diff options
Diffstat (limited to 'Source/Jennisys/examples/mod2/jennisys-synth_Set.dfy')
| -rw-r--r-- | Source/Jennisys/examples/mod2/jennisys-synth_Set.dfy | 304 |
1 files changed, 304 insertions, 0 deletions
diff --git a/Source/Jennisys/examples/mod2/jennisys-synth_Set.dfy b/Source/Jennisys/examples/mod2/jennisys-synth_Set.dfy new file mode 100644 index 00000000..fea364d6 --- /dev/null +++ b/Source/Jennisys/examples/mod2/jennisys-synth_Set.dfy @@ -0,0 +1,304 @@ +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 Double(p: int, q: int)
+ modifies this;
+ requires p != q;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p, q};
+ {
+ var gensym80 := new SetNode;
+ gensym80.Double(p, q);
+ this.elems := {q, p};
+ this.root := gensym80;
+
+ // repr stuff
+ this.Repr := {this} + this.root.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym80.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 gensym75 := new SetNode;
+ gensym75.Init(t);
+ this.elems := {t};
+ this.root := gensym75;
+
+ // repr stuff
+ this.Repr := {this} + this.root.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym75.Valid();
+ }
+
+
+ method SingletonZero()
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {0};
+ {
+ this.Singleton(0);
+ }
+
+
+ method Sum(p: int, q: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {p + q};
+ {
+ this.Singleton(p + q);
+ }
+
+}
+
+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 *;
+ 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 Double(a: int, b: int)
+ modifies this;
+ requires a != b;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {a, b};
+ {
+ if (b > a) {
+ this.DoubleBase(b, a);
+ } else {
+ var gensym88 := new SetNode;
+ gensym88.Init(a);
+ this.data := b;
+ this.elems := {b, a};
+ this.left := null;
+ this.right := gensym88;
+
+ // repr stuff
+ this.Repr := {this} + this.right.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym88.Valid();
+ }
+ }
+
+
+ method DoubleBase(x: int, y: int)
+ modifies this;
+ requires x > y;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {x, y};
+ {
+ var gensym88 := new SetNode;
+ gensym88.Init(x);
+ this.data := y;
+ this.elems := {y, x};
+ this.left := null;
+ this.right := gensym88;
+
+ // repr stuff
+ this.Repr := {this} + this.right.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym88.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 && this.right != null) {
+ var x_9 := this.left.Find(n);
+ var x_10 := this.right.Find(n);
+ ret := (n == this.data || x_9) || x_10;
+ } else {
+ if (this.left != null && this.right == null) {
+ var x_11 := this.left.Find(n);
+ ret := n == this.data || x_11;
+ } else {
+ if (this.right != null && this.left == null) {
+ var x_12 := this.right.Find(n);
+ ret := n == this.data || x_12;
+ } else {
+ ret := n == this.data;
+ }
+ }
+ }
+ }
+
+
+ method Init(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 Triple(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 < x && y > x) {
+ this.TripleBase(z, x, y);
+ } else {
+ if (x < y && z > y) {
+ this.TripleBase(x, y, z);
+ } else {
+ if (x < z && y > z) {
+ this.TripleBase(x, z, y);
+ } else {
+ if (y < z && x > z) {
+ this.TripleBase(y, z, x);
+ } else {
+ if (z < y && x > y) {
+ this.TripleBase(z, y, x);
+ } else {
+ var gensym82 := new SetNode;
+ var gensym83 := new SetNode;
+ gensym82.Init(y);
+ gensym83.Init(z);
+ this.data := x;
+ this.elems := {y, x, z};
+ this.left := gensym82;
+ this.right := gensym83;
+
+ // repr stuff
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym82.Valid() && gensym83.Valid();
+ }
+ }
+ }
+ }
+ }
+ }
+
+
+ method TripleBase(x: int, y: int, z: int)
+ modifies this;
+ requires x < y;
+ requires y < z;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures elems == {x, y, z};
+ {
+ var gensym89 := new SetNode;
+ var gensym90 := new SetNode;
+ gensym89.Init(z);
+ gensym90.Init(x);
+ this.data := y;
+ this.elems := {x, y, z};
+ this.left := gensym90;
+ this.right := gensym89;
+
+ // repr stuff
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ // assert repr objects are valid (helps verification)
+ assert gensym89.Valid() && gensym90.Valid();
+ }
+
+}
+
+
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