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The geometry of Bayesian programming

Published online by Cambridge University Press:  07 December 2021

Ugo Dal Lago  and
Naohiko Hoshino Open the ORCID record for Naohiko Hoshino [Opens in a new window]
Ugo Dal Lago*
Affiliation:
Department of Computer Science and Engineering, University of Bologna, Bologna, Italy
Naohiko Hoshino
Affiliation:
Department of Computer and Information Sciences, Sojo University, Kumamoto, Japan
*
*Corresponding author. Email: ugo.dallago@unibo.it
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Abstract

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We give two geometry of interaction models for a typed λ-calculus with recursion endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. The models are based on the category of measurable spaces and partial measurable functions, and the category of measurable spaces and s-finite kernels, respectively. The former is proved adequate with respect to both a distribution-based and a sampling-based operational semantics, while the latter is proved adequate with respect to a sampling-based operational semantics.

Keywords

Probabilistic lambda-calculusconditioningBayesian programminggeometry of interaction
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Issue 6 , June 2021 , pp. 633 - 681
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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