Advertisement

Computability in categories

  • M. B. Smyth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)

Keywords

Data Type Recursive Function Suitable Indexing Finite Domain Effective Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berry, G., Modeles completement adequats et stables des lambda-calculus types, These, Universite Paris VII, 1979.Google Scholar
  2. 2.
    Bishop, E., Foundations of Constructive Analysis, McGraw-Hill (N.Y.), 1967.Google Scholar
  3. 3.
    Constable, R., Constructive mathematics and automatic program writers, IFIP (1972), 229–233.Google Scholar
  4. 4.
    Curien, P., Algorithmes sequentiels sur structures de donnees concretes, These de 3e cycles, Universite Paris VII, 1979.Google Scholar
  5. 5.
    Egli, H. & R. Constable, Computability concepts for programming language semantics, Theor. Comp. Sci. 2 (1976).Google Scholar
  6. 6.
    Ehrich, H.-D. & V. Lohberger, Parametric specification of abstract data types, parametric substitution, and graph replacements, Proc. of workshop on "Graphentheoretische Konzepte in der Informatik", ed. — J. Mühlbacher, Hanser-Verl., München, 1977.Google Scholar
  7. 7.
    Freyd, P., Abelian Categories, Harper and Row, 1964.Google Scholar
  8. 8.
    Hennessy, M. & G. Plotkin, Full abstraction for a simple parallel programming language, MFCS '79, LNCS 74, 1979.Google Scholar
  9. 9.
    Herrlich, H. & D. Strecker, Category Theory, Allyn and Bacon, 1978.Google Scholar
  10. 10.
    Kahn, G. & G. Plotkin, Domaines concrets, Rapport No. 336, IRIA Laboria, 1978.Google Scholar
  11. 11.
    Kanda, A., Thesis, University of Warwick, 1979.Google Scholar
  12. 12.
    Kanda, A., Fully effective solutions of recursive domain equations, MFCS '79, LNCS 74, 1979.Google Scholar
  13. 13.
    Kanda, A. & D. Park, When are two effectively given domains identical?, Proc. 4th GI Conf. in T.C.S., Aachen, LNCS 67, 1979.Google Scholar
  14. 14.
    Lehmann, D., Categories for fixpoint semantics, Theory of Computation Report No. 15, University of Warwick, 1976.Google Scholar
  15. 15.
    Lehmann, D., On the algebra of order, Mathematics Institute, Hebrew University, Jerusalem.Google Scholar
  16. 16.
    Lehmann, D. & M. Smyth, The algebraic specification of data types; a synthetic approach, Report No. 119, Dept. of Computer Studies, University of Leeds, 1978 (also to appear in Math. Syst. Theory).Google Scholar
  17. 17.
    Martin Löf, P., Constructive mathematics and computer programming, 6th Int. Congress for Logic, Methodology and Phil. of Science, Hannover, 1979.Google Scholar
  18. 18.
    Myhill, J. & J. Shepherdson, Effective operations on partial recursive functions, Zeitschr. f. math. Logik u. Grundl. d. Math., 1956.Google Scholar
  19. 19.
    Plotkin, G., A power-domain construction, SIAM J. Comput. 5 (1976), 452–487.Google Scholar
  20. 20.
    Rogers, H., Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.Google Scholar
  21. 21.
    Scott, D., Continuous lattices, Lecture Notes in Math. 274, Springer, 1974.Google Scholar
  22. 22.
    Scott, D., Data types as lattices, SIAM J. Comput. 5 (1976), 522–587.Google Scholar
  23. 23.
    Smyth, M., Effectively given domains, Theor. Comp. Sci. 5 (1977), 257–274.Google Scholar
  24. 24.
    Smyth, M., Power Domains, J. Comp. Syst. Sci. 16, (1978), 23–26.Google Scholar
  25. 25.
    Smyth, M., D. Phil Thesis, University of Oxford, 1978.Google Scholar
  26. 26.
    Smyth, M. & G. Plotkin, Category-theoretic solution of recursive domain equations, D.A.I. Report 60, University of Edinburgh, 1978.Google Scholar
  27. 27.
    Smyth, M., Computability in Categories, Theory of Computation Report, University of Warwick, 1979.Google Scholar
  28. 28.
    Tang, A., Recursion theory and descriptive set theory in effectively given T0 spaces, Ph.D. Thesis, Princeton University (1974).Google Scholar
  29. 29.
    Bergstra, J. & J. Tucker, Algebraic specifications of computable and semi-computable data structures, Dept. of Computer Science Report 1W115, Math. Cent., Amsterdam, 1979.Google Scholar
  30. 30.
    Wand, M., Fixed-point constructions in order-enriched categories, TR 23, Computer Science Dept., Indiana University, 1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • M. B. Smyth
    • 1
  1. 1.Dept. of Computer StudiesUniversity of LeedsLeedsEngland

Personalised recommendations