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A Generalised Union of Rely-Guarantee and Separation Logic Using Permission Algebras

Authors Vincent Jackson , Toby Murray , Christine Rizkallah

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Vincent Jackson
  • The University of Melbourne, Australia
Toby Murray
  • The University of Melbourne, Australia
Christine Rizkallah
  • The University of Melbourne, Australia

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Vincent Jackson, Toby Murray, and Christine Rizkallah. A Generalised Union of Rely-Guarantee and Separation Logic Using Permission Algebras. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITP.2024.23

Abstract

This paper describes GenRGSep, an Isabelle/HOL library for the development of RGSep logics using a general algebraic state model. In particular, we develop an algebraic state models based on resource algebras that assume neither the presence of unit resources or the cancellativity law. If a new resource model is required, its components need only be proven an instance of a permission algebra, and then they can be composed together using tuples and functions.
The proof of soundness is performed by Vafeiadis' operational soundness method. This method was originally formulated with respect to a concrete heap model. This paper adapts it to account for the absence of both units as well as the cancellativity law.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Concurrency
  • Theory of computation → Separation logic
Keywords
  • verification
  • concurrency
  • rely-guarantee
  • separation logic
  • resource algebras

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