Uni cation in Extensions of Shallow Equational Theories

We show that uni cation in certain extensions of shallow equational theories is decidable Our extensions generalize the known classes of shallow or standard equational theories In order to prove de cidability of uni cation in the extensions a class of Horn clause sets called sorted shallow equational theories is introduced This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories We show that satura tion under sorted superposition is e ective on sorted shallow equational theories So called semi linear equational theories can be e ectively trans formed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories