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# [Frama-c-discuss] ACSL by Example: contradiction in Count axiomatic

• Subject: [Frama-c-discuss] ACSL by Example: contradiction in Count axiomatic
• From: efremov at ispras.ru (Denis Efremov)
• Date: Mon, 17 Apr 2017 15:41:50 +0300

```Hello!

In "ACSL By Example Version 14.1.0"
(https://cdn0.scrvt.com/fokus/c8efcdaac330d718/6cc5d3fc9481/ACSL-by-Example_14_1_0.pdf),
Listing 3.32 p.46 (The logic function Count) there is the definition:

axiomatic Count {
logic integer Count{L}(value_type *a, integer m, integer n, value_type

axiom CountSectionEmpty:
\forall value_type *a, v, integer m, n;
n <= m ==> Count(a, m, n, v) == 0;

axiom CountSectionHit:
\forall value_type *a, v, integer n, m;
a[n] == v ==> Count(a, m, n + 1, v) == Count(a, m, n, v) + 1;

...
}

With contradiction in it (tested with WP):

value_type a = 5;

assert Count(&a + 1, 0, -1, (value_type) 5) == 0;
assert Count(&a + 1, 0, 0, (value_type) 5)  == 0;
assert Count(&a + 1, 0, 0, (value_type) 5)  == Count(&a + 1, 0, -1,
(value_type) 5) + 1;
assert 0 == 1;

Suggested fix is to add premise m < n to CountSectionHit and
CountSectionMiss axioms e.g.:

axiom CountSectionHit:
\forall value_type *a, v, integer n, m;
(m < n) && a[n] == v ==> Count(a, m, n + 1, v) == Count(a, m,
n, v) + 1;

Complete example attached.

Found by AstraVer project team (http://linuxtesting.org/astraver).
We have already notified "ACSL By Example" authors.

---

typedef int value_type;

// ACSL By Example (14.1.0) Listing 3.32 (p.46)
// Count axiomatic w/o CountSectionRead axiom
/*@
axiomatic Count {
logic integer Count{L}(value_type *a, integer m, integer n, value_type

axiom CountSectionEmpty:
\forall value_type *a, v, integer m, n;
n <= m ==> Count(a, m, n, v) == 0;

axiom CountSectionHit:
\forall value_type *a, v, integer n, m;
a[n] == v ==> Count(a, m, n + 1, v) == Count(a, m, n, v) + 1;

axiom CountSectionMiss:
\forall value_type *a, v, integer n, m;
a[n] != v ==> Count(a, m, n + 1, v) == Count(a, m, n, v);
}*/

/*@ assigns \nothing;
*/
void test(void)
{
value_type a = 5;
//@ assert Count(&a + 1, 0, -1, (value_type) 5) == 0;
//@ assert Count(&a + 1, 0, 0, (value_type) 5) == 0;
//@ assert Count(&a + 1, 0, 0, (value_type) 5) == Count(&a + 1, 0,
-1, (value_type) 5) + 1;
//@ assert 0 == 1;
}

```