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Internal type theory

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Types for Proofs and Programs (TYPES 1995)

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

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Abstract

We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory. Then we define categories with families formally in Martin-Löf's intensional intuitionistic type theory. Finally, we discuss the coherence problem for these internal categories with families.

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Authors and Affiliations

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

    Peter Dybjer

Authors
  1. Peter Dybjer
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Editor information

Stefano Berardi Mario Coppo

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© 1996 Springer-Verlag Berlin Heidelberg

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Dybjer, P. (1996). Internal 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_66

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  • DOI: https://doi.org/10.1007/3-540-61780-9_66

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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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