A correct, precise and efficient integration of set-sharing, freeness and linearity for the analysis of finite and rational tree languages

TL;DR

This paper introduces a novel, correct, and efficient method for combining set-sharing, freeness, and linearity information to improve the precision and efficiency of logic program analysis for finite and rational trees.

Contribution

It presents a new combination of abstract domains with an improved unification operator, ensuring correctness and polynomial-time implementation.

Findings

The analysis is correct for finite and rational trees.

Redundant information can be eliminated without loss of precision.

The approach achieves polynomial-time complexity.

Abstract

It is well-known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in (Bagnara et al. 2002; Zaffanella et al. 2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties.