Frama-C-discuss mailing list archives

Claude.Marche at inria.fr (Claude Marché) · Thu, 26 Mar 2009 17:19:45 +0100

I guess there is also a tricky point, because the way your code is 
written. Using directly return statements without using the diff 
variable should make things simpler. With the diff variable, it might be 
necessary to specify that diff is not modified in the loop... (i.e 
remains 0)

sorry I can't help more without running the example and see precisely 
what VC are not proved.

- Claude

PAREAUD, Thomas wrote:
> Thank you for this answer.
> 
> Is the 3) point is equivalent to add the predicate below in the loop invariant declaration?
> 
> loop invariant
>       [...]
>    && \forall integer k ; 0 <= k < (\at(nbBytes, Pre) - nbBytes) ==> (*(\at(pString1, Pre)+k) == *(\at(pString2, Pre)+k));
> 
> This line is equivalent to the following one:
> 
> \forall integer k ; 0 <= k < (\at(nbBytes, Pre) - nbBytes) ==> (*(pString1-k) == *(pString2-k));
> 
> 
> But none of the two solutions makes solver proving anything.
> 
> Have you any other idea?
> --
> Thomas Pareaud
> 
> 
>  
> 
> -----Message d'origine-----
> De : frama-c-discuss-bounces at lists.gforge.inria.fr [mailto:frama-c-discuss-bounces at lists.gforge.inria.fr] De la part de Claude March?
> Envoy? : jeudi 26 mars 2009 16:19
> ? : Frama-C public discussion
> Objet : Re: [Frama-c-discuss] Named behavior, proof obligations and ACSL annotations: the string comparison example
> 
> A few hints:
> 
> 1) use integer instead of int in annotations. It will probably not help, 
> but is better practice
> 
> 2) split the identity into two, w.r.t your disjunction.
> 
> 3) add a loop invariant expressing that the chars visited so far are 
> equal, otherwise you will not be able to prove anything.
> 
> - Claude
> 
> PAREAUD, Thomas wrote:
>> Dear all,
>>
>> I am a recent user of Frama-C and its Jessie plug-in.
>> I tried for several days to train to this tool.
>>
>> Below, there is an example of a function that compare two strings.
>> There are four different behaviors:
>> - zero: the number of byte to compare equals 0 (return 0)
>> - identity: the two strings are identical (return 0)
>> - positive: it exists a position such as every char before this position
>> were identical between the two strings, and the char at this position is
>> greater in the first string that in the second one.
>> - negative: it exists a position such as every char before this position
>> were identical between the two strings, and the char at this position is
>> lower in the first string that in the second one.
>>
>> I managed to prove the "Safety" (verified by the Yices solver thanks to
>> the loop invariant I introduced) and "zero" behaviors. 
>> Nevertheless, I did not manage to prove neither identity, nor positive,
>> nor negative behaviors.
>>
>> You can find the detail of the code and ACSL annotations below.
>>
>> Does someone have a proposition?
>>
>> Best regards,
>> --
>> Thomas Pareaud
>>
>>
>>
>> /*@ requires nbBytes >= 0;
>>   @ requires \valid(pString1 + (0..(nbBytes-1))); 
>>   @ requires \valid(pString2 + (0..(nbBytes-1)));
>>   @ requires nbBytes!=0 ==> \exists int j ; 0<=j<nbBytes &&
>> *(pString1+j)==0;
>>   @ requires nbBytes!=0 ==> \exists int j ; 0<=j<nbBytes &&
>> *(pString2+j)==0;
>>   @ assigns \nothing;
>>   @ behavior zero:
>>   @   assumes nbBytes == 0;
>>   @   ensures \result == 0;
>>   @ behavior identity: 
>>   @   assumes 
>>   @     nbBytes > 0 
>>   @     && (
>>   @       (\forall int i; 0<=i<nbBytes ==> *(pString1+i)==*(pString2+i))
>>   @       || (\exists int j; 0<=j<nbBytes && *(pString1+j)==0 &&
>> (\forall int i; 0<=i<=j ==> *(pString1+i)==*(pString2+i)))
>>   @     );
>>   @   ensures \result == 0;
>>   @ behavior postive: 
>>   @   assumes nbBytes > 0 && \exists int j; *(pString1+j)>*(pString2+j)
>> && (\forall int i; 0<=i<j<nbBytes ==> *(pString1+i)==*(pString2+i)); 
>>   @   ensures \result > 0;
>>   @ behavior negative: 
>>   @   assumes nbBytes > 0 && \exists int j; *(pString1+j)<*(pString2+j)
>> && (\forall int i; 0<=i<j<nbBytes ==> *(pString1+i)==*(pString2+i)); 
>>   @   ensures \result < 0;
>>   @ disjoint behaviors zero, identity, non_identity;
>>  */
>> int strncmp(const char *pString1, const char *pString2, unsigned int
>> nbBytes)
>> {
>>   int diff = 0;
>>
>>   if (nbBytes == 0)
>>   {
>>     diff = 0;
>>   }
>>   else
>>   {
>> /*@ loop invariant 
>>   @   0 < nbBytes <= \at(nbBytes, Pre) 
>>   @   && \at(pString1, Pre) + \at(nbBytes, Pre) == pString1 + nbBytes 
>>   @   && \at(pString2, Pre) + \at(nbBytes, Pre) == pString2 + nbBytes ;
>>   @ loop assigns \nothing;
>>   @ loop variant nbBytes;
>>   */
>>     while ((nbBytes-- != 0) && (*pString1 == *pString2))
>>     {
>> 		if ((nbBytes == 0) || (*pString1 == '\0')){
>> 			break;
>> 		}
>> 		pString1++;
>> 		pString2++;
>>     }
>> 	diff = (((int)*pString1) - ((int)*pString2));
>>   }
>>
>>   return diff;
>> }
>>
>>
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-- 
Claude March?                          | tel: +33 1 72 92 59 69
INRIA Saclay - ?le-de-France           | mobile: +33 6 33 14 57 93
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