Freeness Analysis for Logic Programs - And Correctness?

Several proposals for computing freeness information for logic. programs ha.ve been put forward in recent literature. The availability of such information has proven useful in a variety of applications, including parallelization of Prolog programs, optimizations in Prolog compilers, as well as for improving the precision of other analyses. While these proposals have illustrated the importance of such analyses, they lack formal justification. Moreover, several have been found incorrect. This paper introduces a novel domain of abstract equation systems describing possible sharing and definite freeness of terms in a system of equations. A simple and intuitive abstract unification algorithm is presented, providing the core of a correct and precise sharing and freeness analysis for logic programs. Our contribution is not only a correct algorithm, but perhaps primarily, the systematic approach in which it is derived by mimicking each step in a suitable concrete unification algorithm. Consequently, the abstract algorithm is intuitive as it resembles the concrete algorithm. It is easy to justify as the proof of correctness boils down to showing that each step in the concrete algorithm is mimicked by a corresponding step in the abstract algorithm. Finally, it is precise as each step mimics only those situations which can arise in the concrete algorithm. ·This work was funded in part by the ESPRIT project 5246 PRINCE and by "Prog. Fin. Sistemi informatid e Calcolo Parallelo' of CNR, grant 0.91.00026.69. t Dept. of Computer Science, KU Leuven, Belgium. {codi8h,aaurice llcs .kul.euven. ae. be 'Dept. of Computing Science, TUE, Eindhoven, The Netherlands. v8jnddlinfo. win. tue.nl SDip. di Mat. Pura e App., Universiti di Padova, Italy. filelpdaat1.unipd.it 'Supported by the Belgian National Fund for Scientific Research.

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