An Efficient Coq Tactic for Deciding Kleene Algebras

Thomas Braibant (1) , Damien Pous (1)

1 SARDES - System architecture for reflective distributed computing environments

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.

Mots clés: Coq; reflexive tactic; Kleene algebra; finite automata; decision procedure

Domaines: Logiciel mathématique [cs.MS]; Mathématique discrète [cs.DM]

Thomas Braibant, Damien Pous. An Efficient Coq Tactic for Deciding Kleene Algebras. 2010. ⟨hal-00383070v3⟩