Top-down and Bottom-up Evaluation Procedurally Integrated

TL;DR

This paper presents an integrated approach combining top-down and bottom-up evaluation methods in logic programming, enabling more declarative and efficient Prolog programs through variant and subsumptive tabling.

Contribution

It introduces a procedural integration of top-down and bottom-up evaluation in logic programming using variant and subsumptive tabling with abstraction.

Findings

Enables fully declarative expression of programs previously requiring procedural features

Improves efficiency of logic program evaluation through integrated tabling mechanisms

Demonstrates practical benefits in Prolog program execution

Abstract

This paper describes how XSB combines top-down and bottom-up computation through the mechanisms of variant tabling and subsumptive tabling with abstraction, respectively. It is well known that top-down evaluation of logical rules in Prolog has a procedural interpretation as recursive procedure invocation (Kowalski 1986). Tabling adds the intuition of short-circuiting redundant computations (Warren 1992) .This paper shows how to introduce into tabled logic program evaluation a bottom-up component, whose procedural intuition is the initialization of a data structure, in which a relation is initially computed and filled, on first demand, and then used throughout the remainder of a larger computation for efficient lookup. This allows many Prolog programs to be expressed fully declaratively, programs which formerly required procedural features, such as assert, to be made efficient. This paper is under consideration for acceptance in "Theory and Practice of Logic Programming (TPLP)".