Internal Strict Propositions Using Point-Free Equations

Authors István Donkó, Ambrus Kaposi



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Author Details

István Donkó
  • Eötvös Loránd University, Budapest, Hungary
Ambrus Kaposi
  • Eötvös Loránd University, Budapest, Hungary

Acknowledgements

Thanks to Christian Sattler for discussions on the topics of this paper. Many thanks to the anonymous reviewers for their comments and suggestions.

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István Donkó and Ambrus Kaposi. Internal Strict Propositions Using Point-Free Equations. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.TYPES.2021.6

Abstract

The setoid model of Martin-Löf’s type theory bootstraps extensional features of type theory from intensional type theory equipped with a universe of definitionally proof irrelevant (strict) propositions. Extensional features include a Prop-valued identity type with a strong transport rule and function extensionality. We show that a setoid model supporting these features can be defined in intensional type theory without any of these features. The key component is a point-free notion of propositions. Our construction suggests that strict algebraic structures can be defined along the same lines in intensional type theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
Keywords
  • Martin-Löf’s type theory
  • intensional type theory
  • function extensionality
  • setoid model
  • homotopy type theory

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