Pure Type Systems with definitions

  • Paula Severi
  • Erik Poll
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 813)


In this paper, an extension of Pure Type Systems (PTS's) with definitions is presented. We prove this extension preserves many of the properties of PTS's. The main result is a proof that for many PTS's, including the Calculus of Constructions, this extension preserves strong normalisation.


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  1. [Bar92]
    H.P. Barendregt. Lambda calculi with types. In D. M. Gabbai, S. Abramsky, and T. S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 1. Oxford University Press, 1992.Google Scholar
  2. [CH88]
    Thierry Coquand and Gérard Huet. The Calculus of Constructions. Information and Computation, 76:95–120, 1988.Google Scholar
  3. [Coq85]
    Thierry Coquand. Une Theorie des Constructions. PhD thesis, Université Paris VII, 1985.Google Scholar
  4. [Coq86]
    Thierry Coquand. An analysis of Girard's paradox. In Logic in Computer Science, pages 227–236. IEEE, 1986.Google Scholar
  5. [dB80]
    N.G. de Bruijn. A survey of the project AUTOMATH. In J.P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, pages 579–606. Academic Press, 1980.Google Scholar
  6. [dV85]
    Roel de Vrijer. A direct proof of the finite developments theorem. Journal of Symbolic Logic, 50(2):339–343, 1985.Google Scholar
  7. [Dea91]
    G. Dowek et al. The Coq proof assistant version 5.6, users guide. Rapport de Recherche 134, INRIA, 1991.Google Scholar
  8. [Gir72]
    J.-Y. Girard. Interprétation fonctionelle et élimination des coupures de l'arithmétique d'ordre supérieur. PhD thesis, Université Paris VII, 1972.Google Scholar
  9. [GN91]
    Herman Geuvers and Mark-Jan Nederhof. A modular proof of strong normalisation for the Calculus of Constructions. Journal of Functional Programming, 1(2):155–189, 1991.Google Scholar
  10. [Hel91]
    Leen Helmink. Goal directed proof construction in type theory. In Procs. of the first Workshop on Logical Frameworks. Cambridge University Press, 1991.Google Scholar
  11. [HHP93]
    Robert Harper, Furio Honsell, and Gordon Plotkin. A framework for defining logics. Journal of the ACM, 40(1):143–184, 1993.Google Scholar
  12. [LP92]
    Zhaohui Luo and Robert Pollack. LEGO proof development system: User's manual. Technical Report ECS-LFCS-92-211, LFCS-University of Edinburgh, 1992.Google Scholar
  13. [Luo89]
    Z. Luo. ECC, the Extended Calculus of Constructions. In Logic in Computer Science, pages 386–395. IEEE, 1989.Google Scholar
  14. [Rey74]
    John C. Reynolds. Towards a theory of type structure. In Programming Symposium: Colloque sur la Programmation, volume 19 of LNCS, pages 408–425. Springer, 1974.Google Scholar
  15. [SP93]
    Paula Severi and Erik Poll. Pure type systems with definitions. Computing Science Note (93/24), Eindhoven University of Technology, 1993.Google Scholar
  16. [vD80]
    D. T. van Daalen. The Language Theory of Automath. PhD thesis, Eindhoven University of Technology, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Paula Severi
    • 1
  • Erik Poll
    • 1
  1. 1.Eindhoven University of TechnologyMB Eindhoven

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