Advertisement

A universal domain technique for profinite posets

  • Carl A. Gunter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 194)

Abstract

We introduce a category of what we call profinite domains. This category of domains differs from most of the familiar ones in having a categorical coproduct as well as being cartesian closed. Study of these domains is carried out through the use of an equivalent category of pre-orders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous functors. Necessary conditions for the existence of such solutions are also given and used to derive results about solutions of some important equations. A new universal bounded complete domain is also demonstrated using a functor which has bounded complete domains as its fixed points.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gunter, C. 1985 Profinite Solutions for Recursive Domain Equations. Doctoral Dissertation, University of Wisconsin, Madison, 1985, 181 pp.Google Scholar
  2. Kamimura, T. and Tang, A. 1984 Finitely Continuous Posets. Technical Report, no. TR-84-1, University of Kansas, 1984, 26 pp.Google Scholar
  3. Lambek, J. and Scott, P.J. 1984 Introduction to Higher-Order Categorical Logic Pre-print, 1984, 200+ pp.Google Scholar
  4. MacQueen, D., Plotkin, G. D. and Sethi, R. 1984 An ideal model for recursive polymorhpic types. In: Eleventh Symposium on Principles of Programming Languages, edited by K. Kennedy. Association for Computing Machinery, 1984, pp. 165–174.Google Scholar
  5. 1976 A powerdomain construction. SIAM Journal of Computing, vol. 5 (1976), pp. 452–487.CrossRefGoogle Scholar
  6. 1978 T w as a universal domain. Journal of Computer System Sciences, vol. 17 (1978b), pp.209–236.CrossRefGoogle Scholar
  7. 1972 Continuous Lattices. In: Toposes, Algebraic Geometry and Logic, edited by F. W. Lawvere. Lecture Notes in Mathematics, vol. 274, Springer-Verlag, 1972, pp. 97–136.Google Scholar
  8. 1976 Data types as lattices. SIAM Journal of Computing, vol. 5 (1976), pp. 522–587.CrossRefGoogle Scholar
  9. Scott, D. S. 1981a Lectures on a mathematical theory of computation. Technical Report, no. PRG-19, Oxford University Computing Laboratory, 1981a, 148 pp.Google Scholar
  10. Scott, D. S. 1981b Some ordered sets in computer science. In: Ordered Sets, edited by I. Rival. D. Reidel Publishing Company, 1981b, pp. 677–718.Google Scholar
  11. 1982 Domains for denotational semantics. In: ICALP 82, edited by M. Nielsen, E. M. Schmidt. Lecture Notes in Computer Science, vol. 140, Springer-Verlag, 1982, pp. 577–613.Google Scholar
  12. Smyth, M. B. 1983 The largest cartesian closed category of domains. Theoretical Computer Science, vol. 27 (1983), pp. 109–119.CrossRefGoogle Scholar
  13. Stoy, J. E. 1977 Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. M.I.T. Press, 1977, 414 pp.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Carl A. Gunter
    • 1
  1. 1.Department of Computer ScienceCarnegie-Mellon UniversityPittsburgh

Personalised recommendations