Unification in Extensions of Shallow Equational Theories

Florent Jacquemard 1 Christoph Meyer Christoph Weidenbach
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We show that unification 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 decidability of unification 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 saturation under sorted superposition is effective on sorted shallow equational theories. So called semi-linear equational theories can be effectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.
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https://hal.inria.fr/inria-00098740
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Submitted on : Tuesday, September 26, 2006 - 8:22:19 AM
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Florent Jacquemard, Christoph Meyer, Christoph Weidenbach. Unification in Extensions of Shallow Equational Theories. [Intern report] 98-R-387 || jacquemard98a, 1998, 33 p. ⟨inria-00098740⟩

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