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International Conference on Category Theory and Computer Science

CTCS 1991: Category Theory and Computer Science pp 197–218Cite as

Relating models of impredicative type theories

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 530))

Abstract

The object of study of this paper is the categorical semantics of three impredicative type theories, viz. Higher Order λ-calculus Fω, the Calculus of Constructions and Higher Order ML. The latter is particularly interesting because it is a two-level type theory with type dependency at both levels. Having described appropriate categorical structures for these calculi, we establish translations back and forth between all of them. Most of the research in the paper concerns the theory of fibrations and comprehension categories.

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Author information

Authors and Affiliations

  1. Dep. Comp. Sci., Nijmegen, NL.

    Bart Jacobs

  2. Dip. Informatica, Genova, I.

    Eugenio Moggi

  3. Fak. Math. & Inform., Passau, D.

    Thomas Streicher

Authors
  1. Bart Jacobs
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  2. Eugenio Moggi
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  3. Thomas Streicher
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Editor information

David H. Pitt Pierre-Louis Curien Samson Abramsky Andrew M. Pitts Axel Poigné David E. Rydeheard

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© 1991 Springer-Verlag Berlin Heidelberg

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Jacobs, B., Moggi, E., Streicher, T. (1991). Relating models of impredicative type theories. In: Pitt, D.H., Curien, PL., Abramsky, S., Pitts, A.M., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. CTCS 1991. Lecture Notes in Computer Science, vol 530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013467

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  • DOI: https://doi.org/10.1007/BFb0013467

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54495-1

  • Online ISBN: 978-3-540-38413-7

  • eBook Packages: Springer Book Archive

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