diff options
| author |  mikebarnett <unknown> | 2009-07-15 21:03:41 +0000 |
|---|---|---|
| committer | mikebarnett <unknown> | 2009-07-15 21:03:41 +0000 |
| commit | ce1c2de044c91624370411e23acab13b0381949b (patch) | |
| tree | 592539996fe08050ead5ee210c973801611dde40 /Test/test2/Quantifiers.bpl | |
Initial set of files.
Diffstat (limited to 'Test/test2/Quantifiers.bpl')
| -rw-r--r-- | Test/test2/Quantifiers.bpl | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/Test/test2/Quantifiers.bpl b/Test/test2/Quantifiers.bpl new file mode 100644 index 00000000..d368fe1f --- /dev/null +++ b/Test/test2/Quantifiers.bpl @@ -0,0 +1,154 @@ +// ----------------------------------------------------------------------- single trigger
+
+function f(int, int) returns (int);
+
+axiom (forall x: int, y: int :: f(x,y) < x+y);
+axiom (forall x: int :: { f(x,10) } f(x,10) == 3);
+
+procedure P(a: int, b: int)
+ requires a <= 25 && b <= 30;
+{
+ start:
+ assert f(a,b) <= 100;
+ return;
+}
+
+procedure Q(a: int, b: int)
+ requires a + 2 <= b;
+{
+ start:
+ assert f(a,b) == 3; // not provable with the trigger given above
+ return;
+}
+
+procedure R(a: int, b: int)
+ requires a + 2 <= b;
+{
+ start:
+ assume b <= 10 && 8 <= a;
+ assert f(a,b) == 3; // now, the trigger should fire
+ return;
+}
+
+// ----------------------------------------------------------------------- multi trigger
+
+function g(int, int) returns (int);
+
+axiom (forall x: int, y: int :: { g(x,10),g(x,y) } g(x,y) == 3); // multi-trigger
+
+procedure S(a: int, b: int)
+ requires a + 2 <= b;
+{
+ start:
+ assert g(a,b) == 3; // not provable with the trigger given above
+ return;
+}
+
+procedure T(a: int, b: int)
+ requires a + 2 <= b;
+{
+ start:
+ assume b <= 10 && 8 <= a;
+ assert g(a,b) == 3; // this should trigger
+ return;
+}
+
+// ----------------------------------------------------------------------- several triggers
+
+function h(int, int) returns (int);
+
+axiom (forall y: int :: { g(y,y) } { h(y,h(y,10)) } h(y, h(y,y)) == y); // several triggers
+
+procedure U0(a: int)
+{
+ start:
+ assert h(a,h(a,a)) == a; // not provable with the triggers given above
+ return;
+}
+
+procedure U1(a: int, b: int)
+{
+ start:
+ assume g(a,b) == 5;
+ assert h(a,h(a,a)) == a; // not provable with the triggers given above
+ return;
+}
+
+procedure V0(a: int, b: int)
+ requires a == b;
+{
+ start:
+ assume g(a,b) == 5;
+ assert h(a,h(a,a)) == a; // this should trigger
+ return;
+}
+
+procedure V1(a: int, b: int)
+{
+ start:
+ assume a == 10;
+ assert h(a,h(a,a)) == a; // this should trigger
+ return;
+}
+
+procedure V2(a: int, b: int)
+{
+ start:
+ assume 0 <= h(a,h(a,10));
+ assume a == 17;
+ assert h(a,h(a,a)) == a; // this should trigger
+ return;
+}
+
+// ----------------------------------------------------------------------- negated triggers
+
+function ka(ref) returns (int);
+function kb(ref) returns (int);
+function kbSynonym(ref) returns (int);
+function isA(ref, name) returns (bool);
+function isB(ref, name) returns (bool);
+const $T: name;
+
+axiom (forall o: ref ::
+ isA(o, $T) ==> ka(o) < ka(o)); // automatically inferred triggers can be both isA(o,$T) and ka(o)
+
+axiom (forall o: ref ::
+ {:nopats isB(o, $T) }
+ isB(o, $T) ==> kb(o) < kbSynonym(o)); // prevent isB(o,$T) from being used as a trigger
+
+axiom (forall o: ref :: kb(o) == kbSynonym(o));
+
+procedure W(o: ref, e: int)
+ requires isB(o, $T);
+{
+ start:
+ assert e > 20; // the isB axiom should not trigger, so this cannot be proved
+ return;
+}
+
+procedure X0(o: ref, e: int)
+ requires isA(o, $T);
+{
+ start:
+ assert e > 20; // this should trigger the isA axiom, so anything is provable
+ return;
+}
+
+procedure X1(o: ref, e: int, u: int)
+ requires isB(o, $T);
+{
+ start:
+ assume f(kb(o), kb(o)) == u;
+ assert e > 20; // this should now trigger the isB axiom, so anything is provable
+ return;
+}
+
+procedure X2(o: ref, e: int, u: int)
+ requires isB(o, $T);
+{
+ start:
+ assert e > 20; // error is report here, providing evidence that the isB axiom has not been triggered
+ return;
+}
+
+type name, ref;
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