Monoids over domains

Authors:
Michael Mislove
Affiliations:
Department of Mathematics, Tulane University, New Orleans, LA 70118
Venue:
Mathematical Structures in Computer Science
Year:
2006

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Abstract

In this paper, we describe three distinct monoids over domains, each with a commutative analog, which define bag domain monoids. Our results were inspired by work by Varacca (Varacca 2003), and they lead to a constructive approach to his Hoare indexed valuations over a continuous poset $P$. We use our constructive approach to describe an analog of the probabilistic power domain, and the laws that characterise it, that forms a Scott-closed subset of Varacca's construct. We call these the Hoare random variables over $P$.