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-rw-r--r--Test/z3api/boog25.bpl568
1 files changed, 284 insertions, 284 deletions
diff --git a/Test/z3api/boog25.bpl b/Test/z3api/boog25.bpl
index 0ee4163c..eff6e2fb 100644
--- a/Test/z3api/boog25.bpl
+++ b/Test/z3api/boog25.bpl
@@ -1,284 +1,284 @@
-type name;
-type ref;
-type byte;
-function OneByteToInt(byte) returns (int);
-function TwoBytesToInt(byte, byte) returns (int);
-function FourBytesToInt(byte, byte, byte, byte) returns (int);
-axiom(forall b0:byte, c0:byte :: {OneByteToInt(b0), OneByteToInt(c0)} OneByteToInt(b0) == OneByteToInt(c0) ==> b0 == c0);
-axiom(forall b0:byte, b1: byte, c0:byte, c1:byte :: {TwoBytesToInt(b0, b1), TwoBytesToInt(c0, c1)} TwoBytesToInt(b0, b1) == TwoBytesToInt(c0, c1) ==> b0 == c0 && b1 == c1);
-axiom(forall b0:byte, b1: byte, b2:byte, b3:byte, c0:byte, c1:byte, c2:byte, c3:byte :: {FourBytesToInt(b0, b1, b2, b3), FourBytesToInt(c0, c1, c2, c3)} FourBytesToInt(b0, b1, b2, b3) == FourBytesToInt(c0, c1, c2, c3) ==> b0 == c0 && b1 == c1 && b2 == c2 && b3 == c3);
-
-// Mutable
-var Mem_BYTE:[int]byte;
-var alloc:[int]name;
-
-
-function Field(int) returns (name);
-function Base(int) returns (int);
-
-// Constants
-const unique UNALLOCATED:name;
-const unique ALLOCATED: name;
-const unique FREED:name;
-
-const unique BYTE:name;
-
-function Equal([int]bool, [int]bool) returns (bool);
-function Subset([int]bool, [int]bool) returns (bool);
-function Disjoint([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);
-function Intersection([int]bool, [int]bool) returns ([int]bool);
-function Difference([int]bool, [int]bool) returns ([int]bool);
-function Dereference([int]bool, [int]int) returns ([int]bool);
-function Inverse(f:[int]int, x:int) returns ([int]bool);
-
-function AtLeast(int, int) returns ([int]bool);
-function Rep(int, int) returns (int);
-axiom(forall n:int, x:int, y:int :: {AtLeast(n,x)[y]} AtLeast(n,x)[y] ==> x <= y && Rep(n,x) == Rep(n,y));
-axiom(forall n:int, x:int, y:int :: {AtLeast(n,x),Rep(n,x),Rep(n,y)} x <= y && Rep(n,x) == Rep(n,y) ==> AtLeast(n,x)[y]);
-axiom(forall n:int, x:int :: {AtLeast(n,x)} AtLeast(n,x)[x]);
-axiom(forall n:int, x:int, z:int :: {PLUS(x,n,z)} Rep(n,x) == Rep(n,PLUS(x,n,z)));
-axiom(forall n:int, x:int :: {Rep(n,x)} (exists k:int :: Rep(n,x) - x == n*k));
-
-/*
-function AtLeast(int, int) returns ([int]bool);
-function ModEqual(int, int, int) returns (bool);
-axiom(forall n:int, x:int :: ModEqual(n,x,x));
-axiom(forall n:int, x:int, y:int :: {ModEqual(n,x,y)} ModEqual(n,x,y) ==> ModEqual(n,y,x));
-axiom(forall n:int, x:int, y:int, z:int :: {ModEqual(n,x,y), ModEqual(n,y,z)} ModEqual(n,x,y) && ModEqual(n,y,z) ==> ModEqual(n,x,z));
-axiom(forall n:int, x:int, z:int :: {PLUS(x,n,z)} ModEqual(n,x,PLUS(x,n,z)));
-axiom(forall n:int, x:int, y:int :: {ModEqual(n,x,y)} ModEqual(n,x,y) ==> (exists k:int :: x - y == n*k));
