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Conference papers

Deciding Kleene Algebras in Coq

Thomas Braibant 1 Damien Pous 1, *
* Corresponding author
1 SARDES - System architecture for reflective distributed computing environments
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : 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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Submitted on : Friday, May 20, 2011 - 1:09:12 PM
Last modification on : Friday, February 4, 2022 - 3:21:37 AM
Long-term archiving on: : Saturday, December 3, 2016 - 8:42:52 PM


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Thomas Braibant, Damien Pous. Deciding Kleene Algebras in Coq. ITP, Aug 2010, Edinburgh, United Kingdom. pp.163-178, ⟨10.1007/978-3-642-14052-5_13⟩. ⟨hal-00383070v5⟩



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