We present a set of tools for rewriting modulo associativity and
commutativity (AC) 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 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.Comment: 16
