Higher-order Games with Dependent Types

12/15/2022

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by   Martín Escardó, et al.

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This paper generalises the notion of a higher-order game, by accounting for history-dependent games where the set of available moves at a given position in the game depends on the moves played up to that point. This is achieved by modelling game trees as a certain type of dependent type trees, which allows us to directly account for finite games of unbounded length. In previous work this was instead done by considering either a fixed game length, or games of countable length with a continuous outcome function. We make use of the concepts from dependent type theory in order to formalise this, and we have also implemented all our definitions, constructions, results and proofs in the dependently-typed programming language Agda.