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# [Frama-c-discuss] hint assertions and understanding cooperation between wp and value plugin

• Subject: [Frama-c-discuss] hint assertions and understanding cooperation between wp and value plugin
• From: Maurice.Bremond at inria.fr (Maurice Bremond)
• Date: Mon, 25 Apr 2016 12:52:42 +0200

```Thank you very much LoÃ¯c and Boris for your answers! This improved my
understanding of wp and value cooperation.

The need of float model for this was a bit fuzzy for me, so following your
remarks, I checked my assumptions with frama-c:

/*@ lemma sq_double: \forall double x; x*x >= 0.; */

is verifiable and value analysis shows that x*x >= 0
with -val-subdivide-non-linear 1094

So, in this case, I understand that the proof had the meaning I wanted!
But, then this makes me realize that something like:

#include <__fc_builtin.h>

/*@ lemma sq_double: \forall real x; x*x - .2 * x + 0.01 >= 0.; */
int main()
{
double x = Frama_C_double_interval(-1., 1.);
double x1 = x*x - .2 * x + 0.01;
/*@ assert x1 >= 0; */
}

is ok in the real model with:
frama-c -val t.c -wp -wp-prover z3

and hopefully cannot be verified with:
frama-c -val t.c -wp -wp-prover z3 -wp-model float

On the other side, (x - .1)*(x - .1) >= 0 is verifiable with -wp
-wp-model float but I did not manage to verify it with the value plugin
alone and -val-subdivide-non-linear (I stopped the computation after
99999)

```