THORSTEN ALTENKIRCH THORSTEN.ALTENKIRCH@NOTTINGHAM.AC.UK
Professor of Computer Science
Constructing a universe for the setoid model
Altenkirch, Thorsten; Boulier, Simon; Kaposi, Ambrus; Sattler, Christian; Sestini, Filippo
Authors
Simon Boulier
Ambrus Kaposi
Christian Sattler
Filippo Sestini
Contributors
Stefan Kiefer
Editor
Christine Tasson
Editor
Abstract
The setoid model is a model of intensional type theory that validates certain extensionality principles, like function extensionality and propositional extensionality, the latter being a limited form of univalence that equates logically equivalent propositions. The appeal of this model construction is that it can be constructed in a small, intensional, type theoretic metatheory, therefore giving a method to boostrap extensionality. The setoid model has been recently adapted into a formal system, namely Setoid Type Theory (SeTT). SeTT is an extension of intensional Martin-Löf type theory with constructs that give full access to the extensionality principles that hold in the setoid model.
Although already a rich theory as currently defined, SeTT currently lacks a way to internalize the notion of type beyond propositions, hence we want to extend SeTT with a universe of setoids. To this aim, we present the construction of a (non-univalent) universe of setoids within the setoid model, first as an inductive-recursive definition, which is then translated to an inductive-inductive definition and finally to an inductive family. These translations from more powerful definition schemas to simpler ones ensure that our construction can still be defined in a relatively small metatheory which includes a proof-irrelevant identity type with a strong transport rule.
Citation
Altenkirch, T., Boulier, S., Kaposi, A., Sattler, C., & Sestini, F. (2021). Constructing a universe for the setoid model. In S. Kiefer, & C. Tasson (Eds.), Foundations of Software Science and Computation Structures : 24th International Conference, FOSSACS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 – April 1, 2021, Proceedings (1-21). https://doi.org/10.1007/978-3-030-71995-1_1
Presentation Conference Type | Edited Proceedings |
---|---|
Conference Name | 24th International Conference on Foundations of Software Science and Computation Structures (FOSSACS 2021) |
Start Date | Mar 27, 2021 |
End Date | Apr 1, 2021 |
Acceptance Date | Feb 1, 2021 |
Online Publication Date | Mar 23, 2021 |
Publication Date | Mar 23, 2021 |
Deposit Date | May 28, 2021 |
Publicly Available Date | Jun 1, 2021 |
Publisher | Springer Publishing Company |
Pages | 1-21 |
Series Title | Lecture notes in computer science |
Series Number | 12650 |
Series ISSN | 0302-9743 |
Book Title | Foundations of Software Science and Computation Structures : 24th International Conference, FOSSACS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 – April 1, 202 |
ISBN | 9783030719944 |
DOI | https://doi.org/10.1007/978-3-030-71995-1_1 |
Public URL | https://nottingham-repository.worktribe.com/output/5421642 |
Publisher URL | https://link.springer.com/chapter/10.1007%2F978-3-030-71995-1_1 |
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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