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Automated verification of refinement laws

Hofner, P., Struth, G. and Sutcliffe, G. (2009) Automated verification of refinement laws. Annals of Mathematics and Artificial Intelligence, 55 (1-2). pp. 35-62. ISSN 1012-2443

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Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Springer. This is an author produced version of a paper subsequently published in Annals of Mathematics and Artificial Intelligence. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Refinement calculus; Kleene algebras; Automated deduction; Action systems
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 30 Oct 2009 11:23
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1007/s10472-009-9151-8
Status: Published
Publisher: Springer Verlag
Refereed: Yes
Identification Number: 10.1007/s10472-009-9151-8
URI: http://eprints.whiterose.ac.uk/id/eprint/10049

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