A Tactic for Rewriting modulo AC in Coq

Thomas Braibant (1) , Damien Pous (2)

1 LIG - Laboratoire d'Informatique de Grenoble
2 PLUME - Preuves et Langages

We present a set of tools for rewriting modulo associativity and commutativity in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision proce- dure for equality modulo AC; second, an OCaml Coq plug-in for pattern matching modulo AC. Our decision procedure stems from Barendregt's two level approach, but allows to reason with several A/AC operations at the same time, by working with an arbitrary signature.

Mots clés: Coq proof assistant; decision procedure; reflexive tactic; rewriting; modulo AC; associativity; commutativity

Domaines: Logiciel mathématique [cs.MS]; Logique en informatique [cs.LO]

Thomas Braibant, Damien Pous. A Tactic for Rewriting modulo AC in Coq. 2011. ⟨hal-00484871v2⟩