-axiom(forall x:int, n:int, y:int :: {AtLeast(n,x)[y]}{ModEqual(n,x,y)} AtLeast(n,x)[y] <==> x <= y && ModEqual(n,x,y));
-axiom(forall x:int, n:int :: {AtLeast(n,x)} AtLeast(n,x)[x]);
-*/
-
-function Array(int, int, int) returns ([int]bool);
-axiom(forall x:int, n:int, z:int :: {Array(x,n,z)} z <= 0 ==> Equal(Array(x,n,z), Empty()));
-axiom(forall x:int, n:int, z:int :: {Array(x,n,z)} z > 0 ==> Equal(Array(x,n,z), Difference(AtLeast(n,x),AtLeast(n,PLUS(x,n,z)))));
-
-
-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]);
-
-/* this formulation of Union IS more complete than the earlier one */
-/* (A U B)[e], A[d], A U B = Singleton(c), d != e */
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T)[x]} Union(S,T)[x] <==> S[x] || T[x]);
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T), S[x]} S[x] ==> Union(S,T)[x]);
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T), T[x]} T[x] ==> Union(S,T)[x]);
-
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T)[x]} Intersection(S,T)[x] <==> S[x] && T[x]);
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T), S[x]} S[x] && T[x] ==> Intersection(S,T)[x]);
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T), T[x]} S[x] && T[x] ==> Intersection(S,T)[x]);
-
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Difference(S,T)[x]} Difference(S,T)[x] <==> S[x] && !T[x]);
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {Difference(S,T), S[x]} S[x] ==> Difference(S,T)[x] || T[x]);
-
-axiom(forall x:int, S:[int]bool, M:[int]int :: {Dereference(S,M)[x]} Dereference(S,M)[x] ==> (exists y:int :: x == M[y] && S[y]));
-axiom(forall x:int, S:[int]bool, M:[int]int :: {M[x], S[x], Dereference(S,M)} S[x] ==> Dereference(S,M)[M[x]]);
-axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])} !S[x] ==> Equal(Dereference(S,M[x := y]), Dereference(S,M)));
-axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])}
- S[x] && Equal(Intersection(Inverse(M,M[x]), S), Singleton(x)) ==> Equal(Dereference(S,M[x := y]), Union(Difference(Dereference(S,M), Singleton(M[x])), Singleton(y))));
-axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])}
- S[x] && !Equal(Intersection(Inverse(M,M[x]), S), Singleton(x)) ==> Equal(Dereference(S,M[x := y]), Union(Dereference(S,M), Singleton(y))));
-
-axiom(forall f:[int]int, x:int :: {Inverse(f,f[x])} Inverse(f,f[x])[x]);
-axiom(forall f:[int]int, x:int, y:int :: {Inverse(f[x := y],y)} Equal(Inverse(f[x := y],y), Union(Inverse(f,y), Singleton(x))));
-axiom(forall f:[int]int, x:int, y:int, z:int :: {Inverse(f[x := y],z)} y == z || Equal(Inverse(f[x := y],z), Difference(Inverse(f,z), Singleton(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)} 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]));
-axiom(forall x:int, S:[int]bool, T:[int]bool :: {S[x], Disjoint(S,T), T[x]} !(S[x] && Disjoint(S,T) && T[x]));
-axiom(forall S:[int]bool, T:[int]bool :: {Disjoint(S,T)} Disjoint(S,T) || (exists x:int :: S[x] && T[x]));
-
