An Efficient Coq Tactic for Deciding Kleene Algebras [chapter]

Thomas Braibant, Damien Pous
2010 Lecture Notes in Computer Science  
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.
doi:10.1007/978-3-642-14052-5_13 fatcat:5dcm5rz4jrcohh55ectexyd7gu