Deciding Kleene Algebras in Coq

@article{Braibant2012DecidingKA,
  title={Deciding Kleene Algebras in Coq},
  author={Thomas Braibant and Damien Pous},
  journal={Log. Methods Comput. Sci.},
  year={2012},
  volume={8}
}
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… Expand
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