Abstract

This paper is concerned with the relationship between-calculus and ��-calculus. The-calculus talks about functions and their applicative behaviour. This contrasts with the ��-calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and therefore functions can be seen as a special form of processes. We study how the functions of the-calculus (the computable functions) can be represented as ��-calculus processes. The ��-calculus semantics of a language induces a notion of equality on the terms of that language. We therefore also analyse the equality among functions that is induced by their representation as ��-calculus processes. This paper is intended as a tutorial. It however contains some original contributions. The main ones are: the use of well-known Continuation Passing Style transforms to derive the encodings into ��-calculus and prove their correctness; the encoding of typed-calculi.

Citations