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Elementary Probability Theory in the Eindhoven Style

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Mathematics of Program Construction (MPC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7342))

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Abstract

We extend the Eindhoven quantifier notation to elementary probability theory by adding “distribution comprehensions” to it.

Even elementary theories can be used in complicated ways, and this occurs especially when reasoning about computer programs: an instance of this is the multi-level probabilistic structures that arise in probabilistic semantics for security.

Our exemplary case study in this article is therefore the probabilistic reasoning associated with a quantitative noninterference semantics based on Hidden Markov Models of computation. But we believe the proposal here will be more generally applicable than that, and so we also revisit a number of popular puzzles, to illustrate the new notation’s wider utility.

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Author information

Authors and Affiliations

  1. University of New South Wales, NSW, 2052, Australia

    Carroll Morgan

Authors
  1. Carroll Morgan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, 28660, Boadilla del Monte, Madrid, Spain

    Pablo Nogueira

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Morgan, C. (2012). Elementary Probability Theory in the Eindhoven Style. In: Gibbons, J., Nogueira, P. (eds) Mathematics of Program Construction. MPC 2012. Lecture Notes in Computer Science, vol 7342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31113-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-31113-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31112-3

  • Online ISBN: 978-3-642-31113-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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