Optimizations of Bottom - Up Eval

Memoization, such as that performed by bottom-up evaluation, helps detect loops, avoid repeated computation when subgoals are generated repeatedly, and in conjunction with a fair search strategy, 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. Current bottom-up evaluation techniques (and other mem-oization techniques), are very ineecient for programs that generate facts containing large non-ground terms. We present an eecient bottom-up evaluation technique for programs that generate non-ground facts. We show that bottom-up evaluation can be implemented with a time cost that is within a log log factor of (a model of) Prolog evaluation, for all queries on deenite clause programs; conversely, there are programs where bottom-up evaluation is arbitrarily better than Prolog. These results signiicantly extend earlier results comparing bottom-up evaluation and top-down evaluation, An implementation of our technique enables us to run some programs faster (asymptotically and practically) than using either Prolog or unoptimized bottom-up evaluation.