Advertisement

Polymorphism is not set-theoretic

  • John C. Reynolds
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 173)

Abstract

The polymorphic, or second-order, typed lambda calculus is an extension of the typed lambda calculus in which polymorphic functions can be defined. In this paper, we will prove that the standard set-theoretic model of the ordinary typed lambda calculus cannot be extended to model this language extension.

Keywords

Ordinary Variable Type Expression Language Extension Cartesian Closed Category Lambda Expression 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Reynolds, J. C., Towards a Theory of Type Structure, Proc. Colloque sur la Programmation, Lecture Notes in Computer Science 19, Springer-Verlag, New York, 1974, pp. 408–425.Google Scholar
  2. [2]
    Girard, J.-Y., Interprétation Fonctionelle et Elimination des Coupures dans l'Arithmétique d'Ordre Supérieur, Thèse de Doctorat d'Etat, Paris, 1972.Google Scholar
  3. [3]
    Reynolds, J. C., Types, Abstraction and Parametric Polymorphism, Information Processing 83, R. E. A. Mason (ed.), Elsevier Science Publishers B.V. (North-Holland) 1983, pp. 513–523.Google Scholar
  4. [4]
    Strachey, C., Fundamental Concepts in Programming Languages, Lecture Notes, International Summer School in Computer Programming, Copenhagen, August 1967.Google Scholar
  5. [5]
    Lehmann, D., and Smyth, M. B., Algebraic Specification of Data Types: A Synthetic Approach, Math. Systems Theory 14 (1981), pp. 97–139.Google Scholar
  6. [6]
    Smyth, M. B., and Plotkin, G. D., The Category-Theoretic Solution of Recursive Domain Equations, SIAM Journal on Computing 11, 4 (November 1982), pp. 761–783.Google Scholar
  7. [7]
    Arbib, M. A., and Manes, E. G., Arrows, Structures, and Functors: The Categorical Imperative, Academic Press, New York, 1975, p. 95.Google Scholar
  8. [8]
    McCracken, N. J., An Investigation of a Programming Language with a Polymorphic Type Structure, Ph. D. dissertation, Syracuse University, June 1979.Google Scholar
  9. [9]
    McCracken, N. J., A Finitary Retract Model for the Polymorphic Lambda-Calculus, to appear in Information and Control.Google Scholar
  10. [10]
    Fortune, S., Leivant, D., and O'Donnell, M., The Expressiveness of Simple and Second-Order Type Structures, Journal of the ACM 30, 1 (January 1983), pp. 151–185.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • John C. Reynolds
    • 1
    • 2
  1. 1.INRIA Centre de Sophia AntipolisValbonneFrance
  2. 2.Syracuse UniversitySyracuseU.S.A.

Personalised recommendations