Lawson-compactness for the Probabilistic Powerdomain
نویسنده
چکیده
منابع مشابه
The troublesome probabilistic powerdomain
In [12] it is shown that the probabilistic powerdomain of a continuous domain is again continuous. The category of continuous domains, however, is not cartesian closed, and one has to look at subcategories such as RB, the retracts of bifinite domains. [8] offers a proof that the probabilistic powerdomain construction can be restricted to RB. In this paper, we give a counterexample to Graham’s p...
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We show that the first author’s QRB-domains coincide with Li and Xu’s QFS-domains, and also with Lawson-compact quasi-continuous dcpos, with stably-compact locally finitary compact spaces, with sober QFSspaces, and with sober QRB-spaces. The first three coincidences were discovered independently by Lawson and Xi. The equivalence with sober QFS-spaces is then applied to give a novel, direct proo...
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For the semantics of probabilistic features in programming mainly two approaches are used for building models. One is the Giry monad of Borel probability measures over metric spaces, and the other is Jones’ probabilistic powerdomain monad [6] over dcpos (directed complete partial orders). This paper places itself in the second domain theoretical tradition. The probabilistic powerdomain monad is...
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Is there any cartesian-closed category of continuous domains that would be closed under Jones and Plotkin’s probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for quasi-continuous dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the !QRB-dom...
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