Certification of Automated Termination Proofs

  • Authors:

  • Evelyne Contejean;Pierre Courtieu;Julien Forest;Olivier Pons;Xavier Urbain

  • Affiliations:

  • LRI, Université Paris-Sud, CNRS, INRIA Futurs, Orsay F-91405,;Cédric --- Conservatoire national des arts et métiers,;Cédric --- Conservatoire national des arts et métiers,;Cédric --- Conservatoire national des arts et métiers,;Cédric --- Conservatoire national des arts et métiers,

  • Venue:
  • FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
  • Year:
  • 2007

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Abstract

Nowadays, formal methods rely on tools of different kinds: proof assistants with which the user interacts to discover a proof step by step; and fully automated tools which make use of (intricate) decision procedures. But while some proof assistants can checkthe soundness of a proof, they lack automation. Regarding automated tools, one still has to be satisfied with their answers Yes/No/Do not know, the validity of which can be subject to question, in particular because of the increasing size and complexity of these tools.In the context of rewriting techniques, we aim at bridging the gap between proof assistants that yield formal guarantees of reliability and highly automated tools one has to trust. We present an approach making use of both shallow and deep embeddings. We illustrate this approach with a prototype based on the CiME rewriting toolbox, which can discover involved termination proofs that can be certified by the Coqproof assistant, using the Coccinellelibrary for rewriting.