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# [Frama-c-discuss] Problem with werify mod 256 and cast to uint8 equivalence for uint64_t

• Subject: [Frama-c-discuss] Problem with werify mod 256 and cast to uint8 equivalence for uint64_t
• From: sztfg at yandex.ru (sztfg at yandex.ru)
• Date: Mon, 21 Mar 2016 04:57:53 +0300

```I was trying to prove this code using alt-ergo:

/* ALWAYS TRUE */
/*@ ensures \result == 1;
*/
uint8_t test_uint8_cast_mod256_eq (uint64_t a)
{
return ((a)%256 == (uint8_t)(a));
}

how it looks like:

goal test_uint8_cast_mod256_eq_post:
forall i : int.
is_uint64(i) ->
(to_uint8(i) = (safe_comp_mod(i, 256)))

but it failed. Maybe need to add some axioms related safe_comp_mod?

Adding new axioms to .mlw file:

axiom A_1 : forall i : int. (0 <= i) -> (to_uint8(i) = (safe_comp_mod(i, 256)))

axiom A_2 : forall i : int. (0 <= i) -> (to_uint16(i) = (safe_comp_mod(i, 65536)))

axiom A_3 : forall i : int. (0 <= i) -> (to_uint32(i) = (safe_comp_mod(i, 4294967296)))

axiom A_4 : forall i : int. (0 <= i) -> (to_uint64(i) = (safe_comp_mod(i, 18446744073709551616)))

... and after that I can prove it. But maybe I doing something wrong, and this thing can be proved without adding axioms? Or maybe need to add more general axiom?

I tried this axiom:

axiom A_GENERIC : forall i,j : int. ((0 <= i) and (i < j)) -> (i = (safe_comp_mod(i, j)))

but it doesn't work

```