-function Unified([name][int]int) returns ([int]int);
-axiom(forall M:[name][int]int, x:int :: {Unified(M)[x]} Unified(M)[x] == M[Field(x)][x]);
-axiom(forall M:[name][int]int, x:int, y:int :: {Unified(M[Field(x) := M[Field(x)][x := y]])} Unified(M[Field(x) := M[Field(x)][x := y]]) == Unified(M)[x := y]);
-// Memory model
-
-var Mem: [name][int]int;
-
-function Match(a:int, t:name) returns (bool);
-function HasType(v:int, t:name) returns (bool);
-function Values(t:name) returns ([int]bool);
-
-axiom(forall v:int, t:name :: {Values(t)[v]} Values(t)[v] ==> HasType(v, t));
-axiom(forall v:int, t:name :: {HasType(v, t), Values(t)} HasType(v, t) ==> Values(t)[v]);
-
-// Field declarations
-
-
-// Type declarations
-
-const unique INT4_name:name;
-const unique PINT4_name:name;
-
-// Field definitions
-
-// Type definitions
-
-axiom(forall a:int :: {Match(a, INT4_name)}
- Match(a, INT4_name) <==> Field(a) == INT4_name);
-axiom(forall v:int :: HasType(v, INT4_name));
-
-axiom(forall a:int :: {Match(a, PINT4_name)}
- Match(a, PINT4_name) <==> Field(a) == PINT4_name);
-axiom(forall v:int :: {HasType(v, PINT4_name)} {Match(v, INT4_name)}
- HasType(v, PINT4_name) <==> (v == 0 || (v > 0 && Match(v, INT4_name))));
-
-function MINUS_BOTH_PTR_OR_BOTH_INT(a:int, b:int, size:int) returns (int);
-axiom(forall a:int, b:int, size:int :: {MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size)}
-size * MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size) <= a - b && a - b < size * (MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size) + 1));
-
-function MINUS_LEFT_PTR(a:int, a_size:int, b:int) returns (int);
-axiom(forall a:int, a_size:int, b:int :: {MINUS_LEFT_PTR(a,a_size,b)} MINUS_LEFT_PTR(a,a_size,b) == a - a_size * b);
-
-function PLUS(a:int, a_size:int, b:int) returns (int);
-axiom(forall a:int, a_size:int, b:int :: {PLUS(a,a_size,b)} PLUS(a,a_size,b) == a + a_size * b);
-
-function MULT(a:int, b:int) returns (int); // a*b
-axiom(forall a:int, b:int :: {MULT(a,b)} MULT(a,b) == a * b);
-
-function DIV(a:int, b:int) returns (int); // a/b
-
-axiom(forall a:int, b:int :: {DIV(a,b)}
-a >= 0 && b > 0 ==> b * DIV(a,b) <= a && a < b * (DIV(a,b) + 1)
-);
-
-axiom(forall a:int, b:int :: {DIV(a,b)}
-a >= 0 && b < 0 ==> b * DIV(a,b) <= a && a < b * (DIV(a,b) - 1)
-);
-
-axiom(forall a:int, b:int :: {DIV(a,b)}
-a < 0 && b > 0 ==> b * DIV(a,b) >= a && a > b * (DIV(a,b) - 1)
-);
-
-axiom(forall a:int, b:int :: {DIV(a,b)}
-a < 0 && b < 0 ==> b * DIV(a,b) >= a && a > b * (DIV(a,b) + 1)
-);
-
-function BINARY_BOTH_INT(a:int, b:int) returns (int);
-
-function POW2(a:int) returns (bool);
-axiom POW2(1);
-axiom POW2(2);
-axiom POW2(4);
-axiom POW2(8);
-axiom POW2(16);
-axiom POW2(32);
-axiom POW2(64);
-axiom POW2(128);
-axiom POW2(256);
-axiom POW2(512);
-axiom POW2(1024);
-axiom POW2(2048);
-axiom POW2(4096);
-axiom POW2(8192);
-axiom POW2(16384);
-axiom POW2(32768);
-axiom POW2(65536);
-axiom POW2(131072);
-axiom POW2(262144);
