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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...

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;

}

```