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class List<T> {
ghost var Repr: set<object>;
ghost var list: seq<T>;
var root: Node<T>;
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 Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [];
{
this.list := [];
this.root := null;
// repr stuff
this.Repr := {this};
}
method Singleton(t: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [t];
{
var gensym65 := new Node<T>;
gensym65.data := t;
gensym65.list := [t];
gensym65.next := null;
this.list := [t];
this.root := gensym65;
// repr stuff
gensym65.Repr := {gensym65};
this.Repr := {this} + this.root.Repr;
}
method Double(p: T, q: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p, q];
{
var gensym66 := new Node<T>;
var gensym67 := new Node<T>;
gensym66.data := p;
gensym66.list := [p, q];
gensym66.next := gensym67;
gensym67.data := q;
gensym67.list := [q];
gensym67.next := null;
this.list := [p, q];
this.root := gensym66;
// repr stuff
gensym67.Repr := {gensym67};
gensym66.Repr := {gensym66} + gensym66.next.Repr;
this.Repr := {this} + this.root.Repr;
}
}
class Node<T> {
ghost var Repr: set<object>;
ghost var list: seq<T>;
var data: T;
var next: Node<T>;
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) &&
(next != null ==> list == [data] + next.list) &&
(|list| > 0)
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(next != null ==> next.Valid_self() && (next.next != null ==> next.next.Valid_self()))
}
method Init(t: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [t];
{
this.data := t;
this.list := [t];
this.next := null;
// repr stuff
this.Repr := {this};
}
method Double(p: T, q: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p, q];
{
var gensym71 := new Node<T>;
gensym71.data := q;
gensym71.list := [q];
gensym71.next := null;
this.data := p;
this.list := [p, q];
this.next := gensym71;
// repr stuff
gensym71.Repr := {gensym71};
this.Repr := {this} + this.next.Repr;
}
}
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