International Conference on Interactive Theorem Proving

ITP 2015: Interactive Theorem Proving pp 203-220 | Cite as

A Formalized Hierarchy of Probabilistic System Types

Proof Pearl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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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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