Advertisement

A type theoretical view of Böhm-trees

  • Toshihiko Kurata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1210)

Abstract

Two variations of the intersection type assignment system are studied in connection with Böhm-trees. One is the intersection type assignment system with a non-standard subtype relation, by means of which we characterize whereabouts of D in Böhm-trees. The other is a refinement of the intersection type assignment system whose restricted typability is shown to coincide with finiteness of Böhm-trees.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. van Bakel, Complete restrictions of the intersection type descipline, Theoretical Computer Science 102 (1992), 135–163.Google Scholar
  2. 2.
    H. P. Barendregt, The Lambda Calculus: Its Syntax and Semantics, revised edition, North-Holland, Amsterdam, 1984.Google Scholar
  3. 3.
    H. P. Barendregt, M. Coppo and M. Dezani-Ciancaglini, A filter lambda model and the completeness of type assignment, Journal of Symbolic Logic 48 (1983), 931–940.Google Scholar
  4. 4.
    M. Coppo, M. Dezani-Ciancaglini and B. Venneri, Functional characters of solvable terms, Zeitschrift für Mathematische Logik und Grundlagen der Mathmatik 27 (1981), 45–58.Google Scholar
  5. 5.
    M. Coppo, M. Dezani-Ciancaglini and M. Zacchi, Type theories, normal forms and D∞ lambda-models, Information and Computation 72 (1987), 85–116.Google Scholar
  6. 6.
    J. Y. Girard, Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieur, Thèse de doctorat d'état, Université Paris VII, 1972.Google Scholar
  7. 7.
    J. Y. Girard, P. Taylor and Y. Lafont, Proofs and Types, Cambridge University Press, 1989.Google Scholar
  8. 8.
    J. R. Hindley, The completeness theorem for typing λ-terms, Theoretical Computer Science 22 (1983), 1–17.Google Scholar
  9. 9.
    F. Honsell and S. Ronchi Delia Rocca, An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus, Journal of Computer and System Sciences 45 (1992), 49–75.Google Scholar
  10. 10.
    J. L. Krivine, Lambda-Calculus, Types and Models, Ellis Horwood, 1993.Google Scholar
  11. 11.
    J. C. Mitchell, Type systems for programming languages, Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics, The MIT Press/Elsevier, 1990.Google Scholar
  12. 12.
    G. D. Plotkin, λ-definability in the full type hierarchy, in: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, ed. J. R. Hindley and J. P. Seldin, Academic Press, New York, 363–373.Google Scholar
  13. 13.
    G. Pottinger, A type assignment for the strongly normalizable λ-terms, in: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, ed. J. R. Hindley and J. P. Seldin, Academic Press, New York, 363–373.Google Scholar
  14. 14.
    R. Statman, Logical relations and the typed lambda calculus, Information and Control 65 (1985), 85–97.Google Scholar
  15. 15.
    W. W. Tait, Intensional interpretation of functionals of finite type, Journal of Symbolic Logic 32 (1967), 198–212.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Toshihiko Kurata
    • 1
  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

Personalised recommendations