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Data types as objects

  • Adi Shamir
  • William W. Wadge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)

Abstract

In this paper we present a new approach to the semantics of data types, in which the types themselves are incorporated as elements in the domain of data objects. The approach allows types to have subtypes, allows genuinely polymorphic functions, and gives a precise semantics for recursive type definitions (including definitions with parameters). In addition, the approach yields simple and straight forward methods for proving type properties of recursive definitions. These methods include a new fixedpoint rule which permits case analysis.

References

  1. 1.
    R. Milner, L. Morris and M. Newey, "A logic for computable functions with reflexive and polymorphic types", proceedings of the Symposium on Proving and Improving Programs, Arc et Senans 1975, pp371–394.Google Scholar
  2. 2.
    A. Church, "A formulation of the simple theory of types", Journal of Symbolic Logic, v5 (1940), pp56–68.Google Scholar
  3. 3.
    Yeung, PhD thesis, Queen Mary College, London, 1976.Google Scholar
  4. 4.
    Dana Scott, "Data types as lattices", SIAM Journal on Computing, v5 (1976), pp522–587.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Adi Shamir
    • 1
  • William W. Wadge
    • 2
  1. 1.Mathematics Dept. MITCambridgeUSA
  2. 2.Computer Science Dept.University of WarwickCoventryEngland

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