Wiring the π-Calculus to Denotational Semantics

We introduce a dialect of the Asynchronous π-calculus, called AWπ, in which (1) an input name may be owned, at any time, by at most one process; (2) each name has either only the input or only the output capability. As a result, special processes called wires (aka forwarders, that is, processes that receive values at one name and re-transmit) behave as substitutions when composed with any AWπ process. Thus AWπ naturally yields a category, whose morphisms are AWπ processes (modulo the reference behavioural equivalence, barbed congruence) and whose objects are types; and where wires act as identity morphisms. We show that the category of processes can be further organised into (sub)categories with the structures needed for the interpretation of common higher-order language features in the literature by drawing on insights from game semantics; notably, we construct a relative Seely category, the categorical structure that concurrent game semantics has. At the same time, AWπ follows the tradition of ordinary π-calculi in that expressiveness is preserved and the operational and algebraic theory are developed in a similar manner, notwithstanding substantial technical differences in their development and proofs. In short, the goal of AWπ is to remain faithful to the operational and algebraic tradition of the π-calculi while connecting to the tradition of denotational models for programming languages.