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Soundness, idempotence and commutativity of set-sharing

Hill, P.M., Bagnara, R. and Zaffanella, E. (2002) Soundness, idempotence and commutativity of set-sharing. Theory and Practice of Logic Programming, 02 (02). pp. 155-201. ISSN 1471-0684

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Abstract

It is important that practical data-flow analyzers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study.

In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the soundness of Sharing assume the occurs-check. This paper provides a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. Results for soundness, idempotence and commutativity for abstract unification using this abstraction function are proven.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 Cambridge University Press.
Keywords: abstract interpretation, logic programming, occurs-check, rational trees, set-sharing
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 12 May 2006
Last Modified: 08 Feb 2013 17:06
Published Version: http://dx.doi.org/10.1017/S1471068401001338
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: DOI:10.1017/S1471068401001338
URI: http://eprints.whiterose.ac.uk/id/eprint/1199

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