Probabilistic coherence spaces as a model of higher-order probabilistic computation

Authors:
Vincent Danos;Thomas Ehrhard
Affiliations:
Preuves, Programmes et Systèmes, UMR 7126 -- CNRS, Université Paris Diderot, Paris 7, France and School of Informatics, University of Edinburgh, United Kingdom;Preuves, Programmes et Systèmes, UMR 7126 -- CNRS, Université Paris Diderot, Paris 7, France
Venue:
Information and Computation
Year:
2011

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Abstract

We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.