Replication in concurrent combinators

Abstract

We establish the behavioural representability of input prefix and replication, which are two basic operators of the asynchronous ν-calculus [5, 6] (cf. [2]), an offspring of π-calculus [14, 11], in a system of concurrent combinators which is an extension of cc [7]. Systems of concurrent combinators axe simple formal systems based on a finite number of atoms with fixed interaction rules and two connectives for term formation, namely, concurrent composition and name hiding. Since such a system does not own inductively defined syntactic constructs for prefix or replication, their representability using a fixed number of atoms is theoretically interesting, reminiscent of the similar results obtained by Schönfinkel and Curry in the context of the classical combinators.