Constructing differential categories and deconstructing categories of games

  • Authors:

  • Jim Laird;Giulio Manzonetto;Guy Mccusker

  • Affiliations:

  • Department of Computer Science, University of Bath, Bath, BA2 7AY, UK;Univ. Paris 13, Sorbonne Paris Cité, LIPN, UMR 7030, CNRS, F-93430 Villetaneuse, France;Department of Computer Science, University of Bath, Bath, BA2 7AY, UK

  • Venue:
  • Information and Computation
  • Year:
  • 2013

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Abstract

Differential categories were introduced by Blute, Cockett and Seely to axiomatize categorically Ehrhard and Regnier@?s syntactic differential operator. We present an abstract construction that takes a symmetric monoidal category and yields a differential category, and show how this construction may be applied to categories of games. In one instance, we recover the 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, and shows how the differential combinator may be encoded in the imperative language. The second instance corresponds to a new Cartesian differential category of games. We give a model of a simply-typed resource calculus, Resource PCF, in this category and show that it possesses the finite definability property. Comparison with a semantics based on Bucciarelli, Ehrhard and Manzonetto@?s relational model reveals that the latter also possesses this property and is fully abstract.