Tactics for Reasoning 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 procedure for equality modulo AC; second, an OCaml Coq plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.

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

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

Thomas Braibant, Damien Pous. Tactics for Reasoning modulo AC in Coq. 2011. ⟨hal-00484871v3⟩