Gluing for type theory
Paper in proceeding, 2019

The relationship between categorical gluing and proofs using the logical relation technique is folklore. In this paper we work out this relationship for Martin-Löf type theory and show that parametricity and canonicity arise as special cases of gluing. The input of gluing is two models of type theory and a pseudomorphism between them and the output is a displayed model over the first model. A pseudomorphism preserves the categorical structure strictly, the empty context and context extension up to isomorphism, and there are no conditions on preservation of type formers. We look at three examples of pseudomorphisms: the identity on the syntax, the interpretation into the set model and the global section functor. Gluing along these result in syntactic parametricity, semantic parametricity and canonicity, respectively.

Author

Ambrus Kaposi

Simon Huber

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Christian Sattler

Logic and Types

Leibniz International Proceedings in Informatics, LIPIcs

18688969 (ISSN)

Vol. 131 25:1-25:19

4th International Conference on Formal Structures for Computation and Deduction
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Subject Categories

Algebra and Logic

Computer Science

DOI

10.4230/LIPIcs.FSCD.2019.25

More information

Created

11/15/2023