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# [Frama-c-discuss] Requirements as hypothesis for assumes ?

• Subject: [Frama-c-discuss] Requirements as hypothesis for assumes ?
• From: nicolas.stouls at insa-lyon.fr (Nicolas Stouls)
• Date: Tue, 04 Aug 2009 14:04:10 +0200

```Dear,

When proving a function including a function call, such as the following g function:

/*@ requires Rf;
@ behavior a:
@   assumes Af;
@   ensures Ef;
*/
int f(int x){....}

/*@ requires Rg;
@ ensures Eg;
*/
int g(int x){
<instructions1>
y=f(z);
<instructions2>
}

Here is the proof obligation that we need to proof to establish the correctness
of g:

Rg => [<instructions1>;y=f(z);<instructions2>]Eg

In Jessie, it seems to be rewrites into a formula like:

Rg => [<instructions1>](Rf & (Af & Ef => [<instructions2>]Eg))

And then split into two PO separating precondition and postcondition:

1) Rg => [<instructions1>]Rf
2) Rg => [<instructions1>](Af & Ef => [<instructions2>]Eg)

However, it could be appreciate to have [<instructions1>]Rf as hypothesis of
(2). Indeed, (1) can be an interesting hypothesis in order to establish if the
assumes clause Af holds or not.

An extreme example is the one where (Af = Rf). In a such case, we need to
establish (1) during the proof of (2).

Do you think than adding the requirement clause as hypothesis as in the
following have any sense ?

1) Rg => [<instructions1>]Rf
2) Rg && [<instructions1>]Rf => [<instructions1>](Af & Ef =>[<instructions2>]Eg)

Thanks,
Nicolas.
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```