Optimal matching for sharing and linearity analysis

TL;DR

This paper develops optimal abstract matching operators for sharing and linearity analysis in logic programs, enhancing static analysis precision through domain-specific operator derivation.

Contribution

It introduces an optimal matching operator for the domain ShLin^ω, applicable to various sharing and linearity analysis domains, improving static analysis accuracy.

Findings

Provides an optimal matching operator for ShLin^ω domain

Enables derivation of optimal operators for related domains

Improves precision of static analysis in logic programming

Abstract

Static analysis of logic programs by abstract interpretation requires designing abstract operators which mimic the concrete ones, such as unification, renaming and projection. In the case of goal-driven analysis, where goal-dependent semantics are used, we also need a backward-unification operator, typically implemented through matching. In this paper we study the problem of deriving optimal abstract matching operators for sharing and linearity properties. We provide an optimal operator for matching in the domain ${\mathtt{ShLin}^{\omega}}$, which can be easily instantiated to derive optimal operators for the domains ${\mathtt{ShLin}^{2}}$ by Andy King and the reduced product $\mathtt{Sharing} \times \mathtt{Lin}$.