Combining interaction nets with externally defined programs

Abstract

Many calculi, for instance the lambda-calculus and term rewriting systems, have benefitted from extensions, especially to include data structures and operations which are more naturally defined in another language. A simple example of this is PCF where the lambda-calculus is extended to include natural numbers and some basic functions over this type, which avoids having to use inefficient encodings of numbers. In this paper we present a generalization of interaction nets along these lines. We begin by adding a fixed set of constants and predefined functions, before presenting the main contribution of the paper which is a system of interaction nets combined with an external language where functions and richer data types can be defined.