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.
|Title of host publication||Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings|
|Editors||Luca Aceto, Monika Henzinger, Jiri Sgall|
|Place of Publication||Heidelberg, Germany|
|Number of pages||12|
|Publication status||Published - 2011|
|Name||Lecture Notes in Computer Science|
Laird, J., Manzonetto, G., & McCusker, G. (2011). Constructing differential categories and deconstructing categories of games. In L. Aceto, M. Henzinger, & J. Sgall (Eds.), Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings (pp. 186-197). (Lecture Notes in Computer Science; Vol. 6756). Heidelberg, Germany: Springer. https://doi.org/10.1007/978-3-642-22012-8_14