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Game semantics as a singular functor, and definability as geometric realisation

Abstract : Game semantics is a class of models of programming languages in which types are interpreted as games and programs as strategies. Though originally designed for sequential languages, its scope has recently been extended to concurrent ones. A salient feature of game semantics is the notion of innocence, which requires strategies to be determined by their values on a certain class of plays, called views. In previous work, we have obtained a representation theorem for Tsukada and Ong's categories of views and plays, in particular by constructing an embedding V of views into a coslice of a certain presheaf category. We here exploit this result to exhibit an efficient categorical account of two crucial constructions of game semantics. First, we recover the interpretation of normal forms into innocent strategies as the singular functor associated to V. Second, the corresponding geometric realisation functor yields the standard definability result saying that any innocent strategy is (isomorphic to) the interpretation of a normal form.
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Contributor : Tom Hirschowitz Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2017 - 9:46:43 AM
Last modification on : Friday, January 28, 2022 - 3:00:02 PM
Long-term archiving on: : Monday, August 28, 2017 - 12:23:59 AM


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  • HAL Id : hal-01527171, version 1



Clovis Eberhart, Tom Hirschowitz. Game semantics as a singular functor, and definability as geometric realisation. 2017. ⟨hal-01527171⟩



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