Jean Goubault-Larrecq - QRB-Domains and the Probabilistic Powerdomain

lmcs:956 - Logical Methods in Computer Science, February 29, 2012, Volume 8, Issue 1 -
QRB-Domains and the Probabilistic Powerdomain

Authors: Jean Goubault-Larrecq

    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.

    Volume: Volume 8, Issue 1
    Published on: February 29, 2012
    Accepted on: June 25, 2015
    Submitted on: January 27, 2011
    Keywords: Computer Science - Programming Languages,D.3.1, F.1.2, F.3.2

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