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Conference Paper

Unification in Extensions of Shallow Equational Theories

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44688

Jacquemard,  Florent
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44784

Meyer,  Christoph
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45719

Weidenbach,  Christoph
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Jacquemard, F., Meyer, C., & Weidenbach, C. (1998). Unification in Extensions of Shallow Equational Theories. In T. Nipkow (Ed.), Proceedings of the 9th International Conference on Rewriting Techniques and Applications (RTA-98) (pp. 76-90). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-38A7-2
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.