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[Frama-c-discuss] embedded loops

  • Subject: [Frama-c-discuss] embedded loops
  • From: Romain.Jobredeaux at supelec.fr (Romain Jobredeaux)
  • Date: Mon, 07 Mar 2011 20:16:51 +0100
Hello,

I am trying to annotate 2 functions (code is included at the end of  
the message) with very similar structure:
or_scalar computes, given a rowB by colB float matrix b and a float a,  
a new matrix c where c[i][j] == (a!=0 || b[i][j]!=0)
equal_scalar computes, given the same parameters, a matrix c where  
c[i][j]= (a == b[i][j])
The annotations are also very similar, however for some reason  
alt-ergo proves every obligation on or_scalar, but doesn't even seem  
to try to prove the outer loop invariant on equal_scalar...

Thank you for your help,

Romain Jobredeaux



/*@ requires rowB > 0 && colB > 0  ;

   @ requires (\valid(b+ (0..rowB-1)) && (\forall integer  k; 0 <= k <  
rowB ==> \valid(b[k] +(0..colB-1) ) ));

   @ requires (\valid(c+ (0..rowB-1)) && (\forall integer  k; 0 <= k <  
rowB ==> \valid(c[k] +(0..colB-1) ) ));

   @ ensures  \forall integer i; \forall integer j;  (0 <= i < rowB &&  
0 <=j < colB)  ==> (c[i][j] == (a!=0 || b[i][j]!=0));

   @*/

int** or_scalar(float a,float** b,int rowB,int colB,int **c)

{

     int i=0,j=0;

/*@ loop invariant   (0 <= i <= rowB) && (\forall integer l;  \forall  
integer k; (0<=l<colB && 0 <= k <i) ==>

   @             c[k][l]  == (a!=0 || b[k][l]!=0)) ;

   @ loop variant   rowB-i;

   @*/

     while ( i < rowB )

     {

	j=0;

/*@ loop invariant   (0 <= j <= colB) && (\forall integer k;  (0<=k<j) ==>

	  @             c[i][k]  == (a!=0 || b[i][k]!=0)) ;

           @ loop variant   colB-j;

           @*/

         while ( j<colB)

         {

             c[i][j]= (a!=0) || (b[i][j]!=0);

             j++;

         }

	/*@ assert  \forall integer k;  0<=k<colB ==>  (c[i][k]  ==  (a!=0 ||  
b[i][k]!=0)) ; */

         i++;

     }

     return c;

}



/*@ requires rowB > 0 && colB > 0  ;

   @ requires (\valid(b+ (0..rowB-1)) && (\forall integer  k; 0 <= k <  
rowB ==> \valid(b[k] +(0..colB-1) ) ));

   @ requires (\valid(c+ (0..rowB-1)) && (\forall integer  k; 0 <= k <  
rowB ==> \valid(c[k] +(0..colB-1) ) ));

   @ ensures  \forall integer i; \forall integer j;  (0 <= i < rowB &&  
0 <=j < colB)  ==> (c[i][j] == (b[i][j]==a));

   @*/

int** equal_scalar(float a,float** b,int rowB,int colB,int **c)

{

     int i=0,j=0;

/*@ loop invariant   (0 <= i <= rowB) && (\forall integer l;  \forall  
integer k; (0<=l<colB && 0 <= k <i) ==>

   @             c[k][l]  == (b[k][l]==a)) ;

   @ loop variant   rowB-i;

   @*/

     while ( i < rowB )

     {

	j=0;

/*@ loop invariant   (0 <= j <= colB) && (\forall integer k;  (0<=k<j) ==>

	  @             c[i][k]  == (b[i][k]==a)) ;

           @ loop variant   colB-j;

           @*/

         while ( j<colB)

         {

             c[i][j]= (b[i][j] == a);

             j++;

         }

	/*@ assert  \forall integer k;  0<=k<colB ==>  (c[i][k]  ==   
(b[i][k]==a)) ; */

         i++;

     }

     return c;

}