Braibant, Thomas and Pous, Damien - Deciding Kleene Algebras in Coq

lmcs:1043 - Logical Methods in Computer Science, March 2, 2012, Volume 8, Issue 1
Deciding Kleene Algebras in Coq

Authors: Braibant, Thomas and Pous, Damien

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.


Source : oai:arXiv.org:1105.4537
DOI : 10.2168/LMCS-8(1:16)2012
Volume: Volume 8, Issue 1
Published on: March 2, 2012
Submitted on: June 25, 2015
Keywords: Computer Science - Logic in Computer Science,Computer Science - Symbolic Computation,F 1.1, F 3.1, F.4.1, F.4.3, D 2.4


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