diff options
Diffstat (limited to 'Test/og/treiber-stack.bpl')
| -rw-r--r-- | Test/og/treiber-stack.bpl | 202 |
1 files changed, 0 insertions, 202 deletions
diff --git a/Test/og/treiber-stack.bpl b/Test/og/treiber-stack.bpl deleted file mode 100644 index e1c509ab..00000000 --- a/Test/og/treiber-stack.bpl +++ /dev/null @@ -1,202 +0,0 @@ -// RUN: %boogie -noinfer -typeEncoding:m -useArrayTheory "%s" > "%t"
-// RUN: %diff "%s.expect" "%t"
-type Node = int;
-const unique null: Node;
-type lmap;
-function {:linear "Node"} dom(lmap): [Node]bool;
-function map(lmap): [Node]Node;
-function {:builtin "MapConst"} MapConstBool(bool) : [Node]bool;
-
-function EmptyLmap(): (lmap);
-axiom (dom(EmptyLmap()) == MapConstBool(false));
-
-function Add(x: lmap, i: Node, v: Node): (lmap);
-axiom (forall x: lmap, i: Node, v: Node :: dom(Add(x, i, v)) == dom(x)[i:=true] && map(Add(x, i, v)) == map(x)[i := v]);
-
-function Remove(x: lmap, i: Node): (lmap);
-axiom (forall x: lmap, i: Node :: dom(Remove(x, i)) == dom(x)[i:=false] && map(Remove(x, i)) == map(x));
-
-procedure {:yields} {:layer 0,1} ReadTopOfStack() returns (v:Node);
-ensures {:right} |{ A: assume dom(Stack)[v] || dom(Used)[v]; return true; }|;
-
-procedure {:yields} {:layer 0,1} Load(i:Node) returns (v:Node);
-ensures {:right} |{ A: assert dom(Stack)[i] || dom(Used)[i]; goto B,C;
- B: assume dom(Stack)[i]; v := map(Stack)[i]; return true;
- C: assume !dom(Stack)[i]; return true; }|;
-
-procedure {:yields} {:layer 0,1} Store({:linear_in "Node"} l_in:lmap, i:Node, v:Node) returns ({:linear "Node"} l_out:lmap);
-ensures {:both} |{ A: assert dom(l_in)[i]; l_out := Add(l_in, i, v); return true; }|;
-
-procedure {:yields} {:layer 0,1} TransferToStack(oldVal: Node, newVal: Node, {:linear_in "Node"} l_in:lmap) returns (r: bool, {:linear "Node"} l_out:lmap);
-ensures {:atomic} |{ A: assert dom(l_in)[newVal];
- goto B,C;
- B: assume oldVal == TopOfStack; TopOfStack := newVal; l_out := EmptyLmap(); Stack := Add(Stack, newVal, map(l_in)[newVal]); r := true; return true;
- C: assume oldVal != TopOfStack; l_out := l_in; r := false; return true; }|;
-
-procedure {:yields} {:layer 0,1} TransferFromStack(oldVal: Node, newVal: Node) returns (r: bool);
-ensures {:atomic} |{ A: goto B,C;
- B: assume oldVal == TopOfStack; TopOfStack := newVal; Used := Add(Used, oldVal, map(Stack)[oldVal]); Stack := Remove(Stack, oldVal); r := true; return true;
- C: assume oldVal != TopOfStack; r := false; return true; }|;
-
-var {:layer 0} TopOfStack: Node;
-var {:linear "Node"} {:layer 0} Stack: lmap;
-
-
-function {:inline} Inv(TopOfStack: Node, Stack: lmap) : (bool)
-{
- BetweenSet(map(Stack), TopOfStack, null)[TopOfStack] &&
- Subset(BetweenSet(map(Stack), TopOfStack, null), Union(Singleton(null), dom(Stack)))
-}
-
-var {:linear "Node"} {:layer 0} Used: lmap;
-
-procedure {:yields} {:layer 1} push(x: Node, {:linear_in "Node"} x_lmap: lmap)
-requires {:layer 1} dom(x_lmap)[x];
-requires {:layer 1} Inv(TopOfStack, Stack);
-ensures {:layer 1} Inv(TopOfStack, Stack);
-ensures {:atomic} |{ A: Stack := Add(Stack, x, TopOfStack); TopOfStack := x; return true; }|;
-{
- var t: Node;
- var g: bool;
- var {:linear "Node"} t_lmap: lmap;
-
- yield;
