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# [Frama-c-discuss] new axiomatic "function"

• Subject: [Frama-c-discuss] new axiomatic "function"
• From: Christoph.Weber at first.fraunhofer.de (Christoph Weber)
• Date: Mon, 19 Jan 2009 08:49:54 +0100

```Salut,

some time ago, I posted an annotated function "remove_copy".

To get the proof, an axiom and an assertion had to be added.
Today, I would like to post a modification of this algorithm.
This one is called "unique_copy". It copies elements from a source array to a destination array.
If consecutive elements are equal, only the first one is copied.

I modified the annotation from remove_copy accordingly. This time, each element is compared with its predecessor.

I would like to know if something needs to be added to get the proof or if the axiomatization I chose is inconsistent.

The Function:

/*@ axiomatic Function_unique_copy {

logic integer function_unique_copy{La,Lb}(int* a, int* b, integer i_a, integer i_b);

axiom function_unique_copy_empty{La,Lb}:
\forall int* a, int* b, integer i_a, i_b;
0 > i_a && 0 > i_b ==> function_unique_copy{La,Lb}(a, b, i_a, i_b) == 0;

axiom function_unique_copy_first_element{La,Lb}:
\forall int* a, int* b, integer i_a, i_b;
0 == i_a ==>
function_unique_copy{La,Lb}(a, b, i_a, i_b) ==
function_unique_copy{La,Lb}(a, b, i_a-1, i_b-1) + 1;

axiom function_unique_copy_equal{La,Lb}:
\forall int* a, int* b, integer i_a, i_b;
0 < i_a &&
\at(a[i_a],La) == \at(a[i_a-1],La) ==>
function_unique_copy{La,Lb}(a, b, i_a, i_b) ==
function_unique_copy{La,Lb}(a, b, i_a-1, i_b);

axiom function_unique_copy_not_equal{La,Lb}:
\forall int* a, int* b, integer i_a, i_b;
0 < i_a && 0 <= i_b &&
(\at(a[i_a],La) != \at(a[i_a-1],La) <==> \at(a[i_a],La) == \at(b[i_b],Lb)) ==>
function_unique_copy{La,Lb}(a, b, i_a, i_b) ==
function_unique_copy{La,Lb}(a, b, i_a-1, i_b-1) + 1;

axiom function_unique_copy_not_equal_label{La,Lb1,Lb2}:
\forall int* a, int* b, integer i_a, i_b;
(\forall integer i; 0<= i <= i_b ==>
\at(b[i],Lb1) == \at(b[i],Lb2)) ==>
function_unique_copy{La,Lb1}(a,b,i_a,i_b) ==
function_unique_copy{La,Lb2}(a,b,i_a,i_b);
}
*/

/*@
requires 0 <= length;
requires \valid_range(a, 0, length-1);
requires \valid_range(dest, 0, length-1);

ensures 0 <= \result <= length;

ensures \result == function_unique_copy{Old,Here}(a, dest, length-1, \result-1);
*/

int unique_copy_array(int* a, int length, int* dest)
{

int i_a = 0;
int i_dest = 0;

if (length == 0)
return i_dest;

int value = a[i_a];
dest[i_dest] = value;
i_a++;

/*@
loop invariant 0 < i_a <= length;
loop invariant i_dest < i_a;
loop invariant 0 <= i_dest < length;

loop invariant i_dest == function_unique_copy{Pre,Here}(a, dest, i_a-1, i_dest-1);
*/
while (i_a != length)
{
if (!(value == a[i_a]))
{
value = a[i_a];
dest[i_dest] = value;
/*@assert
i_dest+1==function_unique_copy{Pre,Here}(a,dest,i_a,i_dest);
*/
++i_dest;
}

i_a++;
}
return ++i_dest;
}

I appreciate the help

Cheers
Christoph
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