License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2020.9
URN: urn:nbn:de:0030-drops-138880
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Maclean, Harry ; Luo, Zhaohui

Subtype Universes

LIPIcs-TYPES-2020-9.pdf (0.8 MB)


We introduce a new concept called a subtype universe, which is a collection of subtypes of a particular type. Amongst other things, subtype universes can model bounded quantification without undecidability. Subtype universes have applications in programming, formalisation and natural language semantics. Our construction builds on coercive subtyping, a system of subtyping that preserves canonicity. We prove Strong Normalisation, Subject Reduction and Logical Consistency for our system via transfer from its parent system UTT[ℂ]. We discuss the interaction between subtype universes and other sorts of universe and compare our construction to previous work on Power types.

BibTeX - Entry

  author =	{Maclean, Harry and Luo, Zhaohui},
  title =	{{Subtype Universes}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-138880},
  doi =		{10.4230/LIPIcs.TYPES.2020.9},
  annote =	{Keywords: Type theory, coercive subtyping, subtype universe}

Keywords: Type theory, coercive subtyping, subtype universe
Collection: 26th International Conference on Types for Proofs and Programs (TYPES 2020)
Issue Date: 2021
Date of publication: 07.06.2021

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