Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

Comprehensive parametric polymorphism : categorical models and type theory

Ghani, Neil and Nordvall Forsberg, Fredrik and Simpson, Alex (2016) Comprehensive parametric polymorphism : categorical models and type theory. In: Foundations of Software Science and Computation Structures. Lecture Notes in Computer Science, 9634 . Springer Berlin/Heidelberg, pp. 3-19. ISBN 978-3-662-49630-5

Text (Ghani-etal-FOSSACS2016-comprehensive-parametric-polymorphism-categorical-models-type-theory)
Ghani_etal_FOSSACS2016_comprehensive_parametric_polymorphism_categorical_models_type_theory.pdf - Accepted Author Manuscript

Download (423kB) | Preview


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.