## Section: Software

Keywords : reflexive proof, result certification, Farkas Lemma, Positivstellensatz.

### Micromega: a reflexive Coq tactic for arithmetic

Participant : Frédéric Besson.

Micromega is a reflexive Coq tactic able to decide quantifier free fragments of integer arithmetic
[33] . We have implemented, and proved correct, a certificate checker for proofs obtained by Farkas lemma (linear arithmetic) and the
*Positivstellensatz* (non-linear arithmetic). For the specific case of integer linear arithmetic, the certificate checker also accepts
*cutting plane proofs* and proofs obtained from
*branch-and-bound* algorithms.

A nice feature of the micromega checker is that it is built upon the existing Coq ring tactic [44] . Another nice feature is that the certificate generators are off-the-shelf algorithms that do not need to be trusted.

Micromega is now a Coq "contribution" included in the forthcoming Coq 8.2 .