diff options
Diffstat (limited to 'Source/Jennisys/examples/set.dfy')
| -rw-r--r-- | Source/Jennisys/examples/set.dfy | 246 |
1 files changed, 246 insertions, 0 deletions
diff --git a/Source/Jennisys/examples/set.dfy b/Source/Jennisys/examples/set.dfy new file mode 100644 index 00000000..627f1ecb --- /dev/null +++ b/Source/Jennisys/examples/set.dfy @@ -0,0 +1,246 @@ +class Set {
+ ghost var Repr: set<object>;
+ ghost var elems: set<int>;
+
+ var root: SetNode;
+
+ 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 ==> elems == {}) &&
+ (root != null ==> elems == root.elems)
+ }
+
+ function Valid(): bool
+ reads *;
+ {
+ this.Valid_self() &&
+ (root != null ==> root.Valid())
+ }
+
+ method Empty()
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {};
+ {
+ this.elems := {};
+ this.root := null;
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method Singleton(t: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {t};
+ {
+ var gensym66 := new SetNode;
+ gensym66.Init(t);
+ this.elems := {t};
+ this.root := gensym66;
+ this.Repr := {this} + this.root.Repr;
+ }
+
+ method Sum(p: int, q: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p + q};
+ {
+ var gensym68 := new SetNode;
+ gensym68.Init(p+q);
+ this.elems := {p + q};
+ this.root := gensym68;
+ this.Repr := {this} + this.root.Repr;
+ }
+
+ method Double(p: int, q: int)
+ modifies this;
+ requires p != q;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p, q};
+ {
+ var gensym71 := new SetNode;
+ gensym71.Double(p, q);
+ this.elems := {p, q};
+ this.root := gensym71;
+ this.Repr := {this} + this.root.Repr;
+ }
+
+}
+
+class SetNode {
+ ghost var Repr: set<object>;
+ ghost var elems: set<int>;
+
+ var data: int;
+ var left: SetNode;
+ var right: SetNode;
+
+ 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))
+ }
+
+ function Valid(): bool
+ reads *;
+ {
+ this.Valid_self() &&
+ (left != null ==> left.Valid_self() && (left.left != null ==> left.left.Valid_self())) &&
+ (right != null ==> right.Valid_self() && (right.right != null ==> right.right.Valid_self()))
+ }
+
+ method Init(t: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {t};
+ {
+ this.data := t;
+ this.elems := {t};
+ this.left := null;
+ this.right := null;
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method Double(p: int, q: int)
+ modifies this;
+// requires p != q;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p, q};
+ {
+ if (q > p) {
+ var gensym79 := new SetNode;
+ gensym79.Init(q);
+ this.data := p;
+ this.elems := {p, q};
+ this.left := null;
+ this.right := gensym79;
+ this.Repr := {this} + this.right.Repr;
+ } else if (q < p) {
+ var gensym79 := new SetNode;
+ gensym79.Init(p);
+ this.data := q;
+ this.elems := {p, q};
+ this.left := null;
+ this.right := gensym79;
+ this.Repr := {this} + this.right.Repr;
+ } else {
+ this.data := p;
+ this.elems := {p};
+ this.left := null;
+ this.right := null;
+ this.Repr := {this};
+ }
+ }
+
+ method Triple(p: int, q: int, r: int)
+ modifies this;
+ requires p != q;
+ requires q != r;
+ requires r != p;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p, q, r};
+ {
+ if (p < q && r > q) {
+ var gensym83 := new SetNode;
+ var gensym84 := new SetNode;
+ gensym83.Init(r);
+ gensym84.Init(p);
+ this.data := q;
+ this.elems := {p, q, r};
+ this.left := gensym84;
+ this.right := gensym83;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (p < r && q > r) {
+ var gensym85 := new SetNode;
+ var gensym86 := new SetNode;
+ gensym85.Init(q);
+ gensym86.Init(p);
+ this.data := r;
+ this.elems := {p, q, r};
+ this.left := gensym86;
+ this.right := gensym85;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (r < p && q > p) {
+ var gensym84 := new SetNode;
+ var gensym85 := new SetNode;
+ gensym84.Init(q);
+ gensym85.Init(r);
+ this.data := p;
+ this.elems := {p, q, r};
+ this.left := gensym85;
+ this.right := gensym84;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (q < p && r > p) {
+ var gensym82 := new SetNode;
+ var gensym83 := new SetNode;
+ gensym82.Init(r);
+ gensym83.Init(q);
+ this.data := p;
+ this.elems := {p, q, r};
+ this.left := gensym83;
+ this.right := gensym82;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (q < r && p > r) {
+ var gensym85 := new SetNode;
+ var gensym86 := new SetNode;
+ gensym85.Init(p);
+ gensym86.Init(q);
+ this.data := r;
+ this.elems := {p, q, r};
+ this.left := gensym86;
+ this.right := gensym85;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ var gensym82 := new SetNode;
+ var gensym83 := new SetNode;
+ gensym82.Init(p);
+ gensym83.Init(r);
+ this.data := q;
+ this.elems := {p, q, r};
+ this.left := gensym83;
+ this.right := gensym82;
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ }
+ }
+ }
+ }
+ }
+ }
+
+}
+
+
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