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class BHeap {
ghost var Repr: set<object>;
ghost var elems: set<int>;
var data: int;
var left: BHeap;
var right: BHeap;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(left != null ==> left in Repr && left.Repr <= Repr && this !in left.Repr) &&
(right != null ==> right in Repr && right.Repr <= Repr && this !in right.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(elems == ({data} + (if left != null then left.elems else {})) + (if right != null then right.elems else {})) &&
(left != null ==> (forall e :: e in left.elems ==> e < data)) &&
(right != null ==> (forall e :: e in right.elems ==> e < data)) &&
(left == null ==> right == null) &&
(left != null && right == null ==> left.elems == {left.data})
}
function Valid(): bool
reads *;
decreases Repr;
{
this.Valid_self() &&
(left != null ==> left.Valid()) &&
(right != null ==> right.Valid()) &&
(left != null ==> left.Valid_self()) &&
(right != null ==> right.Valid_self()) &&
(left != null && left.left != null ==> left.left.Valid_self()) &&
(left != null && left.right != null ==> left.right.Valid_self()) &&
(right != null && right.left != null ==> right.left.Valid_self()) &&
(right != null && right.right != null ==> right.right.Valid_self())
}
method Dupleton(a: int, b: int)
modifies this;
requires a != b;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {a, b};
{
if (b < a) {
var gensym71 := new BHeap;
var gensym73 := new BHeap;
this.data := a;
this.elems := {b, a};
this.left := gensym73;
this.right := gensym71;
gensym71.data := b;
gensym71.elems := {b};
gensym71.left := null;
gensym71.right := null;
gensym73.data := b;
gensym73.elems := {b};
gensym73.left := null;
gensym73.right := null;
// repr stuff
gensym71.Repr := {gensym71};
gensym73.Repr := {gensym73};
this.Repr := ({this} + {gensym73}) + {gensym71};
// assert repr objects are valid (helps verification)
assert gensym71.Valid() && gensym73.Valid();
} else {
var gensym71 := new BHeap;
var gensym73 := new BHeap;
this.data := b;
this.elems := {a, b};
this.left := gensym73;
this.right := gensym71;
gensym71.data := a;
gensym71.elems := {a};
gensym71.left := null;
gensym71.right := null;
gensym73.data := a;
gensym73.elems := {a};
gensym73.left := null;
gensym73.right := null;
// repr stuff
gensym71.Repr := {gensym71};
gensym73.Repr := {gensym73};
this.Repr := ({this} + {gensym73}) + {gensym71};
// assert repr objects are valid (helps verification)
assert gensym71.Valid() && gensym73.Valid();
}
}
method Find(n: int) returns (ret: bool)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == (n in elems);
decreases Repr;
{
if (this.left == null) {
ret := n == this.data;
} else {
if (this.right != null) {
var x_10 := this.left.Find(n);
var x_11 := this.right.Find(n);
ret := (n == this.data || x_10) || x_11;
} else {
var x_12 := this.left.Find(n);
ret := n == this.data || x_12;
}
}
}
method Singleton(x: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {x};
{
this.data := x;
this.elems := {x};
this.left := null;
this.right := null;
// repr stuff
this.Repr := {this};
}
method Tripleton(x: int, y: int, z: int)
modifies this;
requires x != y;
requires y != z;
requires z != x;
ensures fresh(Repr - {this});
ensures Valid();
ensures elems == {x, y, z};
{
if (z < y && x < y) {
var gensym75 := new BHeap;
var gensym77 := new BHeap;
this.data := y;
this.elems := {z, x, y};
this.left := gensym77;
this.right := gensym75;
gensym75.data := x;
gensym75.elems := {x};
gensym75.left := null;
gensym75.right := null;
gensym77.data := z;
gensym77.elems := {z};
gensym77.left := null;
gensym77.right := null;
// repr stuff
gensym75.Repr := {gensym75};
gensym77.Repr := {gensym77};
this.Repr := ({this} + {gensym77}) + {gensym75};
// assert repr objects are valid (helps verification)
assert gensym75.Valid() && gensym77.Valid();
} else {
if (x < z) {
var gensym75 := new BHeap;
var gensym77 := new BHeap;
this.data := z;
this.elems := {x, y, z};
this.left := gensym77;
this.right := gensym75;
gensym75.data := x;
gensym75.elems := {x};
gensym75.left := null;
gensym75.right := null;
gensym77.data := y;
gensym77.elems := {y};
gensym77.left := null;
gensym77.right := null;
// repr stuff
gensym75.Repr := {gensym75};
gensym77.Repr := {gensym77};
this.Repr := ({this} + {gensym77}) + {gensym75};
// assert repr objects are valid (helps verification)
assert gensym75.Valid() && gensym77.Valid();
} else {
var gensym75 := new BHeap;
var gensym77 := new BHeap;
this.data := x;
this.elems := {z, y, x};
this.left := gensym77;
this.right := gensym75;
gensym75.data := y;
gensym75.elems := {y};
gensym75.left := null;
gensym75.right := null;
gensym77.data := z;
gensym77.elems := {z};
gensym77.left := null;
gensym77.right := null;
// repr stuff
gensym75.Repr := {gensym75};
gensym77.Repr := {gensym77};
this.Repr := ({this} + {gensym77}) + {gensym75};
// assert repr objects are valid (helps verification)
assert gensym75.Valid() && gensym77.Valid();
}
}
}
}
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