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International Workshop on Types for Proofs and Programs

TYPES 1995: Types for Proofs and Programs pp 47–61Cite as

Extracting a proof of coherence for monoidal categories from a proof of normalization for monoids

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

Abstract

This paper studies the problem of coherence in category theory from a type-theoretic viewpoint. We first show how a Curry-Howard interpretation of a formal proof of normalization for monoids almost directly yields a coherence proof for monoidal categories. Then we formalize this coherence proof in intensional intuitionistic type theory and show how it relies on explicit reasoning about proof objects for intensional equality. This formalization has been checked in the proof assistant ALF.

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Authors and Affiliations

  1. Department of Computing Science, Chalmers University of Technology, Göteborg, Sweden

    Ilya Beylin & Peter Dybjer

Authors
  1. Ilya Beylin
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  2. Peter Dybjer
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Stefano Berardi Mario Coppo

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© 1996 Springer-Verlag Berlin Heidelberg

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Beylin, I., Dybjer, P. (1996). Extracting a proof of coherence for monoidal categories from a proof of normalization for monoids. 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_61

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  • DOI: https://doi.org/10.1007/3-540-61780-9_61

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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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