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4 - On Probabilistic λ-Calculi

Published online by Cambridge University Press:  18 November 2020

By
Ugo Dal Lago
Edited by
Gilles Barthe ,
Joost-Pieter Katoen  and
Alexandra Silva
Gilles Barthe
Affiliation:
Max Planck Institute for Security and Privacy
Joost-Pieter Katoen
Affiliation:
RWTH Aachen University, Germany
Alexandra Silva
Affiliation:
University College London
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Summary

Church's λ-calculus has become a universally accepted model of pure functional programming, and its properties have been thoroughly scrutinised by the research community in the last 90 years. Many variations of it have been introduced for the sake of capturing programming with various forms of effects, thus going beyond pure functional programming. This chapter is meant to be a gentle introduction to a family of such calculi, namely probabilistic λ-calculi, in their two main variations: randomised λ-calculi and Bayesian λ-calculi. We focus our attention on the operational semantics, expressive power and termination properties of randomised λ-calculi, only giving some hints and references about denotational models and Bayesian λ-calculi.

Keywords

Probabilistic programminglambda calculussemanticstermination
Type
Chapter
Information
Foundations of Probabilistic Programming , pp. 121 - 144
Publisher: Cambridge University Press
Print publication year: 2020
Creative Commons
Creative Common License - CCCreative Common License - BY
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY 4.0 https://creativecommons.org/cclicenses/

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