Innocent strategies as presheaves and interactive equivalences for CCS

TL;DR

This paper presents a new categorical framework for interpreting CCS using presheaves and innocent strategies, establishing a novel notion of interactive equivalence that unifies testing concepts in concurrency theory.

Contribution

It introduces a presheaf-based model of innocent strategies for CCS and defines an interactive equivalence that aligns fair and must testing.

Findings

Fair and must testing equivalences coincide in this framework

Presheaves on views effectively model innocent strategies

New categorical interpretation of CCS

Abstract

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.