-axiom POW2(524288);
-axiom POW2(1048576);
-axiom POW2(2097152);
-axiom POW2(4194304);
-axiom POW2(8388608);
-axiom POW2(16777216);
-axiom POW2(33554432);
-
-function choose(a:bool, b:int, c:int) returns (x:int);
-axiom(forall a:bool, b:int, c:int :: {choose(a,b,c)} a ==> choose(a,b,c) == b);
-axiom(forall a:bool, b:int, c:int :: {choose(a,b,c)} !a ==> choose(a,b,c) == c);
-
-function BIT_BAND(a:int, b:int) returns (x:int);
-axiom(forall a:int, b:int :: {BIT_BAND(a,b)} a == b ==> BIT_BAND(a,b) == a);
-axiom(forall a:int, b:int :: {BIT_BAND(a,b)} POW2(a) && POW2(b) && a != b ==> BIT_BAND(a,b) == 0);
-axiom(forall a:int, b:int :: {BIT_BAND(a,b)} a == 0 || b == 0 ==> BIT_BAND(a,b) == 0);
-
-function BIT_BOR(a:int, b:int) returns (x:int);
-
-function BIT_BXOR(a:int, b:int) returns (x:int);
-
-function BIT_BNOT(a:int) returns (int);
-
-function LIFT(a:bool) returns (int);
-axiom(forall a:bool :: {LIFT(a)} a <==> LIFT(a) != 0);
-
-function NOT(a:int) returns (int);
-axiom(forall a:int :: {NOT(a)} a == 0 ==> NOT(a) != 0);
-axiom(forall a:int :: {NOT(a)} a != 0 ==> NOT(a) == 0);
-
-function NULL_CHECK(a:int) returns (int);
-axiom(forall a:int :: {NULL_CHECK(a)} a == 0 ==> NULL_CHECK(a) != 0);
-axiom(forall a:int :: {NULL_CHECK(a)} a != 0 ==> NULL_CHECK(a) == 0);
-
-procedure nondet_choice() returns (x:int);
-
-
-procedure havoc_assert(i:int);
-requires (i != 0);
-
-procedure havoc_assume(i:int);
-ensures (i != 0);
-
-procedure __HAVOC_free(a:int);
-modifies alloc;
-ensures (forall x:int :: {alloc[x]} x == a || old(alloc)[x] == alloc[x]);
-ensures (alloc[a] == FREED);
-// Additional checks guarded by tranlator flags
-// requires alloc[a] == ALLOCATED;
-// requires Base(a) == a;
-
-procedure __HAVOC_malloc(obj_size:int) returns (new:int);
-requires obj_size >= 0;
-modifies alloc;
-ensures (new > 0);
-ensures (forall x:int :: {Base(x)} new <= x && x < new+obj_size ==> Base(x) == new);
-ensures (forall x:int :: {alloc[x]} x == new || old(alloc)[x] == alloc[x]);
-ensures old(alloc)[new] == UNALLOCATED && alloc[new] == ALLOCATED;
-
-procedure _strdup(str:int) returns (new:int);
-
-procedure _xstrcasecmp(a0:int, a1:int) returns (ret:int);
-
-procedure _xstrcmp(a0:int, a1:int) returns (ret:int);
-
-
-
-
-
-procedure main ( ) returns ($result.main$3.5$1$:int)
-
-modifies alloc;
-//TAG: no freed locations
-ensures(forall f:int :: {alloc[Base(f)]} old(alloc)[Base(f)] == UNALLOCATED || old(alloc)[Base(f)] == alloc[Base(f)]);
-
-modifies Mem;
-//TAG: no updated memory locations
-ensures(forall f: name, m:int :: {Mem[f][m]} Mem[f][m] == old(Mem[f])[m]);
-free ensures(Mem[Field(0)][0] == old(Mem[Field(0)])[0]);
-
-//TAG: Type Safety Precondition
-requires(forall a:int :: {Mem[Field(a)][a]} HasType(Mem[Field(a)][a], Field(a)));
-//TAG: Type Safety Postcondition
-ensures(forall a:int :: {Mem[Field(a)][a]} HasType(Mem[Field(a)][a], Field(a)));
-ensures(HasType($result.main$3.5$1$, INT4_name));
-{
