Essential intersection type assignment

  • Steffen van Bakel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 761)


This paper introduces a notion of intersection type assignment on the Lambda Calculus that is a restriction of the BCD-system as presented in [4]. This restricted system is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCD-system. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.


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  1. [1]
    Bakel S. van. Complete restrictions of the Intersection Type Discipline. Theoretical Computer Science, 102:135–163, 1992.Google Scholar
  2. [2]
    Bakel S. van. Principal type schemes for the Strict Type Assignment System. Logic and Computation, 1993. To appear.Google Scholar
  3. [3]
    Barendregt H. The Lambda Calculus: its Syntax and Semantics. North-Holland, Amsterdam, revised edition, 1984.Google Scholar
  4. [4]
    Barendregt H., M. Coppo, and M. Dezani-Ciancaglini. A filter lambda model and the completeness of type assignment. The Journal of Symbolic Logic, 48(4):931–940, 1983.Google Scholar
  5. [5]
    Coppo M., M. Dezani-Ciancaglini, and B. Venneri. Functional characters of solvable terms. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 27:45–58, 1981.Google Scholar
  6. [6]
    Curry H.B. and R. Feys. Combinatory Logic. volume 1. North-Holland, Amsterdam, 1958.Google Scholar
  7. [7]
    Dezani-Ciancaglini M. and I. Margaria. A characterisation of F-complete type assignments. Theoretical Computer Science 45:121–157, 1986.Google Scholar
  8. [8]
    Hindley J.R. The principal type scheme of a object in combinatory logic. Transactions of the American Mathematical Society, 146:29–60, 1969.Google Scholar
  9. [9]
    Hindley J.R. The simple semantics for Coppo-Dezani-Sallé type assignment. In M. Dezani and U. Montanari, editors, International symposium on programming, volume 137 of Lecture Notes in Computer Science, pages 212–226. Springer-Verlag, 1982.Google Scholar
  10. [10]
    Hindley J.R. The Completeness Theorem for Typing λ-terms. Theoretical Computer Science, 22(1):1–17, 1983.Google Scholar
  11. [11]
    Hindley R. and G. Longo. Lambda calculus models and extensionality. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 26:289–310, 1980.Google Scholar
  12. [12]
    Mitchell J.C. Polymorphic Type Inference and Containment. Information and Computation, 76:211–249, 1988.Google Scholar
  13. [13]
    Ronchi della Rocca S. and B. Venneri. Principal type schemes for an extended type theory. Theoretical Computer Science, 28:151–169, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Steffen van Bakel
    • 1
  1. 1.Department of Informatics, Faculty of Mathematics and InformaticsUniversity of NijmegenED NijmegenThe Netherlands

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