Simon Castellan ; Pierre Clairambault - Disentangling Parallelism and Interference in Game Semantics

lmcs:7675 - Logical Methods in Computer Science, September 18, 2024, Volume 20, Issue 3 - https://doi.org/10.46298/lmcs-20(3:24)2024
Disentangling Parallelism and Interference in Game SemanticsArticle

Authors: Simon Castellan ; Pierre Clairambault

    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.


    Volume: Volume 20, Issue 3
    Published on: September 18, 2024
    Accepted on: July 26, 2024
    Submitted on: July 13, 2021
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages

    Classifications

    Mathematics Subject Classification 20201

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