Constructing differential categories and deconstructing categories of games

Reference:

Laird, J., Manzonetto, G. and McCusker, G., 2011. Constructing differential categories and deconstructing categories of games. In: Aceto, L., Henzinger, M. and Sgall, J., eds. Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. Vol. 6756. Heidelberg: Springer-Verlag, pp. 186-197. (Lecture Notes in Computer Science)

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Official URL:

http://dx.doi.org/10.1007/978-3-642-22012-8_14

Abstract

We present an abstract construction for building differential categories useful to model resource sensitive calculi, and we apply it to categories of games. In one instance, we recover a category previously used to give a fully abstract model of a nondeterministic imperative language. The construction exposes the differential structure already present in this model. A second instance corresponds to a new Cartesian differential category of games. We give a model of a Resource PCF in this category and show that it enjoys the finite definability property. Comparison with a relational semantics reveals that the latter also possesses this property and is fully abstract.

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