A Theory of Higher Order Communicating Systems

Abstract

A calculus of higher order communicating systems (CHOCS) was presented by the author in ["Proceedings of POPL 89," pp. 143-154, Assoc. Computing Machinery, New York]. This calculus considers sending and receiving processes to be as fundamental as nondeterminism and parallel composition. In this paper we present an investigation of the foundation of the theory of this calculus, together with the full proofs of all major theorems. CHOCS is an extension of Milner′s Calculus of Communicating Systems (CCS) in the sense that all the constructions of CCS are included or may be derived from more fundamental constructs. Most of the mathematical framework of CCS carries over almost unchanged. The operational semantics of CHOCS is given as a labelled transition system and it is a direct extension of the semantics of CCS with value passing. A set of algebraic laws satisfied by the calculus is presented. These are similar to the CCS laws, varying only by introducing obvious extra laws for sending and receiving processes. The power of process passing is underlined by a result showing that recursion can be simulated by means of process passing and communication.