| Summary: | 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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