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class IntList {
ghost var Repr: set<object>;
ghost var list: seq<int>;
var root: IntNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(root != null ==> root in Repr && root.Repr <= Repr && this !in root.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(root == null <==> |list| == 0) &&
(root != null ==> list == root.list)
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(root != null ==> root.Valid())
}
method Double(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [q];
ensures list[0] == p;
ensures list[1] == q;
ensures |list| == 2;
{
var gensym74 := new IntNode;
gensym74.Double(p, q);
this.list := [p] + [q];
this.root := gensym74;
// repr stuff
this.Repr := {this} + this.root.Repr;
// assert repr objects are valid (helps verification)
assert gensym74.Valid();
}
method Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [];
ensures |list| == 0;
{
this.list := [];
this.root := null;
// repr stuff
this.Repr := {this};
}
method OneTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [1, 2];
ensures list[0] == 1;
ensures list[1] == 2;
ensures |list| == 2;
{
this.Double(1, 2);
}
method Singleton(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p];
ensures list[0] == p;
ensures |list| == 1;
{
var gensym73 := new IntNode;
gensym73.Init(p);
this.list := [p];
this.root := gensym73;
// repr stuff
this.Repr := {this} + this.root.Repr;
// assert repr objects are valid (helps verification)
assert gensym73.Valid();
}
method SingletonTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [2];
ensures list[0] == 2;
ensures |list| == 1;
{
this.Singleton(2);
}
method Sum(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p + q];
ensures list[0] == p + q;
ensures |list| == 1;
{
this.Singleton(p + q);
}
method TwoConsecutive(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [p + 1];
ensures list[0] == p;
ensures list[1] == p + 1;
ensures |list| == 2;
{
this.Double(p, p + 1);
}
}
class IntNode {
ghost var Repr: set<object>;
ghost var list: seq<int>;
var data: int;
var next: IntNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(next != null ==> next in Repr && next.Repr <= Repr && this !in next.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(next == null ==> (list == [data] && list[0] == data) && |list| == 1) &&
(next != null ==> list == [data] + next.list) &&
(|list| > 0)
}
function Valid(): bool
reads *;
decreases Repr;
{
this.Valid_self() &&
(next != null ==> next.Valid()) &&
(next != null ==> next.Valid_self()) &&
(next != null && next.next != null ==> next.next.Valid_self())
}
method Double(x: int, y: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [x, y];
ensures list[0] == x;
ensures list[1] == y;
ensures |list| == 2;
{
var gensym87 := new IntNode;
gensym87.Init(y);
this.data := x;
this.list := [x, y];
this.next := gensym87;
// repr stuff
this.Repr := {this} + this.next.Repr;
// assert repr objects are valid (helps verification)
assert gensym87.Valid();
}
method Init(x: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [x];
ensures list[0] == x;
ensures |list| == 1;
{
this.data := x;
this.list := [x];
this.next := null;
// repr stuff
this.Repr := {this};
}
method SingletonZero()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [0];
ensures list[0] == 0;
ensures |list| == 1;
{
this.Init(0);
}
}
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