Comprehensive parametric polymorphism: categorical models and type theory

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Abstract

This paper combines reflexive-graph-category structure for relational parametricity with fibrational models of impredicative polymorphism. To achieve this, we modify the definition of fibrational model of impredicative polymorphism by adding one further ingredient to the structure: comprehension in the sense of Lawvere. Our main result is that such comprehensive models, once further endowed with reflexive-graph-category structure, enjoy the expected consequences of parametricity. This is proved using a type-theoretic presentation of the category-theoretic structure, within which the desired consequences of parametricity are derived. The formalisation requires new techniques because equality relations are not available, and standard arguments that exploit equality need to be reworked.
Original languageEnglish
Title of host publicationFoundations of Software Science and Computation Structures
Subtitle of host publication19th International Conference, FOSSACS 2016, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2-8, 2016, Proceedings
EditorsBart Jacobs, Christof Löding
Pages3-19
Number of pages17
Volume9634
ISBN (Electronic)978-3-662-49630-5
DOIs
Publication statusPublished - 22 Mar 2016

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
ISSN (Print)0302-9743

Keywords

  • polymorphism
  • re exive-graph-category structure
  • parametricity
  • impredicative polymorphism
  • type theory

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  • Projects

  • Prizes

    ETAPS 2016 EATCS best paper award

    Fredrik Nordvall Forsberg (Recipient), Neil Ghani (Recipient) & Alex Simpson (Recipient), 6 Apr 2016

    Prize: Prize (including medals and awards)

    Cite this

    Ghani, N., Nordvall Forsberg, F., & Simpson, A. (2016). Comprehensive parametric polymorphism: categorical models and type theory. In B. Jacobs, & C. Löding (Eds.), Foundations of Software Science and Computation Structures: 19th International Conference, FOSSACS 2016, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2-8, 2016, Proceedings (Vol. 9634, pp. 3-19). (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-662-49630-5_1