Formalizing restriction categories

Chapman, James and Uustalu, Tarmo and Veltri, Niccolò (2017) Formalizing restriction categories. Journal of Formalized Reasoning, 10 (1). pp. 1-36. ISSN 1972-5787

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    Abstract

    Restriction categories are an abstract axiomatic framework by Cockett and Lack for reasoning about (generalizations of the idea of) partiality of functions. In a restriction category, every map defines an endomap on its domain, the corresponding partial identity map. Restriction categories cover a number of examples of different flavors and are sound and complete with respect to the more synthetic and concrete partial map categories. A partial map category is based on a given category (of total maps) and a map in it is a map from a subobject of the domain. In this paper, we report on an Agda formalization of the first chapters of the theory of restriction categories, including the challenging completeness result. We explain the mathematics formalized, comment on the design decisions we made for the formalization, and illustrate them at work.

    Creators(s): Chapman, James ORCID logoORCID: https://orcid.org/0000-0001-9036-8252, Uustalu, Tarmo and Veltri, Niccolò;
    Item type:Article
    ID code:60204
    Keywords:restriction categories, fuctions, Agda formalization, Electronic computers. Computer science, Computer Science(all)
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:15 Mar 2017 14:27
    Last modified:21 Jan 2021 00:55
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/60204
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