Extensional Denotational Semantics of Higher-Order Probabilistic Programs, Beyond the Discrete Case

04/13/2021

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by   Guillaume Geoffroy, et al.

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We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have been proposed before are not. It is organised as a model of propositional linear logic in which all the connectives have intuitive probabilistic interpretations. In addition, it has least fixed points for all maps, so it can interpret recursion.