Abstract
We show the equivalence of several different axiomatizations of the notion of (abstract) probabilistic domain in the category of dcpo's and continuous functions. The axiomatization with the richest set of operations provides probabilistic selection among a finite number of possibilities with arbitrary probabilities, whereas the poorest one has binary choice with equal probabilities as the only operation. The remaining theories lie in between; one of them is the theory of binary choice by Graham [1].
Keywords
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.
References
S.K. Graham. Closure properties of a probabilistic domain construction. In Michael G. Main, A. Melton, Michael Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Language Semantics (MFPLS '87), pages 213–233. Lecture Notes in Computer Science 298, Springer-Verlag, 1988.
R. Heckmann. Product operations in strong monads. In G.L. Burn, S.J. Gay, and M.D. Ryan, editors, Proceedings of the First Imperial College, Department of Computing, Workshop on Theory and Formal Methods, Workshops in Computing, pages 159–170. Springer-Verlag, 1993.
C.J. Jones. Probabilistic Non-Determinism. PhD thesis, Univ. of Edinburgh, 1990.
C.J. Jones and G.D. Plotkin. A probabilistic powerdomain of evaluations. In LICS '89, pages 186–195. IEEE Computer Society Press, 1989.
E. Moggi. Computational lambda-calculus and monads. In 4th LICS Conference, pages 14–23. IEEE, 1989.
E. Moggi. Notions of computation and monads. Information and Computation, 93:55–92, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heckmann, R. (1994). Probabilistic domains. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017479
Download citation
DOI: https://doi.org/10.1007/BFb0017479
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57879-6
Online ISBN: 978-3-540-48373-1
eBook Packages: Springer Book Archive