diff options
| author |  Unknown <t-alekm@A3479878.redmond.corp.microsoft.com> | 2011-07-19 20:16:45 -0700 |
|---|---|---|
| committer | Unknown <t-alekm@A3479878.redmond.corp.microsoft.com> | 2011-07-19 20:16:45 -0700 |
| commit | ac0d3e508ace5e630341b5891112c81bb31bbe7f (patch) | |
| tree | 606d7bf659010b93e460735cf9f7a57f96314928 /Jennisys | |
| parent | 24ab29138656acc8204346ca9e4169b42e4ede3f (diff) | |
- added synthesized code for the examples
Diffstat (limited to 'Jennisys')
| -rw-r--r-- | Jennisys/Jennisys/examples/jennisys-synth_List.dfy | 147 | ||||
| -rw-r--r-- | Jennisys/Jennisys/examples/jennisys-synth_List2.dfy | 207 | ||||
| -rw-r--r-- | Jennisys/Jennisys/examples/jennisys-synth_List3.dfy | 255 | ||||
| -rw-r--r-- | Jennisys/Jennisys/examples/jennisys-synth_Number.dfy | 202 | ||||
| -rw-r--r-- | Jennisys/Jennisys/examples/jennisys-synth_Set.dfy | 344 |
5 files changed, 1155 insertions, 0 deletions
diff --git a/Jennisys/Jennisys/examples/jennisys-synth_List.dfy b/Jennisys/Jennisys/examples/jennisys-synth_List.dfy new file mode 100644 index 00000000..0611c78b --- /dev/null +++ b/Jennisys/Jennisys/examples/jennisys-synth_List.dfy @@ -0,0 +1,147 @@ +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;
+ }
+
+}
+
+
diff --git a/Jennisys/Jennisys/examples/jennisys-synth_List2.dfy b/Jennisys/Jennisys/examples/jennisys-synth_List2.dfy new file mode 100644 index 00000000..13e521a8 --- /dev/null +++ b/Jennisys/Jennisys/examples/jennisys-synth_List2.dfy @@ -0,0 +1,207 @@ +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};
+ }
+
+}
+
+
diff --git a/Jennisys/Jennisys/examples/jennisys-synth_List3.dfy b/Jennisys/Jennisys/examples/jennisys-synth_List3.dfy new file mode 100644 index 00000000..e202412f --- /dev/null +++ b/Jennisys/Jennisys/examples/jennisys-synth_List3.dfy @@ -0,0 +1,255 @@ +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.succ| + 1 && (list[0] == root.data && (forall i: int :: 0 < i && i <= |root.succ| ==> root.succ[i - 1] != null && list[i] == root.succ[i - 1].data)))
+ }
+
+ 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.next := null;
+ gensym65.succ := [];
+ 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 gensym63 := new IntNode;
+ var gensym75 := new IntNode;
+ gensym63.data := 1;
+ gensym63.next := gensym75;
+ gensym63.succ := [gensym75];
+ gensym75.data := 2;
+ gensym75.next := null;
+ gensym75.succ := [];
+ this.list := [1, 2];
+ this.root := gensym63;
+ // repr stuff
+ gensym75.Repr := {gensym75};
+ gensym63.Repr := {gensym63} + gensym63.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.next := null;
+ gensym66.succ := [];
+ 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 gensym64 := new IntNode;
+ var gensym75 := new IntNode;
+ gensym64.data := p;
+ gensym64.next := gensym75;
+ gensym64.succ := [gensym75];
+ gensym75.data := p + 1;
+ gensym75.next := null;
+ gensym75.succ := [];
+ this.list := [p] + [p + 1];
+ this.root := gensym64;
+ // repr stuff
+ gensym75.Repr := {gensym75};
+ gensym64.Repr := {gensym64} + gensym64.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 gensym65 := new IntNode;
+ var gensym77 := new IntNode;
+ gensym65.data := p;
+ gensym65.next := gensym77;
+ gensym65.succ := [gensym77];
+ gensym77.data := q;
+ gensym77.next := null;
+ gensym77.succ := [];
+ this.list := [p] + [q];
+ this.root := gensym65;
+ // repr stuff
+ gensym77.Repr := {gensym77};
+ gensym65.Repr := {gensym65} + gensym65.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.next := null;
+ gensym67.succ := [];
+ 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 succ: seq<IntNode>;
+ ghost 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 ==> |succ| == 0) &&
+ (next != null ==> succ == [next] + next.succ) &&
+ (!(null in succ))
+ }
+
+ function Valid(): bool
+ reads *;
+ {
+ this.Valid_self() &&
+ (next != null ==> next.Valid_self() && (next.next != null ==> next.next.Valid_self()))
+ }
+
+ method Zero()
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures data == 0;
+ ensures succ == [];
+ {
+ this.data := 0;
+ this.next := null;
+ this.succ := [];
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method OneTwo()
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures data == 1;
+ ensures |succ| == 1;
+ ensures succ[0] != null;
+ ensures succ[0].data == 2;
+ {
+ var gensym71 := new IntNode;
+ gensym71.data := 2;
+ gensym71.next := null;
+ gensym71.succ := [];
+ this.data := 1;
+ this.next := gensym71;
+ this.succ := [gensym71];
+ // repr stuff
+ gensym71.Repr := {gensym71};
+ this.Repr := {this} + this.next.Repr;
+ }
+
