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A3PAT, an Approach for Certified Automated Termination Proofs

Evelyne Contejean 1, 2 Pierre Courtieu 3 Julien Forest 3 Andrei Paskevich 1, 2 Olivier Pons 3 Xavier Urbain 1, 2, *
* Corresponding author
1 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
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.
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Evelyne Contejean, Pierre Courtieu, Julien Forest, Andrei Paskevich, Olivier Pons, et al.. A3PAT, an Approach for Certified Automated Termination Proofs. 2010 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, ACM, Jan 2010, Madrid, Spain. pp.63-72, ⟨10.1145/1706356.1706370⟩. ⟨inria-00535655⟩

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