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From: Florian Weimer <fw@deneb.enyo.de>
Newsgroups: comp.lang.ada
Subject: Re: SPARK and integer arithmetic
Date: Sun, 18 Sep 2016 21:49:09 +0200
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* Paul Rubin:

> Florian Weimer <fw@deneb.enyo.de> writes:
>> The intent is that I can write unbounded integer arithmetic in
>> predicates and post-conditions.
>> Not too surprisingly, gnatprove can't deal with this (I've already
>> been told it's beyond alt-ergo, and Z3 can only brute-force it).  But
>> perhaps there is a way to express the unbounded arithmetic so that
>> there is less work left for the prover?
>
> I think there is some way for Spark to use Coq, which can deal with
> things like that easily.  The Wikipedia article on Presburger arithmetic
> also cites http://ieeexplore.ieee.org/document/6987606/?arnumber=6987606
> about using (adapting?) the CVC4 SMT solver on quantifier-free
> arithmetic expressions.

The actual formula in the program uses modular arithmetic, so I don't
think this can be represented efficiently in Presburger arithmetic.
Or am I missing something?