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International Workshop on Types for Proofs and Programs

TYPES 1995: Types for Proofs and Programs pp 153–164Cite as

Conservativity of equality reflection over intensional type theory

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1158)

Abstract

We investigate the relationship between intensional and extensional formulations of Martin-Löf type theory. We exhibit two principles which are not provable in the intensional formulation: uniqueness of identity and functional extensionality. We show that extensional type theory is conservative over the intensional one extended by these two principles, meaning that the same types are inhabited, whenever they make sense. The proof is non-constructive because it uses set-theoretic quotienting and choice of representatives.

Keywords

  • Type Theory
  • Identity Type
  • Elimination Rule
  • Functional Extensionality
  • Canonical Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Fachbereich Mathematik, TH Darmstadt, Schloßgartenstraße 7, D-64289, Darmstadt, Germany

    Martin Hofmann

Authors
  1. Martin Hofmann
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    © 1996 Springer-Verlag Berlin Heidelberg

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    Hofmann, M. (1996). Conservativity of equality reflection over intensional type theory. In: Berardi, S., Coppo, M. (eds) Types for Proofs and Programs. TYPES 1995. Lecture Notes in Computer Science, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61780-9_68

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    • DOI: https://doi.org/10.1007/3-540-61780-9_68

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-61780-8

    • Online ISBN: 978-3-540-70722-6

    • eBook Packages: Springer Book Archive

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