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An Operational Semantics in Isabelle/HOL-CSP

Authors Benoît Ballenghien , Burkhart Wolff

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Author Details

Benoît Ballenghien
  • Laboratoire Méthodes Formelles, University Paris-Saclay, France
Burkhart Wolff
  • Laboratoire Méthodes Formelles, University Paris-Saclay, France

Funding

  • Ballenghien, Benoît: Labex DigiCosme.

Acknowledgements

We would like to thank Catherine Dubois for her remarks on earliest versions of this paper. The present version has been generated and deeply checked with Isabelle/DOF [Brucker and Wolff, 2022; Achim D. Brucker et al., 2023].

Cite As Get BibTex

Benoît Ballenghien and Burkhart Wolff. An Operational Semantics in Isabelle/HOL-CSP. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITP.2024.7

Abstract

The theory of Communicating Sequential Processes going back to Hoare and Roscoe is still today a reference model for concurrency. In the fairly rich literature, several versions of operational semantics have been discussed, which should be consistent with the denotational one.
This work is based on Isabelle/HOL-CSP 2.0, a shallow embedding of the failure-divergence model of denotational semantics proposed by Hoare, Roscoe and Brookes in the eighties. In several ways, HOL-CSP is actually an extension of the original setting in the sense that it admits higher-order processes and infinite alphabets. 
In this paper, we present a construction and formal equivalence proofs between operational CSP semantics and the underlying denotational failure-divergence semantics. The construction is based on a definition of the operational transition operator P ⇝e P’ basically via the After operator and the classical failure-divergence refinement. 
Several choices are discussed to formally derive the operational semantics leading to subtle differences. The derived operational semantics for symbolic Labelled Transition Systems (LTSs) can be potentially used for certifications of model-checker logs as well as combined proof techniques.

Subject Classification

ACM Subject Classification
  • Theory of computation → Higher order logic
  • Theory of computation → Semantics and reasoning
  • General and reference → Verification
Keywords
  • Process-Algebra
  • Semantics
  • Concurrency
  • Computational Models
  • Theorem Proving
  • Isabelle/HOL

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Supplementary Materials

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