Efficient Groundness Analysis in Prolog

TL;DR

This paper presents an efficient Prolog implementation of groundness analysis using a new representation of definite Boolean functions, leading to scalable and fast analysis without the need for widening.

Contribution

It introduces a novel representation and algorithms for definite Boolean functions, optimizing groundness analysis in Prolog for improved efficiency and scalability.

Findings

Analysis runs efficiently on large benchmarks

No widening needed for convergence in large cases

Quadratic-time entailment checking enhances performance

Abstract

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of groundness analysis are investigated, focusing on the domain of definite Boolean functions, Def. The systematic design of the representation of an abstract domain is discussed in relation to its impact on the algorithmic complexity of the domain operations; the most frequently called operations should be the most lightweight. This methodology is applied to Def, resulting in a new representation, together with new algorithms for its domain operations utilising previously unexploited properties of Def -- for instance, quadratic-time entailment checking. The iteration strategy driving the analysis is also discussed and a simple, but very effective, optimisation of induced magic is described. The analysis can be implemented straightforwardly in Prolog and the use of a non-ground representation results in an efficient, scalable tool which does not require widening to be invoked, even on the largest benchmarks. An extensive experimental evaluation is given