axiom "addr_le_def" given to Alt-Ergo considered too weak
ID0002047: This issue was created automatically from Mantis Issue 2047. Further discussion may take place here.
|ID0002047||Frama-Clang||Plug-in > wp||public||2015-01-12||2015-02-12|
|Product Version||-||Target Version||-||Fixed in Version||-|
The loop invariant "xx5" of the attached program "fill1.c" can't be proven with Alt-Ergo. The goal reads fine, viz.:
goal fill_loop_inv_xx5_preserved: forall a_3,a_2,a_1,a : addr. (a_1 <> a_2) -> addr_le(a_3, a_2) -> (region(a.base) <= 0) -> (region(a_3.base) <= 0) -> addr_le(a_3, shift_sint16(a_2, 1))
However, the axiom "addr_le_def" appears to be too weak, it currently reads:
axiom addr_le_def : (forall p:addr. forall q:addr [addr_le(p, q)]. (((p).base = (q).base) -> (addr_le(p, q) -> ((p).offset <= (q).offset))))
While the loop inveriant certainly should be provable, I don't see any way to prove a_3.base=a_2.base with the current version of the file. Moreover, in order for axioms "addr_le_def" and "addr_le_def1" to be a definition of "addr_le(.,.)" in terms of "=" and "<=" etc., axiom "addr_le_def" should be changed to:
axiom addr_le_def : (forall p:addr. forall q:addr [addr_le(p, q)]. (addr_le(p, q) -> p.base = q.base and p.offset <= q.offset))
After that change, Alt-Ergo proves the goal without any problems. The attached file "fill_loop_inv_xx5_preserved_Alt-Ergo.mlw" contains the changed version in a comment at line 408.
If my argument is right, the whole axiomatization should be reviewed to remove similar flaws, which give Frama-C a rather poor performance on address arithmetic. (For that reason, I assigned a higher severity.)
Additional Information :
Originally, I'd submitted this issue to the Alt-Ergo issue tracker, see https://github.com/OCamlPro/alt-ergo/issues/9. I'm indebted to Mohamed Iguernelala for hinting at the weak axiom "addr_le_def", where I had a blind spot.