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The algebraic specification of semicomputable data types

  • J. L. M. Vrancken
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 332)

Abstract

A proof is given for a theorem stating that every semicomputable data type can be specified with only one hidden sort. Preceding this, definitions for the notions signature and algebra are given in the setting of category theory and the notion of a (semi-)computable algebra is discussed.

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References

  1. [BT 1]
    Bergstra, J.A., J.V. Tucker, Algebraic specifications of computable and semicomputable data types, Theoretical Computer Science, 50, 1987.Google Scholar
  2. [BT2]
    —, The Completeness of the Algebraic Specification Methods for Computable Data Types, Information and Control, 54, (1982), pp. 186–200.Google Scholar
  3. [BT3]
    —, A characterisation of computable data types by means of a finite, equational specification method, in J.W. de Bakker and J. v. Leeuwen (eds.) Automata, Languages and Programming, Seventh Colloquium, Noordwijkerhout, 1980, Springer Verlag, Berlin, 1980, pp. 76–90.Google Scholar
  4. [BW]
    Bloom, S.L., E.G.Wagner, Many-sorted theories and their algebras with some applications to data types, In Algebraic Methods in Semantics, edited by M.Nivat, J.C.Reynolds, Cambridge University Press, 1985, pp. 133–68.Google Scholar
  5. [EM]
    Ehrig, H., B. Mahr, Fundamentals of Algebraic Specification 1, EATCS, Monographs on Theoretical Computer Science 6, Springer-Verlag, Berlin, 1985.Google Scholar
  6. [M]
    Malcev, A. I., Constructive algebras, I., Russian Mathematical Surveys 16 (1961) pp. 77–129.Google Scholar
  7. [MacL]
    MacLane,S., Categories for the Working Mathematician, Springer-Verlag, New York Inc., 1971.Google Scholar
  8. [MG]
    J.Meseguer, J.A.Goguen, Initiality, induction and computability. In Algebraic Methods in Semantics, edited by M.Nivat, J.C.Reynolds, Cambridge University Press, 1985, pp. 459–541.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J. L. M. Vrancken
    • 1
  1. 1.Programming Research GroupUniversity of AmsterdamAmsterdam

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