DISENTANGLING PARALLELISM AND INTERFERENCE IN GAME SEMANTICS

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 (IAA(/))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.