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An Efficient Coq Tactic for Deciding Kleene Algebras

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Interactive Theorem Proving (ITP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6172))

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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 almost instantaneously. The corresponding decision procedure was proved correct and complete; correctness is established w.r.t. any model (including binary relations), by formalising Kozen’s initiality theorem.

A preliminary version of this work was presented at the 1st Coq Workshop, 2009.

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Authors and Affiliations

  1. LIG, UMR 5217, CNRS – INRIA,  

    Thomas Braibant & Damien Pous

Authors
  1. Thomas Braibant
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  2. Damien Pous
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Editors and Affiliations

  1. Department of Computer Sciences, University of Texas, Austin, Talyor Hall 2.124, 78712-1188, Austin, TX, USA

    Matt Kaufmann

  2. Computer Laboratory, University of Cambridge, CB3 0FD, Cambridge,, UK

    Lawrence C. Paulson

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Braibant, T., Pous, D. (2010). An Efficient Coq Tactic for Deciding Kleene Algebras. In: Kaufmann, M., Paulson, L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14052-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-14052-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14051-8

  • Online ISBN: 978-3-642-14052-5

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