Wiring the Pi-calculus to Denotational Semantics

2026-05-18

AI Summary

This work aims to bridge the gap between the operational semantics tradition of the π-calculus and its application in denotational semantics for programming languages. To this end, the authors introduce AWpi, a variant of asynchronous π-calculus that restricts name ownership and communication capabilities such that forwarder behavior in process composition becomes equivalent to variable substitution. This equivalence naturally yields a categorical structure with processes as morphisms and types as objects. Notably, the model is the first to preserve both the expressiveness and operational semantics of the π-calculus while directly supporting the relative Seely category structure required by concurrent game semantics, thereby providing a solid denotational foundation for higher-order programming language features.

Abstract

We introduce a dialect of the Asynchronous pi-calculus, called AWpi, 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 AWpi process. Thus AWpi naturally yields a category, whose morphisms are AWpi 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, AWpi follows the tradition of ordinary pi-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 AWpi is to remain faithful to the operational and algebraic tradition of the pi-calculi while connecting to the tradition of denotational models for programming languages.

Problem

• pi-calculus
• denotational semantics
• wires
• category theory
• concurrent game semantics

Innovation

• Asynchronous pi-calculus
• Denotational semantics
• Categorical semantics
• Wires
• Relative Seely category