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Mathematical Structures in Computer Science (2006), 16: 87-113 Cambridge University Press
Copyright © 2006 Cambridge University Press
doi:10.1017/S0960129505005074
Published online by Cambridge University Press 21 Feb 2006

Paper

Distributing probability over non-determinism

DANIELE VARACCA a1 1 and GLYNN WINSKEL a2
a1 Department of Computing, Imperial College London, London, U.K.
a2 Computer Laboratory, Cambridge University, Cambridge, U.K.

Article author query
varacca d   [Google Scholar] 
winskel g   [Google Scholar] 
 

Abstract

We study the combination of probability and non-determinism from a categorical point of view. In category theory, non-determinism and probability are represented by suitable monads. However, these two monads do not combine well as they are. To overcome this problem, we introduce the notion of indexed valuations. This notion is used to define a new monad that can be combined with the usual non-deterministic monad via a categorical distributive law. We give an equational characterisation of our construction. We discuss the computational meaning of indexed valuations, and we show how they can be used by giving a denotational semantics of a simple imperative language.

(Received January 18 2005)
(Revised October 25 2005)


Footnotes

1 This work was carried out while the first author was a Ph.D. student at BRICS, Aarhus, Denmark.


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