[an error occurred while processing this directive]
[an error occurred while processing this directive]
|
|
|
Klaus Keimel Department of Mathematics, Darmstadt University of Technology, Darmstadt, Germany |
|
For the purposes of denotational semantics, Dana Scott has introduced the notion of a semantic domain (see [1]). These are ordered sets which are directed complete and in which every object can be approximated from below by elements of finite type. The order is supposed to model the increase of information content, the elements of finite type should represent objects computable in finite time, and the directed completeness assures the presence of ideal objects but still finitarily approximable.
Each construct in a programming language asks for a construction on semantic domains which models this construct. Non-determinism - like nondeterminstic choice - is modelled by sets of possible results. It is mathematically challenging that the constructions on semantic domains should remain within the same category.
Probabilistic features - like probabilistic choice - are modelled by the probabilistic power domain.
If both kinds of non-determinism occur (see [2]), there is a need for a mixed power domain. After introducing semantic domains, we will present an approach to this mixed power domain based on [3], and we will illustrate it by giving a semantics for the toy language considered in [2].
Dr. Keimel received the Ph. D. from the University of Tuebingen, Germany in 1967 and the Doictorat d'Etat in 1970 from the Faculte des Sciences, in Paris in 1970. Since 1971 he has been at the Darmstadt University of Technology. His research interests are: Ordered and Topological Algebra, Domain Theory, Mathematical Foundations of Computer Science and is the co-author of a recent book on "Continuous Lattices and Domains", Cambridge University Press 2003. [an error occurred while processing this directive]