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A Metatheoretic Analysis of Subtype Universes

Authors Felix Bradley , Zhaohui Luo

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Author Details

Felix Bradley
  • Royal Holloway, University of London, UK
Zhaohui Luo
  • Royal Holloway, University of London, UK

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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)
https://doi.org/10.4230/LIPIcs.TYPES.2022.9

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.

Subject Classification

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

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References

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