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International Conference on Interactive Theorem Proving

ITP 2015: Interactive Theorem Proving pp 203–220Cite as

A Formalized Hierarchy of Probabilistic System Types

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9236))

Abstract

Numerous models of probabilistic systems are studied in the literature. Coalgebra has been used to classify them into system types and compare their expressiveness. In this work, we formalize the resulting hierarchy of probabilistic system types in Isabelle/HOL by modeling the semantics of the different systems as codatatypes. This approach yields simple and concise proofs, as bisimilarity coincides with equality for codatatypes. On the way, we develop libraries of bounded sets and discrete probability distributions and integrate them with the facility for (co)datatype definitions.

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Notes

  1. 1.

    Clearly, this discussion is somewhat esoteric, since in practice one barely is interested to look beyond countable sets. Still, we are interested in keeping the results as general as possible.

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Acknowledgment

We thank Tobias Nipkow for supporting this collaboration and Ana Sokolova for confirming our findings regarding Vardi systems. Jasmin Blanchette, Ondřej Kunčar, and anonymous reviewers helped to improve the presentation through numerous comments and offered stylistic advice. Hölzl is supported by the DFG project Verification of Probabilistic Models in Interactive Theorem Provers (grant Ni 491/15-1). Traytel is supported by the DFG program Program and Model Analysis (doctorate program 1480). The authors are listed alphabetically.

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Authors and Affiliations

  1. Fakultät Für Informatik, Technische Universität München, Munich, Germany

    Johannes Hölzl & Dmitriy Traytel

  2. Department of Computer Science, Institute of Information Security, ETH Zurich, Zurich, Switzerland

    Andreas Lochbihler

Authors
  1. Johannes Hölzl
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  2. Andreas Lochbihler
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  3. Dmitriy Traytel
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Corresponding authors

Correspondence to Johannes Hölzl , Andreas Lochbihler or Dmitriy Traytel .

Editor information

Editors and Affiliations

  1. Department of Informatics, King's College London, London, United Kingdom

    Christian Urban

  2. PLA University of Science and Technology, Nanjing, China

    Xingyuan Zhang

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Hölzl, J., Lochbihler, A., Traytel, D. (2015). A Formalized Hierarchy of Probabilistic System Types. In: Urban, C., Zhang, X. (eds) Interactive Theorem Proving. ITP 2015. Lecture Notes in Computer Science(), vol 9236. Springer, Cham. https://doi.org/10.1007/978-3-319-22102-1_13

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  • DOI: https://doi.org/10.1007/978-3-319-22102-1_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22101-4

  • Online ISBN: 978-3-319-22102-1

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