A Why3 Framework for Reflection Proofs and its Application to GMP's Algorithms

Guillaume Melquiond (1, 2) , Raphaël Rieu-Helft (2, 3)

1 LRI - Laboratoire de Recherche en Informatique
2 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
3 TIS - TrustInSoft

Earlier work showed that automatic verification of GMP's algorithms using Why3 exceeds the current capabilities of automatic solvers. To complete this verification, numerous cut indications had to be supplied by the user, slowing the project to a crawl. This paper shows how we have extended Why3 with a framework for proofs by reflection, with minimal impact on the trusted computing base. This framework makes it easy to write dedicated decision procedures that make full use of Why3's imperative features and are formally verified. We evaluate how much work could have been saved when verifying GMP's algorithms, had this framework been available. This approach opens the way to efficiently tackling the further verification of GMP's algorithms.

Mots clés: Nonlinear integer arithmetic; Proofs by reflection; Decision procedures; Deductive program verification

Domaines: Arithmétique des ordinateurs; Logique en informatique [cs.LO]

Guillaume Melquiond, Raphaël Rieu-Helft. A Why3 Framework for Reflection Proofs and its Application to GMP's Algorithms. 9th International Joint Conference on Automated Reasoning, Jul 2018, Oxford, United Kingdom. pp.178-193, ⟨10.1007/978-3-319-94205-6_13⟩. ⟨hal-01699754v2⟩