- assert {:layer 1} Inv(TopOfStack, Stack);
- t_lmap := x_lmap;
- while (true)
- invariant {:layer 1} dom(t_lmap) == dom(x_lmap);
- invariant {:layer 1} Inv(TopOfStack, Stack);
- {
- call t := ReadTopOfStack();
- call t_lmap := Store(t_lmap, x, t);
- call g, t_lmap := TransferToStack(t, x, t_lmap);
- if (g) {
- assert {:layer 1} map(Stack)[x] == t;
- break;
- }
- yield;
- assert {:layer 1} dom(t_lmap) == dom(x_lmap);
- assert {:layer 1} Inv(TopOfStack, Stack);
- }
- yield;
- assert {:expand} {:layer 1} Inv(TopOfStack, Stack);
-}
-
-procedure {:yields} {:layer 1} pop()
-requires {:layer 1} Inv(TopOfStack, Stack);
-ensures {:layer 1} Inv(TopOfStack, Stack);
-ensures {:atomic} |{ var t: Node;
- A: assume TopOfStack != null; t := TopOfStack; Used := Add(Used, t, map(Stack)[t]); TopOfStack := map(Stack)[t]; Stack := Remove(Stack, t); return true; }|;
-{
- var g: bool;
- var x: Node;
- var t: Node;
-
- yield;
- assert {:layer 1} Inv(TopOfStack, Stack);
- while (true)
- invariant {:layer 1} Inv(TopOfStack, Stack);
- {
- call t := ReadTopOfStack();
- if (t != null) {
- call x := Load(t);
- call g := TransferFromStack(t, x);
- if (g) {
- break;
- }
- }
- yield;
- assert {:layer 1} Inv(TopOfStack, Stack);
- }
- yield;
- assert {:layer 1} Inv(TopOfStack, Stack);
-}
-
-function Equal([int]bool, [int]bool) returns (bool);
-function Subset([int]bool, [int]bool) returns (bool);
-
-function Empty() returns ([int]bool);
-function Singleton(int) returns ([int]bool);
-function Reachable([int,int]bool, int) returns ([int]bool);
-function Union([int]bool, [int]bool) returns ([int]bool);
-
-axiom(forall x:int :: !Empty()[x]);
-
-axiom(forall x:int, y:int :: {Singleton(y)[x]} Singleton(y)[x] <==> x == y);
-axiom(forall y:int :: {Singleton(y)} Singleton(y)[y]);
-
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T)[x]}{Union(S,T),S[x]}{Union(S,T),T[x]} Union(S,T)[x] <==> S[x] || T[x]);
-
-axiom(forall S:[int]bool, T:[int]bool :: {Equal(S,T)} Equal(S,T) <==> Subset(S,T) && Subset(T,S));
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {S[x],Subset(S,T)}{T[x],Subset(S,T)} S[x] && Subset(S,T) ==> T[x]);
-axiom(forall S:[int]bool, T:[int]bool :: {Subset(S,T)} Subset(S,T) || (exists x:int :: S[x] && !T[x]));
-
-////////////////////
-// Between predicate
-////////////////////
-function Between(f: [int]int, x: int, y: int, z: int) returns (bool);
-function Avoiding(f: [int]int, x: int, y: int, z: int) returns (bool);
-
-
-//////////////////////////
-// Between set constructor
-//////////////////////////
-function BetweenSet(f: [int]int, x: int, z: int) returns ([int]bool);
-
-////////////////////////////////////////////////////
-// axioms relating Between and BetweenSet
-////////////////////////////////////////////////////
-axiom(forall f: [int]int, x: int, y: int, z: int :: {BetweenSet(f, x, z)[y]} BetweenSet(f, x, z)[y] <==> Between(f, x, y, z));
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Between(f, x, y, z), BetweenSet(f, x, z)} Between(f, x, y, z) ==> BetweenSet(f, x, z)[y]);
-axiom(forall f: [int]int, x: int, z: int :: {BetweenSet(f, x, z)} Between(f, x, x, x));
-axiom(forall f: [int]int, x: int, z: int :: {BetweenSet(f, x, z)} Between(f, z, z, z));
-
-
