Combining first and higher order rewrite systems with type assignment systems

Abstract

General computational models obtained by integrating different specific models have recently become a stimulating and promising research subject for the computer science community. In particular, combinations of algebraic term rewriting systems and various λ-calculi, either typed or untyped, have been deeply investigated. In the present paper this subject is addressed from the point of view of type assignment. A powerful type assignment system, the one based on intersection types, is combined with term rewriting systems, first and higher order, and relevant properties of the resulting system, like strong normalization and confluence, are proved.