-
-var a : int;
-var b : int;
-var c : int;
-
-c := LIFT (b < a) ;
-assert (c != 0 <==> b < a);
-
-
-}
-
+type name;
+type ref;
+type byte;
+function OneByteToInt(byte) returns (int);
+function TwoBytesToInt(byte, byte) returns (int);
+function FourBytesToInt(byte, byte, byte, byte) returns (int);
+axiom(forall b0:byte, c0:byte :: {OneByteToInt(b0), OneByteToInt(c0)} OneByteToInt(b0) == OneByteToInt(c0) ==> b0 == c0);
+axiom(forall b0:byte, b1: byte, c0:byte, c1:byte :: {TwoBytesToInt(b0, b1), TwoBytesToInt(c0, c1)} TwoBytesToInt(b0, b1) == TwoBytesToInt(c0, c1) ==> b0 == c0 && b1 == c1);
+axiom(forall b0:byte, b1: byte, b2:byte, b3:byte, c0:byte, c1:byte, c2:byte, c3:byte :: {FourBytesToInt(b0, b1, b2, b3), FourBytesToInt(c0, c1, c2, c3)} FourBytesToInt(b0, b1, b2, b3) == FourBytesToInt(c0, c1, c2, c3) ==> b0 == c0 && b1 == c1 && b2 == c2 && b3 == c3);
+
+// Mutable
+var Mem_BYTE:[int]byte;
+var alloc:[int]name;
+
+
+function Field(int) returns (name);
+function Base(int) returns (int);
+
+// Constants
+const unique UNALLOCATED:name;
+const unique ALLOCATED: name;
+const unique FREED:name;
+
+const unique BYTE:name;
+
+function Equal([int]bool, [int]bool) returns (bool);
+function Subset([int]bool, [int]bool) returns (bool);
+function Disjoint([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);
+function Intersection([int]bool, [int]bool) returns ([int]bool);
+function Difference([int]bool, [int]bool) returns ([int]bool);
+function Dereference([int]bool, [int]int) returns ([int]bool);
+function Inverse(f:[int]int, x:int) returns ([int]bool);
+
+function AtLeast(int, int) returns ([int]bool);
+function Rep(int, int) returns (int);
+axiom(forall n:int, x:int, y:int :: {AtLeast(n,x)[y]} AtLeast(n,x)[y] ==> x <= y && Rep(n,x) == Rep(n,y));
+axiom(forall n:int, x:int, y:int :: {AtLeast(n,x),Rep(n,x),Rep(n,y)} x <= y && Rep(n,x) == Rep(n,y) ==> AtLeast(n,x)[y]);
+axiom(forall n:int, x:int :: {AtLeast(n,x)} AtLeast(n,x)[x]);
+axiom(forall n:int, x:int, z:int :: {PLUS(x,n,z)} Rep(n,x) == Rep(n,PLUS(x,n,z)));
+axiom(forall n:int, x:int :: {Rep(n,x)} (exists k:int :: Rep(n,x) - x == n*k));
+
+/*
+function AtLeast(int, int) returns ([int]bool);
+function ModEqual(int, int, int) returns (bool);
+axiom(forall n:int, x:int :: ModEqual(n,x,x));
+axiom(forall n:int, x:int, y:int :: {ModEqual(n,x,y)} ModEqual(n,x,y) ==> ModEqual(n,y,x));
+axiom(forall n:int, x:int, y:int, z:int :: {ModEqual(n,x,y), ModEqual(n,y,z)} ModEqual(n,x,y) && ModEqual(n,y,z) ==> ModEqual(n,x,z));
+axiom(forall n:int, x:int, z:int :: {PLUS(x,n,z)} ModEqual(n,x,PLUS(x,n,z)));
+axiom(forall n:int, x:int, y:int :: {ModEqual(n,x,y)} ModEqual(n,x,y) ==> (exists k:int :: x - y == n*k));
+axiom(forall x:int, n:int, y:int :: {AtLeast(n,x)[y]}{ModEqual(n,x,y)} AtLeast(n,x)[y] <==> x <= y && ModEqual(n,x,y));
+axiom(forall x:int, n:int :: {AtLeast(n,x)} AtLeast(n,x)[x]);
+*/
+
+function Array(int, int, int) returns ([int]bool);
