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 publicationInternational Conference on Foundations of Software Science and Computation Structures [FoSSaCS 2016]
EditorsBart Jacobs, Christof Löding
Place of PublicationBerlin
PublisherSpringer-Verlag
Pages3-19
Number of pages17
Volume9634
ISBN (Electronic)9783662496305
ISBN (Print)9783662496299
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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