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, lazy and 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 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.
The Copying Approach to Tabling, abbrv. CAT, is an alternative to SLG-WAM and based on total copying of the areas that the SLG-WAM freezes to preserve execution states of suspended computations. The disadvantage of CAT as pointed out in a previous paper is that in the worst case, CAT must copy so much that it becomes arbitrarily worse than the SLG-WAM. Remedies to this problem have been studied, but a completely satisfactory solution has not emerged. Here, a hybrid approach is presented: CHAT. Its design was guided by the requirement that for non-tabled (i.e. Prolog) execution no changes to the underlying WAM engine need to be made. CHAT combines certain features of the SLG-WAM with features of CAT, but also introduces a technique for freezing WAM stacks without the use of the SLG-WAM's freeze registers that is of independent interest. Empirical results indicate that CHAT is a better choice for implementing the control of tabling than SLG-WAM or CAT. However, programs with arbitrarily worse behaviour exist.