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DOI: 10.4230/LIPIcs.TYPES.2022.9

A Metatheoretic Analysis of Subtype Universes

Authors: Felix Bradley and Zhaohui Luo

Published in: LIPIcs, Volume 269, 28th International Conference on Types for Proofs and Programs (TYPES 2022)

Abstract

Subtype universes were initially introduced as an expressive mechanisation of bounded quantification extending a modern type theory. In this paper, we consider a dependent type theory equipped with coercive subtyping and a generalisation of subtype universes. We prove results regarding the metatheoretic properties of subtype universes, such as consistency and strong normalisation. We analyse the causes of undecidability in bounded quantification, and discuss how coherency impacts the metatheoretic properties of theories implementing bounded quantification. We describe the effects of certain choices of subtyping inference rules on the expressiveness of a type theory, and examine various applications in natural language semantics, programming languages, and mathematics formalisation.

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Felix Bradley and Zhaohui Luo. A Metatheoretic Analysis of Subtype Universes. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bradley_et_al:LIPIcs.TYPES.2022.9,
  author =	{Bradley, Felix and Luo, Zhaohui},
  title =	{{A Metatheoretic Analysis of Subtype Universes}},
  booktitle =	{28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-285-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{269},
  editor =	{Kesner, Delia and P\'{e}drot, Pierre-Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2022.9},
  URN =		{urn:nbn:de:0030-drops-184520},
  doi =		{10.4230/LIPIcs.TYPES.2022.9},
  annote =	{Keywords: Type theory, coercive subtyping, subtype universes}
}

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A Metatheoretic Analysis of Subtype Universes

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