+ method Init(p: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures data == p;
+ {
+ this.data := p;
+ this.next := null;
+ this.succ := [];
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method InitInc(p: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures data == p + 1;
+ {
+ this.data := p + 1;
+ this.next := null;
+ this.succ := [];
+ // repr stuff
+ this.Repr := {this};
+ }
+
+}
+
+
diff --git a/Jennisys/Jennisys/examples/jennisys-synth_Number.dfy b/Jennisys/Jennisys/examples/jennisys-synth_Number.dfy new file mode 100644 index 00000000..5ede7f5c --- /dev/null +++ b/Jennisys/Jennisys/examples/jennisys-synth_Number.dfy @@ -0,0 +1,202 @@ +class Number {
+ ghost var Repr: set<object>;
+ ghost var num: int;
+
+
+ function Valid_repr(): bool
+ reads *;
+ {
+ this in Repr &&
+ null !in Repr
+ }
+
+ function Valid_self(): bool
+ reads *;
+ {
+ Valid_repr() &&
+ true
+ }
+
+ function Valid(): bool
+ reads *;
+ {
+ this.Valid_self() &&
+ true
+ }
+
+ method Init(p: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num == p;
+ {
+ this.num := p;
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method Double(p: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num == 2 * p;
+ {
+ this.num := 2 * p;
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method Sum(a: int, b: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num == a + b;
+ {
+ this.num := a + b;
+ // repr stuff
+ this.Repr := {this};
+ }
+
+ method Min2(a: int, b: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures a < b ==> num == a;
+ ensures a >= b ==> num == b;
+ {
+ if (a >= b ==> a == b) {
+ this.num := a;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := b;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+
+ method Min22(a: int, b: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num in {a, b};
+ ensures num <= a;
+ ensures num <= b;
+ {
+ if (a <= b) {
+ this.num := a;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := b;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+
+ method Min3(a: int, b: int, c: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num in {a, b, c};
+ ensures num <= a;
+ ensures num <= b;
+ ensures num <= c;
+ {
+ if (a <= b && a <= c) {
+ this.num := a;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ if (c <= a && c <= b) {
+ this.num := c;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := b;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+ }
+
+ method MinSum(a: int, b: int, c: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num in {a + b, a + c, b + c};
+ ensures num <= a + b;
+ ensures num <= b + c;
+ ensures num <= a + c;
+ {
+ if (a + b <= b + c && a + b <= a + c) {
+ this.num := a + b;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ if (a + c <= a + b && a + c <= b + c) {
+ this.num := a + c;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := b + c;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+ }
+
+ method Min4(a: int, b: int, c: int, d: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures num in {a, b, c, d};
+ ensures num <= a;
+ ensures num <= b;
+ ensures num <= c;
+ ensures num <= d;
+ {
+ if (a <= b && (a <= c && a <= d)) {
+ this.num := a;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ if (d <= a && (d <= b && d <= c)) {
+ this.num := d;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ if (c <= a && (c <= b && c <= d)) {
+ this.num := c;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := b;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+ }
+ }
+
+ method Abs(a: int)
+ modifies this;
+ ensures fresh(Repr - {this});
+ ensures Valid();
+ ensures a < 0 ==> num == -a;
+ ensures a >= 0 ==> num == a;
+ {
+ if (!(a >= 0)) {
+ this.num := -a;
+ // repr stuff
+ this.Repr := {this};
+ } else {
+ this.num := a;
+ // repr stuff
+ this.Repr := {this};
+ }
+ }
+
+}
+
+
diff --git a/Jennisys/Jennisys/examples/jennisys-synth_Set.dfy b/Jennisys/Jennisys/examples/jennisys-synth_Set.dfy new file mode 100644 index 00000000..efc9aa07 --- /dev/null +++ b/Jennisys/Jennisys/examples/jennisys-synth_Set.dfy @@ -0,0 +1,344 @@ +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.data := t;
+ gensym66.elems := {t};
+ gensym66.left := null;
+ gensym66.right := null;
+ this.elems := {t};
+ this.root := gensym66;
+ // repr stuff
+ gensym66.Repr := {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.data := p + q;
+ gensym68.elems := {p + q};
+ gensym68.left := null;
+ gensym68.right := null;
+ this.elems := {p + q};
+ this.root := gensym68;
+ // repr stuff
+ gensym68.Repr := {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};
+ {
+ if (q < p) {