-//////////////////////////
-// Axioms for Between
-//////////////////////////
-
-// reflexive
-axiom(forall f: [int]int, x: int :: Between(f, x, x, x));
-
-// step
-axiom(forall f: [int]int, x: int, y: int, z: int, w:int :: {Between(f, y, z, w), f[x]} Between(f, x, f[x], f[x]));
-
-// reach
-axiom(forall f: [int]int, x: int, y: int :: {f[x], Between(f, x, y, y)} Between(f, x, y, y) ==> x == y || Between(f, x, f[x], y));
-
-// cycle
-axiom(forall f: [int]int, x: int, y:int :: {f[x], Between(f, x, y, y)} f[x] == x && Between(f, x, y, y) ==> x == y);
-
-// sandwich
-axiom(forall f: [int]int, x: int, y: int :: {Between(f, x, y, x)} Between(f, x, y, x) ==> x == y);
-
-// order1
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Between(f, x, y, y), Between(f, x, z, z)} Between(f, x, y, y) && Between(f, x, z, z) ==> Between(f, x, y, z) || Between(f, x, z, y));
-
-// order2
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Between(f, x, y, z)} Between(f, x, y, z) ==> Between(f, x, y, y) && Between(f, y, z, z));
-
-// transitive1
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Between(f, x, y, y), Between(f, y, z, z)} Between(f, x, y, y) && Between(f, y, z, z) ==> Between(f, x, z, z));
-
-// transitive2
-axiom(forall f: [int]int, x: int, y: int, z: int, w: int :: {Between(f, x, y, z), Between(f, y, w, z)} Between(f, x, y, z) && Between(f, y, w, z) ==> Between(f, x, y, w) && Between(f, x, w, z));
-
-// transitive3
-axiom(forall f: [int]int, x: int, y: int, z: int, w: int :: {Between(f, x, y, z), Between(f, x, w, y)} Between(f, x, y, z) && Between(f, x, w, y) ==> Between(f, x, w, z) && Between(f, w, y, z));
-
-// This axiom is required to deal with the incompleteness of the trigger for the reflexive axiom.
-// It cannot be proved using the rest of the axioms.
-axiom(forall f: [int]int, u:int, x: int :: {Between(f, u, x, x)} Between(f, u, x, x) ==> Between(f, u, u, x));
-
-// relation between Avoiding and Between
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Avoiding(f, x, y, z)} Avoiding(f, x, y, z) <==> (Between(f, x, y, z) || (Between(f, x, y, y) && !Between(f, x, z, z))));
-axiom(forall f: [int]int, x: int, y: int, z: int :: {Between(f, x, y, z)} Between(f, x, y, z) <==> (Avoiding(f, x, y, z) && Avoiding(f, x, z, z)));
-
-// update
-axiom(forall f: [int]int, u: int, v: int, x: int, p: int, q: int :: {Avoiding(f[p := q], u, v, x)} Avoiding(f[p := q], u, v, x) <==> ((Avoiding(f, u, v, p) && Avoiding(f, u, v, x)) || (Avoiding(f, u, p, x) && p != x && Avoiding(f, q, v, p) && Avoiding(f, q, v, x))));
-
-axiom (forall f: [int]int, p: int, q: int, u: int, w: int :: {BetweenSet(f[p := q], u, w)} Avoiding(f, u, w, p) ==> Equal(BetweenSet(f[p := q], u, w), BetweenSet(f, u, w)));
-axiom (forall f: [int]int, p: int, q: int, u: int, w: int :: {BetweenSet(f[p := q], u, w)} p != w && Avoiding(f, u, p, w) && Avoiding(f, q, w, p) ==> Equal(BetweenSet(f[p := q], u, w), Union(BetweenSet(f, u, p), BetweenSet(f, q, w))));
-axiom (forall f: [int]int, p: int, q: int, u: int, w: int :: {BetweenSet(f[p := q], u, w)} Avoiding(f, u, w, p) || (p != w && Avoiding(f, u, p, w) && Avoiding(f, q, w, p)) || Equal(BetweenSet(f[p := q], u, w), Empty()));
\ No newline at end of file |