+axiom(forall x:int, n:int, z:int :: {Array(x,n,z)} z <= 0 ==> Equal(Array(x,n,z), Empty()));
+axiom(forall x:int, n:int, z:int :: {Array(x,n,z)} z > 0 ==> Equal(Array(x,n,z), Difference(AtLeast(n,x),AtLeast(n,PLUS(x,n,z)))));
+
+
+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]);
+
+/* this formulation of Union IS more complete than the earlier one */
+/* (A U B)[e], A[d], A U B = Singleton(c), d != e */
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T)[x]} Union(S,T)[x] <==> S[x] || T[x]);
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T), S[x]} S[x] ==> Union(S,T)[x]);
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Union(S,T), T[x]} T[x] ==> Union(S,T)[x]);
+
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T)[x]} Intersection(S,T)[x] <==> S[x] && T[x]);
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T), S[x]} S[x] && T[x] ==> Intersection(S,T)[x]);
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Intersection(S,T), T[x]} S[x] && T[x] ==> Intersection(S,T)[x]);
+
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Difference(S,T)[x]} Difference(S,T)[x] <==> S[x] && !T[x]);
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {Difference(S,T), S[x]} S[x] ==> Difference(S,T)[x] || T[x]);
+
+axiom(forall x:int, S:[int]bool, M:[int]int :: {Dereference(S,M)[x]} Dereference(S,M)[x] ==> (exists y:int :: x == M[y] && S[y]));
+axiom(forall x:int, S:[int]bool, M:[int]int :: {M[x], S[x], Dereference(S,M)} S[x] ==> Dereference(S,M)[M[x]]);
+axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])} !S[x] ==> Equal(Dereference(S,M[x := y]), Dereference(S,M)));
+axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])}
+ S[x] && Equal(Intersection(Inverse(M,M[x]), S), Singleton(x)) ==> Equal(Dereference(S,M[x := y]), Union(Difference(Dereference(S,M), Singleton(M[x])), Singleton(y))));
+axiom(forall x:int, y:int, S:[int]bool, M:[int]int :: {Dereference(S,M[x := y])}
+ S[x] && !Equal(Intersection(Inverse(M,M[x]), S), Singleton(x)) ==> Equal(Dereference(S,M[x := y]), Union(Dereference(S,M), Singleton(y))));
+
+axiom(forall f:[int]int, x:int :: {Inverse(f,f[x])} Inverse(f,f[x])[x]);
+axiom(forall f:[int]int, x:int, y:int :: {Inverse(f[x := y],y)} Equal(Inverse(f[x := y],y), Union(Inverse(f,y), Singleton(x))));
+axiom(forall f:[int]int, x:int, y:int, z:int :: {Inverse(f[x := y],z)} y == z || Equal(Inverse(f[x := y],z), Difference(Inverse(f,z), Singleton(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)} 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]));
+axiom(forall x:int, S:[int]bool, T:[int]bool :: {S[x], Disjoint(S,T), T[x]} !(S[x] && Disjoint(S,T) && T[x]));
+axiom(forall S:[int]bool, T:[int]bool :: {Disjoint(S,T)} Disjoint(S,T) || (exists x:int :: S[x] && T[x]));
+
+function Unified([name][int]int) returns ([int]int);
+axiom(forall M:[name][int]int, x:int :: {Unified(M)[x]} Unified(M)[x] == M[Field(x)][x]);
