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Soundness, idempotence and commutativity of set-sharing

Published online by Cambridge University Press:  25 March 2002

PATRICIA M. HILL ,
ROBERTO BAGNARA  and
ENEA ZAFFANELLA
PATRICIA M. HILL
Affiliation:
School of Computing, University of Leeds, Leeds, UK (e-mail: hill@comp.leeds.ac.uk)
ROBERTO BAGNARA
Affiliation:
Department of Mathematics, University of Parma, Parma, Italy (e-mail: bagnara@cs.unipr.it, zaffanella@cs.unipr.it)
ENEA ZAFFANELLA
Affiliation:
Department of Mathematics, University of Parma, Parma, Italy (e-mail: bagnara@cs.unipr.it, zaffanella@cs.unipr.it)
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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.

Keywords

Abstract interpretationlogic programmingoccurs-checkrational treesset-sharing
Type
Research Article
Information
Theory and Practice of Logic Programming , Volume 2 , Issue 2 , March 2002 , pp. 155 - 201
Copyright
© 2002 Cambridge University Press

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