Estimation of the length of interactions in arena game semantics

We estimate the maximal length of interactions between strategies in HO/N game semantics, in the spirit of the work by Schwichtenberg and Beckmann for the length of reduction in simply typed λ-calculus. Because of the operational content of game semantics, the bounds presented here also apply to head linear reduction on λ-terms and to the execution of programs by abstract machines (PAM/KAM), including in presence of computational effects such as nondeterminism or ground type references. The proof proceeds by extracting from the games model a combinatorial rewriting rule on trees of natural numbers, which can then be analysed independently of game semantics or λ-calculus.

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