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| HAL : hal-00383070, version 5 |
| arXiv : 1105.4537 |
| DOI : 10.1007/978-3-642-14052-5_13 |
| Fiche détaillée |  Récupérer au format |
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| ITP, Edinburgh : Royaume-Uni (2010) |
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| Versions disponibles : | v1 (12-05-2009) | v2 (13-08-2009) | v3 (15-02-2010) | v4 (14-06-2010) | v5 (20-05-2011) |
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| Deciding Kleene Algebras in Coq |
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Thomas Braibant 1Damien Pous 2 |
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| (2010) |
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| We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations instantaneously and properly scales to larger expressions. The decision procedure is proved correct and complete: correctness is established w.r.t. any model by formalising Kozen's initiality theorem; a counter-example is returned when the given equation does not hold. The correctness proof is challenging: it involves both a precise analysis of the underlying automata algorithms and a lot of algebraic reasoning. In particular, we have to formalise the theory of matrices over a Kleene algebra. We build on the recent addition of firstorder typeclasses in Coq in order to work efficiently with the involved algebraic structures. |
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| 1 : | SARDES (INRIA Grenoble Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble) |
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INRIA – Institut National Polytechnique de Grenoble (INPG) – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – CNRS : UMR5217 |
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| 2 : | Laboratoire d'Informatique de Grenoble (LIG) |
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CNRS : UMR5217 – INRIA – Université Pierre Mendès-France - Grenoble II – Université Joseph Fourier - Grenoble I – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| SARDES |
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| Domaine | : | Informatique/Logiciel mathématique Informatique/Mathématique discrète |
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| Coq – reflexive tactic – Kleene algebra – finite automata – decision procedure – typeclasses |
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| hal-00383070, version 5 | |
| http://hal.archives-ouvertes.fr/hal-00383070 | |
| oai:hal.archives-ouvertes.fr:hal-00383070 | |
| Contributeur : Damien Pous | |
| Soumis le : Vendredi 20 Mai 2011, 13:09:12 | |
| Dernière modification le : Jeudi 22 Septembre 2011, 10:15:48 | |
