… providing a new AC-unification algorithm which does not … Syntactic Theories and AC-Unification
In this section we recall some basic concepts about syntactic theories and ACunification…

… nominal AC-unification, we give the first formalisation of a first-order AC-unification algorithm.
… notation and recall the concept of a solution in nominal syntactic unification (Definition 20). …

… the constraint is usually interpreted in 7"(~') (syntactic equality), or in some quotient algebra
7"(~'… For example, if '=' is syntactic equality, by such a propagation step the previous equation …

… This chapter presents the unification in combination of equational theories and a new AC-unification
algorithm. Solving equations is a major problem in mathematics and computer …

… s and t, syntactic matching is the problem of finding a substitution \(\sigma \) such that \(\sigma
s = t\), and syntactic … The problem of syntactic unification can be generalised to consider an …

… of the computationally intensive steps in current AC unification algorithms: the extraction of
… we can check for equality modulo AC by checking for syntactic equality. ' It is well known that …

… The syntactic equality will be denoted by ~-. … Before we give the algorithm for elementary
AC-unification, we show how to efficiently solve systems of linear Diophantine equations. …

… As the main part of the paper, we propose an AC unification … AC unification algorithm for
all patterns is obtained by combining the algorithm for pure patterns and an AC unification …

… nominal AC-unification, we give the first formalisation of a first-order AC-unification algorithm.
… notation and recall the concept of a solution in nominal syntactic unification (Definition 20). …

… account for its destinct syntactic flavor. Typical questions that are … Recently another approach
to AC-unification based on the … AC-unification. The practical advantage of a special purpose …