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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 Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [];
{
this.list := [];
this.root := null;
// repr stuff
this.Repr := {this};
}
method SingletonTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [2];
{
var gensym65 := new IntNode;
gensym65.data := 2;
gensym65.list := [2];
gensym65.next := null;
this.list := [2];
this.root := gensym65;
// repr stuff
gensym65.Repr := {gensym65};
this.Repr := {this} + this.root.Repr;
}
method OneTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [1] + [2];
{
var gensym62 := new IntNode;
var gensym69 := new IntNode;
gensym62.data := 1;
gensym62.list := [1, 2];
gensym62.next := gensym69;
gensym69.data := 2;
gensym69.list := [2];
gensym69.next := null;
this.list := [1, 2];
this.root := gensym62;
// repr stuff
gensym69.Repr := {gensym69};
gensym62.Repr := {gensym62} + gensym62.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Singleton(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p];
{
var gensym66 := new IntNode;
gensym66.data := p;
gensym66.list := [p];
gensym66.next := null;
this.list := [p];
this.root := gensym66;
// repr stuff
gensym66.Repr := {gensym66};
this.Repr := {this} + this.root.Repr;
}
method TwoConsecutive(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [p + 1];
{
var gensym63 := new IntNode;
var gensym71 := new IntNode;
gensym63.data := p;
gensym63.list := [p] + [p + 1];
gensym63.next := gensym71;
gensym71.data := p + 1;
gensym71.list := [p + 1];
gensym71.next := null;
this.list := [p] + [p + 1];
this.root := gensym63;
// repr stuff
gensym71.Repr := {gensym71};
gensym63.Repr := {gensym63} + gensym63.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Double(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [q];
{
var gensym64 := new IntNode;
var gensym71 := new IntNode;
gensym64.data := p;
gensym64.list := [p] + [q];
gensym64.next := gensym71;
gensym71.data := q;
gensym71.list := [q];
gensym71.next := null;
this.list := [p] + [q];
this.root := gensym64;
// repr stuff
gensym71.Repr := {gensym71};
gensym64.Repr := {gensym64} + gensym64.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Sum(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p + q];
{
var gensym67 := new IntNode;
gensym67.data := p + q;
gensym67.list := [p + q];
gensym67.next := null;
this.list := [p + q];
this.root := gensym67;
// repr stuff
gensym67.Repr := {gensym67};
this.Repr := {this} + this.root.Repr;
}
}
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) &&
(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 SingletonZero()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [0];
{
this.data := 0;
this.list := [0];
this.next := null;
// repr stuff
this.Repr := {this};
}
}
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