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  . 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  . 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 .