Comprehensive Parametric Polymorphism: Categorical Models and Type Theory

  • Neil Ghani
  • Fredrik Nordvall Forsberg
  • Alex Simpson
Conference paper

DOI: 10.1007/978-3-662-49630-5_1

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9634)
Cite this paper as:
Ghani N., Nordvall Forsberg F., Simpson A. (2016) Comprehensive Parametric Polymorphism: Categorical Models and Type Theory. In: Jacobs B., Löding C. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2016. Lecture Notes in Computer Science, vol 9634. Springer, Berlin, Heidelberg

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Neil Ghani
    • 1
  • Fredrik Nordvall Forsberg
    • 1
  • Alex Simpson
    • 2
  1. 1.Department of Computer and Information SciencesUniversity of StrathclydeGlasgowUK
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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