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Diffstat (limited to 'Test/civl/treiber-stack.bpl')
| -rw-r--r-- | Test/civl/treiber-stack.bpl | 207 |
1 files changed, 207 insertions, 0 deletions
diff --git a/Test/civl/treiber-stack.bpl b/Test/civl/treiber-stack.bpl new file mode 100644 index 00000000..a184886d --- /dev/null +++ b/Test/civl/treiber-stack.bpl @@ -0,0 +1,207 @@ +// RUN: %boogie -noinfer -typeEncoding:m -useArrayTheory "%s" > "%t" +// RUN: %diff "%s.expect" "%t" + +const null: int; +type lmap; +function {:linear "Node"} dom(lmap): [int]bool; +function map(lmap): [int]int; +function {:builtin "MapConst"} MapConstBool(bool) : [int]bool; + +function EmptyLmap(): (lmap); +axiom (dom(EmptyLmap()) == MapConstBool(false)); + +function Add(x: lmap, i: int, v: int): (lmap); +axiom (forall x: lmap, i: int, v: int :: dom(Add(x, i, v)) == dom(x)[i:=true] && map(Add(x, i, v)) == map(x)[i := v]); + +function Remove(x: lmap, i: int): (lmap); +axiom (forall x: lmap, i: int :: dom(Remove(x, i)) == dom(x)[i:=false] && map(Remove(x, i)) == map(x)); + +procedure {:yields} {:layer 0,1} ReadTopOfStack() returns (v:int); +ensures {:right} |{ A: assume v == null || dom(Stack)[v] || Used[v]; return true; }|; + +procedure {:yields} {:layer 0,1} Load(i:int) returns (v:int); +ensures {:right} |{ A: assert dom(Stack)[i] || 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:int, v:int) 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: int, newVal: int, {: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: int, newVal: int) returns (r: bool); +ensures {:atomic} |{ A: goto B,C; + B: assume oldVal == TopOfStack; TopOfStack := newVal; Used[oldVal] := true; Stack := Remove(Stack, oldVal); r := true; return true; + C: assume oldVal != TopOfStack; r := false; return true; }|; + +var {:layer 0} TopOfStack: int; +var {:linear "Node"} {:layer 0} Stack: lmap; + + +function {:inline} Inv(TopOfStack: int, 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: [int]bool; + +function {:inline} {:linear "Node"} NodeCollector(x: int) : [int]bool +{ + MapConstBool(false)[x := true] +} +function {:inline} {:linear "Node"} NodeSetCollector(x: [int]bool) : [int]bool +{ + x +} + +procedure {:yields} {:layer 1} push(x: int, {: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: int; + 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) { + 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() returns (t: int) +requires {:layer 1} Inv(TopOfStack, Stack); +ensures {:layer 1} Inv(TopOfStack, Stack); +ensures {:atomic} |{ A: assume TopOfStack != null; t := TopOfStack; Used[t] := true; TopOfStack := map(Stack)[t]; Stack := Remove(Stack, t); return true; }|; +{ + var g: bool; + var x: int; + + 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 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()));
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