Disentangling Parallelism and Interference in Game Semantics
Simon Castellan, Pierre Clairambault
TL;DR
The paper tackles disentangling parallelism from interference in game semantics by building a causal, fully abstract model for $IA_{//}$ using thin concurrent games. It introduces compositional conditions called parallel innocence and sequentiality, yielding four full abstraction results across all combinations of parallelism and interference on top of $PCF$, thereby extending Abramsky's cube beyond the sequential deterministic setting. The work unifies shared-memory concurrency, state, and higher-order control within a single semantic framework and offers a modern, pedagogical entry point to game semantics. This advances the semantic cube program by bridging classic sequential results with concurrent, stateful effects.
Abstract
Game semantics is a denotational semantics presenting compositionally the computational behaviour of various kinds of effectful programs. One of its celebrated achievement is to have obtained full abstraction results for programming languages with a variety of computational effects, in a single framework. This is known as the semantic cube or Abramsky's cube, which for sequential deterministic programs establishes a correspondence between certain conditions on strategies (''innocence'', ''well-bracketing'', ''visibility'') and the absence of matching computational effects. Outside of the sequential deterministic realm, there are still a wealth of game semantics-based full abstraction results; but they no longer fit in a unified canvas. In particular, Ghica and Murawski's fully abstract model for shared state concurrency (IA) does not have a matching notion of pure parallel program-we say that parallelism and interference (i.e. state plus semaphores) are entangled. In this paper we construct a causal version of Ghica and Murawski's model, also fully abstract for IA. We provide compositional conditions parallel innocence and sequentiality, respectively banning interference and parallelism, and leading to four full abstraction results. To our knowledge, this is the first extension of Abramsky's semantic cube programme beyond the sequential deterministic world.