A general framework for variable aliasing: Towards optimal operators for sharing properties

Abstract

We face the problem of devising optimal unification operators for sharing and linearity analysis of logic programs by abstract interpretation. We propose a new (infinite) domain ShLinω which can be thought of as a general framework from which other domains can be easily derived by abstraction. The advantage is that ShLinω is endowed with very elegant and optimal abstract operators for unification and matching, based on a new concept of sharing graph which plays the same role of alternating paths for pair sharing analysis. We also provide an alternative, purely algebraic description of sharing graphs. Starting from the results for ShLinω, we derive optimal abstract operators for two well-known domains which combine sharing and linearity: ShLin2 by Andy King and the classic Sharing x Lin. © Springer-Verlag Berlin Heidelberg 2003.