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Journal of Logic and Computation Advance Access originally published online on August 6, 2007
Journal of Logic and Computation 2007 17(4):807-841; doi:10.1093/logcom/exm030
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

A Structural Proof of the Soundness of Rely/guarantee Rules

Joey W. Coleman and Cliff B. Jones

School of Computing Science, Newcastle University, NE1 7RU, UK. E-mail: j.w.coleman, cliff.jones{at}ncl.ac.uk


  Abstract

Various forms of rely/guarantee conditions have been used to record and reason about interference in ways that provide compositional development methods for concurrent programs. This article illustrates such a set of rules and proves their soundness. The underlying concurrent language allows fine-grained interleaving and nested concurrency; it is defined by an operational semantics; the proof that the rely/guarantee rules are consistent with that semantics (including termination) is by a structural induction. A key lemma which relates the states which can arise from the extra interference that results from taking a portion of the program out of context makes it possible to do the proofs without having to perform induction over the computation history. This lemma also offers a way to think about expressibility issues around auxiliary variables in rely/guarantee conditions.

Keywords: Rely/guarantee reasoning; structural operational semantics; soundness; structural induction; concurrency


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