Parametricity and Semi-Cubical Types

We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes.Our construction works not only for parametricity, but also for similar interpretations of...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 11
Main Author: Moeneclaey, Hugo
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Computer science
Mathematical model
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes.Our construction works not only for parametricity, but also for similar interpretations of type theory and in fact similar interpretations of any generalized algebraic theory. To be precise we consider a functor forgetting unary operations and equations defining them recursively in a generalized algebraic theory. We show that it has a right adjoint.We use techniques from locally presentable category theory, as well as from quotient inductive-inductive types.
DOI:10.1109/LICS52264.2021.9470728