condition
}
method reverse_in_place_10() returns (r:Node)
requires list;
ensures true;
{
var l : Node := this;
r := null;
var rev : seq<int> := this.reverse_vals();
while (l != null)
invariant l!=null ==> l.list;
invariant r!=null ==> r.list;
invariant rev == (l==null ? nil<int> : l.reverse_vals()) ++ (r==null ? nil<int> : r.vals());
{
var y: Node;
if (r != null) {
unfold r.list; fold r.list;
}
unfold l.list;
// if (l.next != null) {
// unfold l.next.list; fold l.next.list;
// }
y := l.next;
l.next := r;
r := l;
fold r.list;
l := y;
}
assert r.vals() == rev; // should be the post-condition
}
method reverse_in_place_11() returns (r:Node)
requires list;
ensures true;
{
var l : Node := this;
r := null;
var rev : seq<int> := this.reverse_vals();
while (l != null)
invariant l!=null ==> l.list;
invariant r!=null ==> r.list;
invariant rev == (l==null ? nil<int> : l.reverse_vals()) ++ (r==null ? nil<int> : r.vals());
{
var y: Node;
if (r != null) {
unfold r.list; fold r.list;
}
unfold l.list;
if (l.next != null) {
unfold l.next.list; fold l.next.list;
}
y := l.next;
l.next := r;
r := l;
fold r.list;
l := y;
}
assert r.vals() == rev; // should be the post-condition
}
}
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