+ var gensym71 := new SetNode;
+ var gensym75 := new SetNode;
+ gensym71.data := p;
+ gensym71.elems := {p, q};
+ gensym71.left := gensym75;
+ gensym71.right := null;
+ gensym75.data := q;
+ gensym75.elems := {q};
+ gensym75.left := null;
+ gensym75.right := null;
+ this.elems := {p, q};
+ this.root := gensym71;
+ // repr stuff
+ gensym75.Repr := {gensym75};
+ gensym71.Repr := {gensym71} + gensym71.left.Repr;
+ this.Repr := {this} + this.root.Repr;
+ } else {
+ var gensym71 := new SetNode;
+ var gensym75 := new SetNode;
+ gensym71.data := q;
+ gensym71.elems := {p, q};
+ gensym71.left := gensym75;
+ gensym71.right := null;
+ gensym75.data := p;
+ gensym75.elems := {p};
+ gensym75.left := null;
+ gensym75.right := null;
+ this.elems := {p, q};
+ this.root := gensym71;
+ // repr stuff
+ gensym75.Repr := {gensym75};
+ gensym71.Repr := {gensym71} + gensym71.left.Repr;
+ 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.data := q;
+ gensym79.elems := {q};
+ gensym79.left := null;
+ gensym79.right := null;
+ this.data := p;
+ this.elems := {p, q};
+ this.left := null;
+ this.right := gensym79;
+ // repr stuff
+ gensym79.Repr := {gensym79};
+ this.Repr := {this} + this.right.Repr;
+ } else {
+ var gensym79 := new SetNode;
+ gensym79.data := p;
+ gensym79.elems := {p};
+ gensym79.left := null;
+ gensym79.right := null;
+ this.data := q;
+ this.elems := {p, q};
+ this.left := null;
+ this.right := gensym79;
+ // repr stuff
+ gensym79.Repr := {gensym79};
+ this.Repr := {this} + this.right.Repr;
+ }
+ }
+
+ 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.data := r;
+ gensym83.elems := {r};
+ gensym83.left := null;
+ gensym83.right := null;
+ gensym84.data := p;
+ gensym84.elems := {p};
+ gensym84.left := null;
+ gensym84.right := null;
+ this.data := q;
+ this.elems := {p, q, r};
+ this.left := gensym84;
+ this.right := gensym83;
+ // repr stuff
+ gensym83.Repr := {gensym83};
+ gensym84.Repr := {gensym84};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (p < r && q > r) {
+ var gensym85 := new SetNode;
+ var gensym86 := new SetNode;
+ gensym85.data := q;
+ gensym85.elems := {q};
+ gensym85.left := null;
+ gensym85.right := null;
+ gensym86.data := p;
+ gensym86.elems := {p};
+ gensym86.left := null;
+ gensym86.right := null;
+ this.data := r;
+ this.elems := {p, q, r};
+ this.left := gensym86;
+ this.right := gensym85;
+ // repr stuff
+ gensym85.Repr := {gensym85};
+ gensym86.Repr := {gensym86};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (r < p && q > p) {
+ var gensym84 := new SetNode;
+ var gensym85 := new SetNode;
+ gensym84.data := q;
+ gensym84.elems := {q};
+ gensym84.left := null;
+ gensym84.right := null;
+ gensym85.data := r;
+ gensym85.elems := {r};
+ gensym85.left := null;
+ gensym85.right := null;
+ this.data := p;
+ this.elems := {p, q, r};
+ this.left := gensym85;
+ this.right := gensym84;
+ // repr stuff
+ gensym84.Repr := {gensym84};
+ gensym85.Repr := {gensym85};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (q < p && r > p) {
+ var gensym82 := new SetNode;
+ var gensym83 := new SetNode;
+ gensym82.data := r;
+ gensym82.elems := {r};
+ gensym82.left := null;
+ gensym82.right := null;
+ gensym83.data := q;
+ gensym83.elems := {q};
+ gensym83.left := null;
+ gensym83.right := null;
+ this.data := p;
+ this.elems := {p, q, r};
+ this.left := gensym83;
+ this.right := gensym82;
+ // repr stuff
+ gensym82.Repr := {gensym82};
+ gensym83.Repr := {gensym83};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ if (q < r && p > r) {
+ var gensym85 := new SetNode;
+ var gensym86 := new SetNode;
+ gensym85.data := p;
+ gensym85.elems := {p};
+ gensym85.left := null;
+ gensym85.right := null;
+ gensym86.data := q;
+ gensym86.elems := {q};
+ gensym86.left := null;
+ gensym86.right := null;
+ this.data := r;
+ this.elems := {p, q, r};
+ this.left := gensym86;
+ this.right := gensym85;
+ // repr stuff
+ gensym85.Repr := {gensym85};
+ gensym86.Repr := {gensym86};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ } else {
+ var gensym82 := new SetNode;
+ var gensym83 := new SetNode;
+ gensym82.data := p;
+ gensym82.elems := {p};
+ gensym82.left := null;
+ gensym82.right := null;
+ gensym83.data := r;
+ gensym83.elems := {r};
+ gensym83.left := null;
+ gensym83.right := null;
+ this.data := q;
+ this.elems := {p, q, r};
+ this.left := gensym83;
+ this.right := gensym82;
+ // repr stuff
+ gensym82.Repr := {gensym82};
+ gensym83.Repr := {gensym83};
+ this.Repr := ({this} + this.left.Repr) + this.right.Repr;
+ }
+ }
+ }
+ }
+ }
+ }
+
+}
+
+
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