Linear tabling strategies and optimizations

Abstract

Recently there has been a growing interest of research in tabling in the logic programming community because of its usefulness in a variety of application domains including program analysis, parsing, deductive databases, theorem proving, model checking, and logic-based probabilistic learning. The main idea of tabling is to memorize the answers to some subgoals and use the answers to resolve subsequent variant subgoals. Early resolution mechanisms proposed for tabling such as OLDT and SLG rely on suspension and resumption of subgoals to compute fixpoints. 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.

Optimal placement of valves in a water distribution network with CLP(FD)

“…In fact, there exist a library for graph algorithms also in SICStus, while in B-Prolog the table mode (Warren 1992;Zhou et al 2008) lets one easily implement efficient graph predicates. Unluckily, the syntax of ECL i PS e and SICStus/B-Prolog is different, although similar; for example, although both ECL i PS e (Schimpf 2002) and B-Prolog (Zhou 2011) support logical loops, they adopt a different syntax.…”

A Tabled Prolog Program for Solving Sokoban

“…B-Prolog is a tabled Prolog system that is based on linear tabling [19], allows variant subgoals to share answers, and uses the local strategy [9] (also called lazy strategy [19]) to return answers. In B-Prolog, tabled predicates are declared explicitly by declarations in the following form:…”

Efficient tabling of structured data with enhanced hash-consing

“…Tabling, as provided in logic programming systems such as B-Prolog (Zhou et al 2008), XSB (Swift and Warren 2012), YAP (Santos Costa et al 2012), and Mercury (Somogyi and Sagonas 2006), has been shown to be a viable declarative language construct for describing dynamic programming solutions for various kinds of realworld applications, ranging from program analysis, parsing, deductive databases, theorem proving, model checking, to logic-based probabilistic learning. The main idea of tabling is to memorize the answers to subgoals in a table area and use the answers to resolve their variant or subsumed descendants.…”