Extensions of pure type systems

  • Gilles Barthe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 902)

Abstract

We extend pure type systems with quotient types and subset types and establish an equivalence between four strong normalisation problems: subset types, quotient types, definitions and the so-called K-rules. As a corollary, we get strong normalisation of ECC with definitions, subset and quotient types.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Barendregt. Typed λ-calculi, Handbook of logic in computer science, Abramsky and al eds, OUP 1992.Google Scholar
  2. 2.
    G. Barthe. Towards a mathematical vernacular, submitted.Google Scholar
  3. 3.
    G. Barthe. Formalizing mathematics in type theory: fundamentals and case studies, submitted.Google Scholar
  4. 4.
    G. Barthe. An introduction to quotient and congruence types, manuscript, University of Nijmegen, November 1994.Google Scholar
  5. 5.
    R. Constable and al. Implementing Mathematics with the NuPrl Proof Development System, Prenctice Hall, 1986.Google Scholar
  6. 6.
    T. Coquand. A new paradox in type theory, in the proceedings of the 9th Congress of Logic, Methodology and Philosophy of Science.Google Scholar
  7. 7.
    H. Geuvers. Logics and type systems, Ph.D thesis, University of Nijmegen, 1993.Google Scholar
  8. 8.
    H. Geuvers. A short and flexible proof of strong normalisation for the Calculus of Constructions, submitted.Google Scholar
  9. 9.
    M. Hofmann. Extensional concepts in intensional type theory, Ph.D thesis, University of Edinburgh, forthcoming.Google Scholar
  10. 10.
    M. Hofmann. A simple model for quotient types, in these proceedings.Google Scholar
  11. 11.
    B. Jacobs. Categorical Logic and Type Theory, in preparation.Google Scholar
  12. 12.
    B. Jacobs. Quotients in simple Type Theory, submitted.Google Scholar
  13. 13.
    J. Lambek and P.J. Scott. Introduction to higher-order categorical logic, CUP, 1986.Google Scholar
  14. 14.
    Z. Luo. Computation and reasoning: a type theory for computer science, OUP, 1994.Google Scholar
  15. 15.
    N. Mendler. Quotient types via coequalisers in Martin-Lof's type theory, in the informal proceedings of the workshop on logical frameworks, Antibes, May 1990.Google Scholar
  16. 16.
    R. Nederpelt and al (eds). Selected Papers on Automath, North-Holland, 1994.Google Scholar
  17. 17.
    B. Nordstrom, K. Petersson and J. Smith. Programming in Martin-Lof's type theory, OUP, 1990.Google Scholar
  18. 18.
    E. Poll and P. Severi. PTS with definitions, in proceedings of LFCS'94, LNCS 813.Google Scholar
  19. 19.
    G. Pottinger. Definite descriptions and excluded middle in the theory of constructions, TYPES mailing list, November 1989.Google Scholar
  20. 20.
    A. Salvesen and J. Smith. The strength of the subset type in Martin-Lof's type theory, proceedings of LICS'88, 1988.Google Scholar
  21. 21.
    J. Terlouw. Strong normalisation in type systems: a model-theoretical approach, Dirk van Dalen Festschrift, Utrecht, 1993.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Gilles Barthe
    • 1
  1. 1.Faculty of Mathematics and InformaticsUniversity of NijmegenThe Netherlands

Personalised recommendations