Token Machines for Multiport Interaction Combinators

Game semantics [7, 1] and the Geometry of Interaction [6] are semantic frameworks centered around the dynamic, interactive behaviour of the interpreted object rather than on its static, extensional properties. The obtained semantics is often fully abstract, and its concreteness can be exploited in the definition of compilation schemes towards low-level languages, like in the Geometry of Synthesis [5]. Most game semantics models are defined as to reflect the behaviour of sequential languages— the classic notion of a strategy is after all deterministic and sequential. The interest around concurrent forms of game semantics is not at all new, however. Concurrency has been incepted into games both at the level of the interpreting object (e.g. [2, 13, 3]), and at the level of the interpreted object (e.g. [11]). In the Geometry of Interaction, on the other hand, the way towards concurrency has been explored less extensively. If one looks at the most concrete incarnation of GoI, namely the socalled token-machines [4], there is however a very natural way to go parallel, namely considering machines whose internal state consists of possibly many tokens rather than just one [14, 9, 10]. If the interpreted language is sequential and deterministic, however, there is no way the various tokens could interact, and parallelism is then vacuous. If one injects a primitive for synchronization in the underlying calculus, on the other hand, multiple tokens become a necessity, and the model becomes adequate for quantum computation [9]. The authors are currently engaged in defining and studying a Geometry of Interaction model for multiport interaction combinators [12], a concurrent extensions of Lafont’s interaction combinators [8]. The talk will be about this ongoing work.