+axiom(forall M:[name][int]int, x:int, y:int :: {Unified(M[Field(x) := M[Field(x)][x := y]])} Unified(M[Field(x) := M[Field(x)][x := y]]) == Unified(M)[x := y]);
+// Memory model
+
+var Mem: [name][int]int;
+
+function Match(a:int, t:name) returns (bool);
+function HasType(v:int, t:name) returns (bool);
+function Values(t:name) returns ([int]bool);
+
+axiom(forall v:int, t:name :: {Values(t)[v]} Values(t)[v] ==> HasType(v, t));
+axiom(forall v:int, t:name :: {HasType(v, t), Values(t)} HasType(v, t) ==> Values(t)[v]);
+
+// Field declarations
+
+
+// Type declarations
+
+const unique INT4_name:name;
+const unique PINT4_name:name;
+
+// Field definitions
+
+// Type definitions
+
+axiom(forall a:int :: {Match(a, INT4_name)}
+ Match(a, INT4_name) <==> Field(a) == INT4_name);
+axiom(forall v:int :: HasType(v, INT4_name));
+
+axiom(forall a:int :: {Match(a, PINT4_name)}
+ Match(a, PINT4_name) <==> Field(a) == PINT4_name);
+axiom(forall v:int :: {HasType(v, PINT4_name)} {Match(v, INT4_name)}
+ HasType(v, PINT4_name) <==> (v == 0 || (v > 0 && Match(v, INT4_name))));
+
+function MINUS_BOTH_PTR_OR_BOTH_INT(a:int, b:int, size:int) returns (int);
+axiom(forall a:int, b:int, size:int :: {MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size)}
+size * MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size) <= a - b && a - b < size * (MINUS_BOTH_PTR_OR_BOTH_INT(a,b,size) + 1));
+
+function MINUS_LEFT_PTR(a:int, a_size:int, b:int) returns (int);
+axiom(forall a:int, a_size:int, b:int :: {MINUS_LEFT_PTR(a,a_size,b)} MINUS_LEFT_PTR(a,a_size,b) == a - a_size * b);
+
+function PLUS(a:int, a_size:int, b:int) returns (int);
+axiom(forall a:int, a_size:int, b:int :: {PLUS(a,a_size,b)} PLUS(a,a_size,b) == a + a_size * b);
+
+function MULT(a:int, b:int) returns (int); // a*b
+axiom(forall a:int, b:int :: {MULT(a,b)} MULT(a,b) == a * b);
+
+function DIV(a:int, b:int) returns (int); // a/b
+
+axiom(forall a:int, b:int :: {DIV(a,b)}
+a >= 0 && b > 0 ==> b * DIV(a,b) <= a && a < b * (DIV(a,b) + 1)
+);
+
+axiom(forall a:int, b:int :: {DIV(a,b)}
+a >= 0 && b < 0 ==> b * DIV(a,b) <= a && a < b * (DIV(a,b) - 1)
+);
+
+axiom(forall a:int, b:int :: {DIV(a,b)}
+a < 0 && b > 0 ==> b * DIV(a,b) >= a && a > b * (DIV(a,b) - 1)
+);
+
+axiom(forall a:int, b:int :: {DIV(a,b)}
+a < 0 && b < 0 ==> b * DIV(a,b) >= a && a > b * (DIV(a,b) + 1)
+);
+
+function BINARY_BOTH_INT(a:int, b:int) returns (int);
+
+function POW2(a:int) returns (bool);
+axiom POW2(1);
+axiom POW2(2);
+axiom POW2(4);
+axiom POW2(8);
+axiom POW2(16);
+axiom POW2(32);
+axiom POW2(64);
+axiom POW2(128);
+axiom POW2(256);
+axiom POW2(512);
+axiom POW2(1024);
+axiom POW2(2048);
+axiom POW2(4096);
+axiom POW2(8192);
+axiom POW2(16384);
+axiom POW2(32768);
+axiom POW2(65536);
+axiom POW2(131072);
+axiom POW2(262144);
+axiom POW2(524288);
+axiom POW2(1048576);
+axiom POW2(2097152);
+axiom POW2(4194304);
+axiom POW2(8388608);
+axiom POW2(16777216);
+axiom POW2(33554432);
+
