Linear Tabling Strategies and Optimizations

Recently, the iterative approach named linear tabling has received considerable attention because of its simplicity, ease of implementation, and good space efficiency. Linear tabling is a framework from which different methods can be derived based on the strategies used in handling looping subgoals. One decision concerns when answers are consumed and returned. This paper describes two strategies, namely, {it lazy} and {it eager} strategies, and compares them both qualitatively and quantitatively. The results indicate that, while the lazy strategy has good locality and is well suited for finding all solutions, the eager strategy is comparable in speed with the lazy strategy and is well suited for programs with cuts. Linear tabling relies on depth-first iterative deepening rather than suspension to compute fixpoints. Each cluster of inter-dependent subgoals as represented by a top-most looping subgoal is iteratively evaluated until no subgoal in it can produce any new answers. Naive re-evaluation of all looping subgoals, albeit simple, may be computationally unacceptable. In this paper, we also introduce semi-naive optimization, an effective technique employed in bottom-up evaluation of logic programs to avoid redundant joins of answers, into linear tabling. We give the conditions for the technique to be safe (i.e. sound and complete) and propose an optimization technique called {it early answer promotion} to enhance its effectiveness. Benchmarking in B-Prolog demonstrates that with this optimization linear tabling compares favorably well in speed with the state-of-the-art implementation of SLG.