Power domains supporting recursion and failure

  • Reinhold Heckmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 581)


Following the program of Moggi, the semantics of a simple non-deterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle non-termination properly. Instead, a novel construction is proposed and investigated. It embodies both nondeterminism (choice and failure) and possible non-termination caused by recursion.


Algebraic Theory Neutral Element Functional Language Denotational Semantic Informal Reasoning 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Abr91]
    S. Abramsky. A domain equation for bisimulation. Information and Computation, 92:161–218, 1991.Google Scholar
  2. [AL91]
    A. Asperti and G. Longo. Categories, Types, and Structures. Foundations of Computing Series. The MIT Press, 1991.Google Scholar
  3. [CC84]
    W.F. Clocksin and C.S. Mellish. Programming in Prolog. Springer-Verlag, 1984.Google Scholar
  4. [Gun90]
    C.A. Gunter. Relating total and partial correctness interpretations of non-deterministic programs. In P. Hudak, editor, Principles of Programming Languages (POPL '90), pages 306–319. ACM, 1990.Google Scholar
  5. [Hec88]
    R. Heckmann. A functional language for the specification of complex tree transformations. In H. Ganzinger, editor, ESOP '88, pages 175–190. Lecture Notes in Computer Science 300, Springer-Verlag, 1988.Google Scholar
  6. [Hec90]
    R. Heckmann. Power Domain Constructions. PhD thesis, Universität des Saarlandes, 1990.Google Scholar
  7. [Hec91]
    R. Heckmann. Power domain constructions. Science of Computer Programming, 1991. to appear.Google Scholar
  8. [Hoo87]
    R. Hoofman. Powerdomains. Technical Report RUU-CS-87-23, Rijksuniversiteit Utrecht, November 1987.Google Scholar
  9. [HP79]
    M.C.B Hennessy and G.D. Plotkin. Full abstraction for a simple parallel programming language. In J. Becvar, editor, Foundations of Computer Science, pages 108–120. Lecture Notes in Computer Science 74, Springer-Verlag, 1979.Google Scholar
  10. [Law88]
    J.D. Lawson. The versatile continuous order. In Michael G. Main, A. Melton, Michael Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Language Semantics (MFPLS '87), pages 565–622. Lecture Notes in Computer Science 298, Springer-Verlag, 1988.Google Scholar
  11. [LS86]
    J. Lambek and P.J. Scott. Introduction to Higher Order Categorical Logic, volume 7 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1986.Google Scholar
  12. [Mac71]
    S. MacLane. Categories for the Working Mathematician. Springer-Verlag, 1971.Google Scholar
  13. [Mog89]
    E. Moggi. Computational lambda-calculus and monads. In 4th LICS Conference. IEEE, 1989.Google Scholar
  14. [Mog91a]
    E. Moggi. A modular approach to denotational semantics. In D.H. Pitt, P.-L. Curien, S. Abramsky, A.M. Pitts, A. Poigné, and D.E. Rydeheard, editors, Category Theory and Computer Science, pages 138–139. Lecture Notes in Computer Science 530, Springer-Verlag, 1991.Google Scholar
  15. [Mog91b]
    E. Moggi. Notions of computation and monads. Information and Computation, 93:55–92, 1991.Google Scholar
  16. [Plo76]
    G.D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5(3):452–487, 1976.CrossRefGoogle Scholar
  17. [Smy78]
    M.B. Smyth. Power domains. Journal of Computer and System Sciences, 16:23–36, 1978.Google Scholar
  18. [SP82]
    M.B. Smyth and G.D. Plotkin. The category-theoretic solution of recursive domain equations. SIAM Journal on Computing, 11:761–783, 1982.Google Scholar
  19. [Wad90]
    P. Wadler. Comprehending monads. In Symposium on Lisp and Functional Programming, pages 61–78. ACM, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Reinhold Heckmann
    • 1
  1. 1.FB 14 - Informatik Universität des SaarlandesSaarbrückenBundesrepublik Deutschland

Personalised recommendations