2026-07-23T12:54:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16775 2024-03-06T10:58:15Z ddc:004 open_access

Internal Strict Propositions Using Point-Free Equations Donkó, István Kaposi, Ambrus Martin-Löf’s type theory intensional type theory function extensionality setoid model homotopy type theory 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik István Donkó and Ambrus Kaposi 2022 Is Part Of LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TYPES.2021.6 urn:nbn:de:0030-drops-167759 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.6 eng https://creativecommons.org/licenses/by/4.0/legalcode