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0002338Frama-CPlug-in > wppublic2017-12-18 12:432019-03-11 11:26
Sulfur-20171101Ubuntu 17.04
0002338: \false provable from recursive logic definition
Running "frama-c -wp foo.c -wp-prover alt-ergo -wp-prover eprover" on the attached file proves all goals, including a lemma "Check" which just says "\false", from nothing but a recursive definition of a logic int function.
The latter is well-founded since its only recursive call uses a parameter value n==0 which immediately employs the base case.

The problem disappears
(1) when "integer" is used as result type and as 3rd parameter type,
(2) when "a[]" is omitted,
(3) when lemma "Alpha" is renamed to a name lexicographically after "Check", or
(4) when "cvc3" or "cvc4-15" is used instead of "eprover".
The problem remains, however, when "z3" is used.
No tags attached.
c foo.c (220) 2017-12-18 12:43
txt diff.txt (1,575) 2017-12-18 13:28
? eprover.input (3,591) 2017-12-18 16:55
Issue History
2017-12-18 12:43JochenNew Issue
2017-12-18 12:43JochenStatusnew => assigned
2017-12-18 12:43JochenAssigned To => correnson
2017-12-18 12:43JochenFile Added: foo.c
2017-12-18 12:57JochenNote Added: 0006492
2017-12-18 13:28JochenNote Added: 0006493
2017-12-18 13:28JochenFile Added: diff.txt
2017-12-18 14:59corrensonNote Added: 0006495
2017-12-18 16:55JochenNote Added: 0006498
2017-12-18 16:55JochenFile Added: eprover.input
2019-03-09 13:45evdenisNote Added: 0006756
2019-03-09 13:50evdenisNote Added: 0006757
2019-03-11 11:26virgileNote Added: 0006758

2017-12-18 12:57   
The naming dependance (3) reminds me to the closed issue 0002237, where ordering of goals was involved, too. Maybe both issues are related?
2017-12-18 13:28   
Trying to track down the naming dependence (3) somewhat further, I ran the above command with "-wp-out outA" added on the original file "foo.c", and with "-wp-out outD" on a modification of "foo.c" where "AInit" was renamed to "DInit". Then I renamed the files in "outD/typed" appropriately (e.g. "lemma_DInit.ergo" to "lemma_AInit.ergo"), and ran "diff -r outA outD >diff.txt" (attached).

It appears to me the only difference is in file "Axiomatic.why" where the order is "Q_TL_Acc, Q_AInit, Q_Check" in outA/, but "Q_Check, Q_TL_Acc, Q_DInit" in outD/.
2017-12-18 14:59   
Yes I think the order / dependency problem is harmful here... Thanks for the inputs, it would help to fix the entire problem.
2017-12-18 16:55   
I managed to intercept the input given to eprover, and to boil it down to the version in "eprover.input" (attached).

The call "eprover -s -R -xAuto -tAuto --cpu-limit=10 --tstp-in eprover.input" (options as observed from the call by why3) results in "$false" being proven. None of the axioms can be deleted without losing the provability.

A strange list of predicates is involved in the inconsistency, viz.
    base from_int get included infix_ls infix_lseq infix_pl infix_pl1 is_sint32 is_uint32 l_Acc mk_addr mod offset prefix_mn prefix_mn1 separated shift to_sint32 to_uint32 truncate valid_rd valid_rw
(generated from "eprover.input"). Intersting enough, the translation of the lemma "AInit" doesn't appear in the file. It seems that this lemma is needed in the C source only to ensure inclusion of some axioms that participate in the inconsistency.
2019-03-09 13:45   
If the return value type of Acc will be changed from "int" to "integer" then contradiction disappears. Similar bug [^]
I think that maybe it is possible to extract the exact steps to contradiction with z3, because it's very hard to understand eprover output.
2019-03-09 13:50   
> "translation of the lemma "AInit" doesn't appear in the file"

For me it seems like the definition of Acc is self-contradictionary. Definitely Eprover tries to use different values beyond the bounds of the int type.
2019-03-11 11:26   
The situation is slightly different from the one in 2427. In 2427, we had an axiom that compared an int (implicitly converted into integer) with a (potentially outside of the int range) integer. Here, we explicitly convert an integer into an int, which has a perfectly defined semantics in ACSL. Hence, I'd say there's no inherent contradiction as far as ACSL is concerned (the semantics of Acc might not be the one the user has in mind, but that's a different story). in particular,

/*@ lemma AOne{L}: \forall int* a, init; Acc{L}(a,1,init) == a[0] + init; */

should not be provable, and it appears not to be: in the TIP, we can unfold the definition of L_Acc twice to obtain a goal of the form x = to_sint32(x), for x a sum of two int32 (i.e. potentially outside the range of int32) while the axiomatic of the to_sint32 builtin allows this equality only if x is within bounds (axiom id_sint32 in the WP arithmetic model).