Linear Tabling Strategies and Optimizations

TL;DR

This paper explores linear tabling strategies in logic programming, comparing lazy and eager approaches, and introduces semi-naive optimization and early answer promotion to improve efficiency, demonstrating competitive performance with existing methods.

Contribution

It introduces semi-naive optimization and early answer promotion for linear tabling, enhancing efficiency and providing a comprehensive comparison of lazy and eager strategies.

Findings

Lazy strategy has good locality and finds all solutions efficiently.

Eager strategy is comparable in speed and better for programs with cuts.

Optimizations improve linear tabling's performance to rival SLG implementations.

Abstract

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.