QRB-Domains and the Probabilistic Powerdomain

Details QRB-Domains and the Probabilistic Powerdomain QRB-Domains and the Probabilistic Powerdomain

2012-02-10

arxiv.org/abs/1202.2287v2

LMCS 8 (1:14) 2012

Computer Science

Programming Languages

32 pages, 7 figures. An extended abstract already appeared in Proc. 25th Annual IEEE Symposium on Logic in Computer Science (L

Scientific paper

10.2168/LMCS-8(1:14)2012

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 omega-QRB-domains. We show that they form a category omega-QRB with pleasing properties: omega-QRB is closed under the probabilistic powerdomain functor, under finite products, under taking bilimits of expanding sequences, under retracts, and even under so-called quasi-retracts. But... omega-QRB is not Cartesian closed. We conclude by showing that the QRB domains are just one half of an FS-domain, merely lacking control.

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