Frama-C-discuss mailing list archives

This page gathers the archives of the old Frama-C-discuss archives, that was hosted by Inria's gforge before its demise at the end of 2020. To search for mails newer than September 2020, please visit the page of the new mailing list on Renater.

[Frama-c-discuss] [Jessie] loop invariant

```
On 09/12/2013 08:06 PM, Rovedy Aparecida Busquim e Silva wrote:
> Hi,
>
> We have run the example as suggested by Claude
> (http://proval.lri.fr/gallery/ScalarProduct.en.html).
>
> We used the example annotations in our code (attached) and the all VCs
> were proved.
>
> However, we have some doubts:
>
> 1. We have used the lemma bound_int_to_real but we did not understand
> how it works.
> Why the define NMAXR is used?

the lemma says the if some integer n is less or equal 3, then when
converting it to a rel number the result is less or equal 3.0. Seems
stupid but needed to help provers...

> 2. The variable j used in the loop was global in the legacy source
> code. However, the loop invariant  was not proved (loop invariant
> \abs(p - sum(x,j)) <= j * BOUND).
>   We changed the variable j to local and the loop invariant was proved.
>   Does not the loop invariant work with global variable?

It should not make any major difference. However since the context of
the VC would be a bit different (e.g. not the same order of hypotheses),
you may need to increase a little the time limit given to the prover.

I tried your example and I've been abble to prove it, both in case j is
global and when it is local. Although, I needed to modify a bit the
annotations: removing the "loop assigns p,j" that disturbs Jessie, and
replacing "sum(x,...)" by "sum(x+0,...)" because it is refused by
Frama-C kernel. I'm using Frama-C Fluorine 20130601 + Why 2.33 + Why3 +
provers Alt-Ergo, CVC3 and Gappa.

Hope this helps,

- Claude

> Best regards,
> Nanci, Luciana e Rovedy
>
>
>
>
> 2013/9/7 Claude Marche <Claude.Marche at inria.fr>
>>
>>
>>
>> On 09/07/2013 10:56 AM, Claude Marche wrote:
>>>>
>>>> Alternatively, you can force the computation into float in sum
>>>>    @   axiom sum2{L} :
>>>>    @     \forall float *t, integer i, j;
>>>>    @       sum(t,i,j+1) == (float)(sum(t,i,j) + t[j]);
>>>> But this is not a very good idea IMHO: as floating point addition is
>>
>>
>> A very bad idea indeed.
>>
>> - claude
>>
>>
>> _______________________________________________
>> Frama-c-discuss mailing list
>> Frama-c-discuss at lists.gforge.inria.fr
>> http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/frama-c-discuss
>>
>>
>> _______________________________________________
>> Frama-c-discuss mailing list
>> Frama-c-discuss at lists.gforge.inria.fr
>> http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/frama-c-discuss

```