Completion as a Derived Rule of Inference

A simple first step in the investigation of term rewriting systems in higher order logic is to just insert the first order Knuth-Bendix 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.

This paper was written circa 1990 but never published, except as a University of Calgary technical report (number 90/409/33). However, the implementation described in the paper is still distributed with the HOL system; it can be found in the contrib/knuth_bendix directory.