Constructing differential categories and deconstructing categories of games

James Laird, Giulio Manzonetto, Guy McCusker

Research output: Contribution to journalArticle

13 Citations (Scopus)
144 Downloads (Pure)

Abstract

Differential categories were introduced by Blute, Cockett and Seely to axiomatize categorically Ehrhard and Regnierʼs 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. A 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 Manzonettoʼs relational model reveals that the latter also possesses this property and is fully abstract.
Original languageEnglish
Pages (from-to)247-264
Number of pages18
JournalInformation and Computation
Volume222
Early online date26 Oct 2012
DOIs
Publication statusPublished - Jan 2013

Keywords

  • differential categories
  • game semantics
  • full abstraction

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