A3PAT, an approach for certified automated termination proofs

Authors:
Évelyne Contejean;Andrei Paskevich;Xavier Urbain;Pierre Courtieu;Olivier Pons;Julien Forest
Affiliations:
Université Paris-Sud 11 and CNRS, Orsay F-91405, France;Université Paris-Sud 11 and CNRS, Orsay F-91405, France;Université Paris-Sud 11 and CNRS and École nationale supérieure d'informatique pour l'industrie et l'entreprise, Orsay F-91405, France;Conservatoire National des Arts et Métiers, Paris F-75141, France;Conservatoire National des Arts et Métiers, Paris F-75141, France;École nationale supérieure d'informatique pour l'industrie et l'entreprise, Évry F-91025, France
Venue:
Proceedings of the 2010 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Year:
2010

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Abstract

Software engineering, automated reasoning, rule-based programming or specifications often use rewriting systems for which termination, among other properties, may have to be ensured.This paper presents the approach developed in Project A3PAT to discover and moreover certify, with full automation, termination proofs for term rewriting systems. It consists of two developments: the Coccinelle library formalises numerous rewriting techniques and termination criteria for the Coq proof assistant; the CiME3 rewriting tool translates termination proofs (discovered by itself or other tools) into traces that are certified by Coq assisted by Coccinelle. The abstraction level of our formalisation allowed us to weaken premises of some theorems known in the literature, thus yielding new termination criteria, such as an extension of the powerful subterm criterion (for which we propose the first full Coq formalisation). Techniques employed in CiME3 also improve on previous works on formalisation and analysis of dependency graphs.