Variant-based Equational Unification under Constructor Symbols

TL;DR

This paper enhances variant-based equational unification algorithms by incorporating constructor symbols, leading to significant speed improvements in solving unification problems.

Contribution

It introduces a novel integration of constructor symbols into variant-based unification, optimizing the process and reducing unnecessary computations.

Findings

Impressive speedup in unification tasks

Effective handling of constructor symbols

Improved efficiency in positive and negative unification problems

Abstract

Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the variants of a term is available in the most recent version of Maude, version 3.0, which provides quite sophisticated unification features. A variant of a term t is a pair consisting of a substitution sigma and the canonical form of tsigma. Variant-based unification is decidable when the equational theory satisfies the finite variant property. However, this unification procedure does not take into account constructor symbols and, thus, may compute many more unifiers than the necessary or may not be able to stop immediately. In this paper, we integrate the notion of constructor symbol into the variant-based unification algorithm. Our experiments on positive and negative unification problems show an impressive speedup.