Simple game semantics and Day convolution

Clovis Eberhart (1) , Tom Hirschowitz (2) , Alexis Laouar (2)

1 NII - National Institute of Informatics
2 LAMA - Laboratoire de Mathématiques

Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melliès suggested that such categories of games and strategies may be obtained as instances of a simple abstract construction on weak double categories. However, in the particular case of simple games, his construction slightly differs from the standard category. We refine the abstract construction using factorisation systems, and show that the new construction yields the standard category of simple games and strategies. Another perhaps surprising instance is Day's convolution monoidal structure on the category of presheaves over a monoidal category.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]; Catégories et ensembles [math.CT]

Clovis Eberhart, Tom Hirschowitz, Alexis Laouar. Simple game semantics and Day convolution. 2018. ⟨hal-01897309v1⟩