Discussion of Homotopy Type Theory and Univalent Foundations
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From: Erik Palmgren <palmgren@math.su.se>
To: "homotopytypetheory@googlegroups.com"
Subject: [HoTT] New preprint : A model of Martin-Löf extensional type theory with universes formalized in Agda (	arXiv:1909.01414)
Date: Thu, 5 Sep 2019 07:10:58 +0000	[thread overview]
Message-ID: <6AC5AAA7-297B-4644-A116-4182A0FC935E@math.su.se> (raw)

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From type theory to setoids and back
Erik Palmgren<https://arxiv.org/search/math?searchtype=author&query=Palmgren%2C+E>
(Submitted on 3 Sep 2019)
A model of Martin-Löf extensional type theory with universes is formalized in Agda, an interactive proof system based on Martin-Löf intensional type theory. This may be understood, we claim, as a solution to the old problem of modelling the full extensional theory in the intensional theory. Types are interpreted as setoids, and the model is therefore a setoid model. We solve the problem of intepreting type universes by utilizing Aczel's type of iterative sets, and show how it can be made into a setoid of small setoids containing the necessary setoid constructions.
In addition we interpret the bracket types of Awodey and Bauer. Further quotient types should be interpretable.
Comments:       30 pages
Subjects:       Logic (math.LO)
MSC classes:    03B15, 03B35, 03E70, 03F50
Cite as:        arXiv:1909.01414<https://arxiv.org/abs/1909.01414> [math.LO]
        (or arXiv:1909.01414v1<https://arxiv.org/abs/1909.01414v1> [math.LO] for this version)


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