A Formalized Hierarchy of Probabilistic System Types

Proof Pearl
  • Johannes HölzlEmail author
  • Andreas LochbihlerEmail author
  • Dmitriy TraytelEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9236)


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.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Fakultät Für InformatikTechnische Universität MünchenMunichGermany
  2. 2.Department of Computer Science, Institute of Information SecurityETH ZurichZurichSwitzerland

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