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Independence results for calculi of dependent types

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Category Theory and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 389))

Abstract

Based on a categorical semantics for impredicative calculi of dependent types we prove several independence results. Especially we prove that there exists a model where all syntactical concepts can be interpreted with one exception: in the model the strong sum of a family of propositions indexed over a proposition need not be a proposition again. The method of proof consists of restricting the set of propositions in the well-known ω-Set model due to E. Moggi.

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References

  1. M. Hyland, A. Pitts The Theory of Constructions: Categorical Semantics and Topos-Theoretic Models preprint, to appear in the Proceedings of the Conference on Categories in Computer Science and Logic, Contemporary Mathematics, Amer. Math.Soc., 1988.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Univ. Passau, D-8390, West Germany

    Thomas Streicher

Authors
  1. Thomas Streicher
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Editor information

David H. Pitt David E. Rydeheard Peter Dybjer Andrew M. Pitts Axel Poigné

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© 1989 Springer-Verlag Berlin Heidelberg

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Streicher, T. (1989). Independence results for calculi of dependent types. In: Pitt, D.H., Rydeheard, D.E., Dybjer, P., Pitts, A.M., Poigné, A. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018350

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  • DOI: https://doi.org/10.1007/BFb0018350

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51662-0

  • Online ISBN: 978-3-540-46740-3

  • eBook Packages: Springer Book Archive

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