skip to main content
article
Open Access

Typed representation of objects by functions

Published:01 January 1989Publication History
Skip Abstract Section

Abstract

A systematic representation of objects grouped into types by constructions similar to the composition of sets in mathematics is proposed. The representation is by lambda expressions, which supports the representation of objects from function spaces. The representation is related to a rather conventional language of type descriptions in a way that is believed to be new. Ordinary control-expressions (i.e.,case- and let-expressions) are derived from the proposed representation.

References

  1. 1 BARENDREGT, H. P. The Lambda Calculus--Its Syntax and Semantics. North Holland, Amsterdam, 1981.Google ScholarGoogle Scholar
  2. 2 B/~HM, C., AND BERARDUCCI, A. Automatic synthesis of typed A-programs on term algebras. Theor. Comput. Sci. 39 (1985), 135-154.Google ScholarGoogle Scholar
  3. 3 CURRY, H. B., HINDLEY, J. R., AND SELDIN, J.P. Combinatory Logic: Volume II. North Holland, Amsterdam, 1972.Google ScholarGoogle Scholar
  4. 4 GOGUEN, J. A., THATCHER, g. W., AND WAGNER, E. G. An initial algebra approach to the specification, correctness and implementation of abstract data types. In Current Trends in Programming Methodology--IV. R. T. Yeh, Ed. Prentice-Hall, Englewood Cliffs, N.J., 1979, pp. 80-149.Google ScholarGoogle Scholar
  5. 5 HENDERSON, P. Functional Programming Application and Implementation. Prentice-Hall, Englewood Cliffs, N.J., 1980. Google ScholarGoogle Scholar
  6. 6 HOARE, C. A.R. Recursive data structure. Int. J. Comput. Inf. Sci. 4, 2 (1975), 105-132.Google ScholarGoogle Scholar
  7. 7 HOWARD, W.A. The formulae-as-types notion of construction. In To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. J. P. Seldin, and J. R. Hindley, Eds. Academic Press, New York, 1980, pp. 479-490.Google ScholarGoogle Scholar
  8. 8 KAMIN, S. Final data types and their specification. ACM Trans. Program. Lang. Syst. 5, i (Jan. 1983), 97-123. Google ScholarGoogle Scholar
  9. 9 LEIVANT, D. Reasoning about functional programs and complexity classes associated with type disciplines. In 24th Annual Symposium on the Foundation of Computer Science (Tucson, Ariz., Nov. 7-9, 1983). IEEE, New York, 1983, pp. 460-469.Google ScholarGoogle Scholar
  10. 10 MARTIN-LOF, P. Constructive mathematics and computer programming. In 6th International Congress for Logic, Methodology and Philosophy of Science (Hannover, 1979). North-Holland, Amsterdam, 1982, pp. 153-175.Google ScholarGoogle Scholar
  11. 11 MILNER, R. A proposal for standard ML. In Proceedings of the 1984 ACM Symposium on Lisp and Functional Programming (Austin, Tex., Aug. 1984). ACM, New York, 1984, pp. 184-197. Google ScholarGoogle Scholar
  12. 12 MORRIS, J. Types are not sets. In ACM Symposium on Principles of Programming Languages (Boston, 1973) ACM, New York, 1973, pp. 120-124. Google ScholarGoogle Scholar
  13. 13 SCOTT, D. Data types as latices. SIAM J. Comput. 5, 3 (Sept. 1976), 522-577.Google ScholarGoogle Scholar
  14. 14 STEENSGAARD-MADSEN, J. Pascal--clarification and recommended extensions. Acta Inf. 12 (1979) 73-94.Google ScholarGoogle Scholar
  15. 15 STEENSGAARD-MADSEN, J. A statement-oriented approach to data abstraction. ACM Trans. Program. Lang. Syst. 3, i (Jan. 1981), 1-10. Google ScholarGoogle Scholar
  16. 16 STEENGAARD-MADSEN, J. Definition of the programming language MODEF. SIGPLAN Not. 19, 2 (Feb. 1984).Google ScholarGoogle Scholar
  17. 17 WANO, M. Final algebra semantics and data type extensions. J. Comput. Syst. Sci. 19, 1 (Aug. 1979), 27-44.Google ScholarGoogle Scholar
  18. 18 WEANER, P. Classification in object-oriented systems. SIGPLAN Not. 21, 10 (Oct. 1986), 173-182. Google ScholarGoogle Scholar
  19. 19 WIRTH, N. The programming language Pascal, Acta Inf. 1, I (1971), 35-63.Google ScholarGoogle Scholar

Index Terms

  1. Typed representation of objects by functions

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Published in

          cover image ACM Transactions on Programming Languages and Systems
          ACM Transactions on Programming Languages and Systems  Volume 11, Issue 1
          Jan. 1989
          167 pages
          ISSN:0164-0925
          EISSN:1558-4593
          DOI:10.1145/59287
          Issue’s Table of Contents

          Copyright © 1989 ACM

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 January 1989
          Published in toplas Volume 11, Issue 1

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • article

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader