COMBINING TERM REWRITING AND TYPE ASSIGNMENT SYSTEMS

Abstract

Recently some attention has been paid to the properties enjoyed by combinations of term rewriting and λ-calculus based systems. In this paper strong normalization and confluence are proved for λ-terms obtained by merging pure λ-terms and first order canonical term rewriting systems, in the framework of a system which extends the Coppo-Dezani intersection type assignment system. On terms of the resulting calculus we can perform ordinary β and η reductions, as well as the reductions induced in a natural way by the term rewriting systems. In some parts of our analysis we follow rather closely the development contained in a recent paper by Val Breazu-Tannen and Jean Gallier. There, the same properties of strong normalization and confluence are proved for systems obtained by combining the second order polymorphic λ-calculus with first order canonical term rewriting systems. The strong normalization result of Breazu-Tannen and Gallier is proved to be implied by the corresponding property of our system.