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On the interaction between sharing and linearity

Published online by Cambridge University Press:  24 September 2009

GIANLUCA AMATO  and
FRANCESCA SCOZZARI
GIANLUCA AMATO
Affiliation:
Dipartimento di Science, Università “G. d'Annunzio” di Chieti–Pescara, Pescara, Italy (e-mail: [email protected], [email protected])
FRANCESCA SCOZZARI
Affiliation:
Dipartimento di Science, Università “G. d'Annunzio” di Chieti–Pescara, Pescara, Italy (e-mail: [email protected], [email protected])
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Abstract

In the analysis of logic programs, abstract domains for detecting sharing and linearity information are widely used. Devising abstract unification algorithms for such domains has proved to be rather hard. At the moment, the available algorithms are correct but not optimal; i.e., they cannot fully exploit the information conveyed by the abstract domains. In this paper, we define a new (infinite) domain ShLinω which can be thought of as a general framework from which other domains can be easily derived by abstraction. ShLinω makes the interaction between sharing and linearity explicit. We provide a constructive characterization of the optimal abstract unification operator on ShLinω, and we lift it to two well-known abstractions of ShLinω, namely, to the classical Sharing × Lin abstract domain and to the more precise ShLin2 abstract domain by Andy King. In the case of single-binding substitutions, we obtain optimal abstract unification algorithms for such domains.

Keywords

static analysisabstract interpretationsharinglinearityunification
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 10 , Issue 1 , January 2010 , pp. 49 - 112
Copyright
Copyright © Cambridge University Press 2009

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