Deciding equality in the constructor theory

Abstract

We give a decision procedure for the satisfiability of finite sets of ground equations and disequations in the constructor theory: the terms used may contain both uninterpreted and constructor function symbols. Constructor function symbols are by definition injective and terms built with distinct constructors are themselves distinct. This corresponds to properties of (co-) inductive type constructors in inductive type theory. We do this in a framework where function symbols can be partially applied and equations between functions are allowed. We describe our algorithm as an extension of congruence-closure and give correctness, completeness and termination arguments. We then proceed to discuss its limits and extension possibilities by describing its implementation in the Coq proof assistant. © Springer-Verlag Berlin Heidelberg 2007.