+function choose(a:bool, b:int, c:int) returns (x:int);
+axiom(forall a:bool, b:int, c:int :: {choose(a,b,c)} a ==> choose(a,b,c) == b);
+axiom(forall a:bool, b:int, c:int :: {choose(a,b,c)} !a ==> choose(a,b,c) == c);
+
+function BIT_BAND(a:int, b:int) returns (x:int);
+axiom(forall a:int, b:int :: {BIT_BAND(a,b)} a == b ==> BIT_BAND(a,b) == a);
+axiom(forall a:int, b:int :: {BIT_BAND(a,b)} POW2(a) && POW2(b) && a != b ==> BIT_BAND(a,b) == 0);
+axiom(forall a:int, b:int :: {BIT_BAND(a,b)} a == 0 || b == 0 ==> BIT_BAND(a,b) == 0);
+
+function BIT_BOR(a:int, b:int) returns (x:int);
+
+function BIT_BXOR(a:int, b:int) returns (x:int);
+
+function BIT_BNOT(a:int) returns (int);
+
+function LIFT(a:bool) returns (int);
+axiom(forall a:bool :: {LIFT(a)} a <==> LIFT(a) != 0);
+
+function NOT(a:int) returns (int);
+axiom(forall a:int :: {NOT(a)} a == 0 ==> NOT(a) != 0);
+axiom(forall a:int :: {NOT(a)} a != 0 ==> NOT(a) == 0);
+
+function NULL_CHECK(a:int) returns (int);
+axiom(forall a:int :: {NULL_CHECK(a)} a == 0 ==> NULL_CHECK(a) != 0);
+axiom(forall a:int :: {NULL_CHECK(a)} a != 0 ==> NULL_CHECK(a) == 0);
+
+procedure nondet_choice() returns (x:int);
+
+
+procedure havoc_assert(i:int);
+requires (i != 0);
+
+procedure havoc_assume(i:int);
+ensures (i != 0);
+
+procedure __HAVOC_free(a:int);
+modifies alloc;
+ensures (forall x:int :: {alloc[x]} x == a || old(alloc)[x] == alloc[x]);
+ensures (alloc[a] == FREED);
+// Additional checks guarded by tranlator flags
+// requires alloc[a] == ALLOCATED;
+// requires Base(a) == a;
+
+procedure __HAVOC_malloc(obj_size:int) returns (new:int);
+requires obj_size >= 0;
+modifies alloc;
+ensures (new > 0);
+ensures (forall x:int :: {Base(x)} new <= x && x < new+obj_size ==> Base(x) == new);
+ensures (forall x:int :: {alloc[x]} x == new || old(alloc)[x] == alloc[x]);
+ensures old(alloc)[new] == UNALLOCATED && alloc[new] == ALLOCATED;
+
+procedure _strdup(str:int) returns (new:int);
+
+procedure _xstrcasecmp(a0:int, a1:int) returns (ret:int);
+
+procedure _xstrcmp(a0:int, a1:int) returns (ret:int);
+
+
+
+
+
+procedure main ( ) returns ($result.main$3.5$1$:int)
+
+modifies alloc;
+//TAG: no freed locations
+ensures(forall f:int :: {alloc[Base(f)]} old(alloc)[Base(f)] == UNALLOCATED || old(alloc)[Base(f)] == alloc[Base(f)]);
+
+modifies Mem;
+//TAG: no updated memory locations
+ensures(forall f: name, m:int :: {Mem[f][m]} Mem[f][m] == old(Mem[f])[m]);
+free ensures(Mem[Field(0)][0] == old(Mem[Field(0)])[0]);
+
+//TAG: Type Safety Precondition
+requires(forall a:int :: {Mem[Field(a)][a]} HasType(Mem[Field(a)][a], Field(a)));
+//TAG: Type Safety Postcondition
+ensures(forall a:int :: {Mem[Field(a)][a]} HasType(Mem[Field(a)][a], Field(a)));
+ensures(HasType($result.main$3.5$1$, INT4_name));
+{
+
+var a : int;
+var b : int;
+var c : int;
+
+c := LIFT (b < a) ;
+assert (c != 0 <==> b < a);
+
+
+}
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-24 01:03:08 +0000