Type theory in type theory using quotient inductive types

Altenkirch, Thorsten and Kaposi, Ambrus (2016) Type theory in type theory using quotient inductive types. In: POPL '16 The 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, 20-22 January 2016, St Petersburg, Florida, United States of America.

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Abstract

We present an internal formalisation of a type heory with dependent types in Type Theory using a special case of higher inductive types from Homotopy Type Theory which we call quotient inductive types (QITs). Our formalisation of type theory avoids referring to preterms or a typability relation but defines directly well typed objects by an inductive definition. We use the elimination principle to define the set-theoretic and logical predicate interpretation. The work has been formalized using the Agda system extended with QITs using postulates.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published in: POPL '16 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. New York : ACM, c2016, p. 18-29. ISBN: 9781450335492 doi:10.1145/2837614.2837638
Keywords: Higher Inductive Types, Homotopy Type Theory, Logical Relations, Metaprogramming, Agda
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Computer Science
Depositing User: Altenkirch, Thorsten
Date Deposited: 04 Jan 2016 12:11
Last Modified: 14 Sep 2016 07:54
URI: http://eprints.nottingham.ac.uk/id/eprint/31169

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