A calculus of higher order communicating systems

In this paper we present A Calculus of Higher Order Communicating Systems. This calculus considers sending and receiving processes to be as fundamental as nondeterminism and parallel composition. The calculus is an extension of CCS [Mil80] in the sense that all the constructions of CCS are included or may be derived from more fundamental constructs and most of the mathematical framework of CCS carries over almost unchanged. Clearly CCS with processes as first class objects is a powerful metalanguage and we show that it is possible to simulate the untyped λ-calculus in CHOCS. The relationship between CHOCS and the untyped λ-calculus is further strengthened by a result showing that the recursion operator is unnecessary in the sense that recursion can be simulated by means of process passing and communication. As pointed out by R. Milner in [Mil80], CCS has its limitations when one wants to describe unboundedly expanding systems as e.g. an unbounded number of procedure invocations in an imperative concurrent programming language. We show how neatly CHOCS may describe both call by value and call by reference parameter mechanisms for the toy language of chapter 6 in [Mil80].