Optimizations of Bottom-Up Evaluation with Non-Ground Terms

Bottom-up evaluation of logic programs can be seen as an implementation of memoization. Memoization helps detect loops, avoid repeated computation when subgoals are generated repeatedly, and in conjunction with a fair search strategy, as in bottom-up evaluation, ensures that evaluation is complete. Programs that generate non-ground facts (i.e., facts containing universally quantiied variables) and also need memoization are important in several contexts such as the implementation of meta-interpreters, abstract interpretation and partial evaluation. Current bottom-up evaluation techniques (and other memoing techniques), while eecient for programs that generate only ground facts, are very ineecient for programs that generate non-ground facts. In this paper we present an eecient bottom-up evaluation technique for programs that generate non-ground facts. The technique includes a combination of a modiied Magic rewriting technique, and a run-time evaluation technique that incorporates several new optimizations. The technique maintains extra information with query and answer facts in order to speed upànswer-return' uniications. The technique has been implemented, and enables us to run some programs faster (asymptotically and practically) than using either Prolog or unoptimized bottom-up evaluation. The underlying ideas can also be used to adapt other memoing strategies (e.g., QSQR, Alexander Templates) with similar gains in eeciency. We also show that bottom-up evaluation can be implemented with a time cost that is within a log log factor of Prolog, (or a log factor using our simpler implementation) for all queries on deenite clause programs; conversely, there are programs where bottom-up evaluation is arbitrarily better than Prolog. These results provide important insight into the relation between bottom-up evaluation and top-down evaluation, and signiicantly extend earlier results on the subject. 0 This paper has an appendix containing details that may be useful to the referees. However, the paper is self-contained without the appendix and the appendix does not form a part of the paper.