Book section : Chapter
Quantitative information flow with Monads in Haskell
- Abstract:
- Monads are a popular feature of the programming language Haskell because they can model many different notions of computation in a uniform and purely functional way. Our particular interest here is the probability monad, which can be -- and has been -- used to synthesise models for probabilistic programming. Quantitative Information Flow, or QIF, arises when security is combined with probability, and concerns the measurement of the amount of information that 'leaks' from a probabilistic program's state to a (usually) hostile observer: that is, not 'whether' leaks occur but rather 'how much?' Recently it has been shown that QIF can be seen monadically, a 'lifting' of the probability monad so that programs become functions from distributions to distributions of distributions: the codomain is 'hyper distributions'. Haskell's support for monads therefore suggests a synthesis of an executable model for QIF. Here, we provide the first systematic and thorough account of doing that: using distributions of distributions to synthesise a model for Quantitative Information Flow in terms of monads in Haskell.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 382.7KB, Terms of use)
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- Publisher copy:
- 10.1017/9781108770750.013
- Publisher:
- Cambridge University Press
- Host title:
- Foundations of Probabilistic Programming
- Chapter number:
- 12
- Publication date:
- 2020-11-18
- DOI:
- EISBN:
- 9781108770750
- Language:
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English
- Keywords:
- Subtype:
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Chapter
- Pubs id:
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1087468
- Local pid:
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pubs:1087468
- Deposit date:
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2020-02-14
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- Copyright holder:
- Barthe et al.
- Copyright date:
- 2020
- Rights statement:
- © Gilles Barthe, Joost-Pieter Katoen and Alexandra Silva 2021. This work is in copyright. It is subject to statutory exceptions and to the provisions of relevant licensing agreements; with the exception of the Creative Commons version the link for which is provided, no reproduction of any part of this work may take place without the written permission of Cambridge University Press. An online version of this work is published at doi.org/10.1017/9781108770750 under a Creative Commons Open Access license CC-BY which permits re-use, distribution and reproduction in any medium for any purpose providing appropriate credit to the original work is given and any changes made are indicated.
- Notes:
- This chapter will appear in Foundations of Probabilistic Programming, published by Cambridge University Press.
- Licence:
- CC Attribution (CC BY)
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