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Relating models of impredicative type theories

  • Bart Jacobs
  • Eugenio Moggi
  • Thomas Streicher
Conference paper
Part of the Lecture Notes in Computer Science book series (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 , 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.

Keywords

Type Theory Natural Transformation Categorical Semantic Category Theory Generic Object 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Bart Jacobs
    • 1
  • Eugenio Moggi
    • 2
  • Thomas Streicher
    • 3
  1. 1.Dep. Comp. Sci.NijmegenNL.
  2. 2.Dip. InformaticaGenovaI.
  3. 3.Fak. Math. & Inform.PassauD.

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