An Algebraic Approach to Sharing Analysis of Logic Programs

This paper describes an algebraic approach to the sharing analysis of logic programs based on an abstract domain of set logic programs. Set logic programs are logic programs in which the terms are sets of variables and unification is based on an associative, commutative, and idempotent equality theory. We show that the proposed domain is isomorphic to the set-sharing domain of Jacobs and Langen and argue that there are good reasons to adopt our representation: (1) the abstract domain and the abstract operations defined are based on a theory for sets and set unification, resulting in a more intuitive approach to sharing analysis; (2) the abstract substitutions are like substitutions and can be applied to (abstract) atoms. This facilitates program analyses performed as abstract compilation. Finally (3) our representation makes explicit the “domain” of interest of an abstract substitution – which solves some technical problems in defining the domain of Jacobs and Langen.

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