Finite-Tree Analysis for Constraint Logic-Based Languages: The Complete Unabridged Version

TL;DR

This paper introduces a new data-flow analysis method for logic programming languages that use rational trees, enabling automatic detection of variables bound to finite terms to improve program analysis and correctness.

Contribution

It presents a novel abstract interpretation-based analysis that determines which program variables are guaranteed to be finite, addressing issues with infinite rational trees.

Findings

The analysis accurately identifies finite variables in logic programs.

It improves the safety and correctness of program analysis involving rational trees.

The method enhances the efficiency of logic language implementations.

Abstract

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can provide very efficient representations of grammars and other useful objects). Unfortunately, the use of infinite rational trees has problems. For instance, many of the built-in and library predicates are ill-defined for such trees and need to be supplemented by run-time checks whose cost may be significant. Moreover, some widely-used program analysis and manipulation techniques are correct only for those parts of programs working over finite trees. It is thus important to obtain, automatically, a knowledge of the program variables (the finite variables) that, at the program points of interest, will always be bound to finite terms. For these reasons, we propose here a new data-flow analysis, based on abstract interpretation, that captures such information.