Innocent strategies as presheaves and interactive equivalences for CCS (expanded version)

TL;DR

This paper presents a new categorical framework for reasoning about CCS, using presheaves and game semantics to define innocent strategies and interactive equivalences, leading to novel insights into testing equivalences.

Contribution

It introduces a presheaf-based model of innocent strategies for CCS, with decomposition results and a coalgebraic translation for recursive equations, along with a new notion of interactive equivalence.

Findings

Must testing is finer than in standard CCS due to spatial fairness.

Innocent strategies form a final coalgebra for a polynomial functor.

The framework captures testing equivalences close to Beffara's interpretation.

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 equip innocent strategies with a simple notion of interaction. We then prove decomposition results for innocent strategies, and, restricting to presheaves of finite ordinals, prove that innocent strategies are a final coalgebra for a polynomial functor derived from the game. This leads to a translation of CCS with recursive equations. Finally, 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 consider analogues of fair testing and must testing. We show that must testing is strictly finer in our model than in CCS, since it avoids what we call 'spatial unfairness'. Still, it differs from fair testing, and we show that it coincides with a relaxed form of fair testing.