Efficient unification of quantified terms

Abstract

Conventional logic-programming languages rely fundamentally on symbolic computation with quantifier-free terms. Much theoretical logic uses the richer vocabulary of quantified terms, however. In this paper we sketch some first steps in a program of research for developing data structures and algorithms to support efficient computation directly on quantified terms. We describe a simple concept of quantified term, and efficient unification algorithms for both structure-sharing and non-structure-sharing representations of those terms. The efficiency of the approach results from the techniques used to represent terms, which enable naive substitution to implement correct substitution for quantified terms. The non-structure- sharing unification algorithm described here has been prototyped by modification of a conventional logic-programming interpreter.