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Constructing differential categories and deconstructing categories of games


Reference:

Laird, J., Manzonetto, G. and McCusker, G., 2013. Constructing differential categories and deconstructing categories of games. Information and Computation, 222, pp. 247-264.

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    Official URL:

    http://dx.doi.org/10.1016/j.ic.2012.10.015

    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.

    Details

    Item Type Articles
    CreatorsLaird, J., Manzonetto, G. and McCusker, G.
    DOI10.1016/j.ic.2012.10.015
    Uncontrolled Keywordsdifferential categories, game semantics, full abstraction
    DepartmentsFaculty of Science > Computer Science
    Publisher Statementdifflong.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Information and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information and Computation, vol 222, 2013, DOI 10.1016/j.ic.2012.10.015
    RefereedYes
    StatusPublished
    ID Code32257

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