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Subtype Universes

Authors Harry Maclean , Zhaohui Luo

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Harry Maclean
  • Royal Holloway, University of London, UK
Zhaohui Luo
  • Royal Holloway, University of London, UK

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Harry Maclean and Zhaohui Luo. Subtype Universes. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 9:1-9:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Type theory
  • coercive subtyping
  • subtype universe


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