COMPLETION AS A DERIVED RULE OF INFERENCE

Abstract

A simple first step in the investigation of term rewriting systems in higher order logic is to just insert the first order completion algorithm unchanged into the more complicated logic. This paper presents the details of how this is done in Mike Gordon's HOL system, an implementation of Church's Simple Type Theory. We present completion as a derived rule of inference, not (as usual) as an ad hoc procedure. The completion rule presented here is easily adaptable to other natural deduction logics with equality.