Abstract
This paper gives a procedure for solving disequations modulo equational theories, and to decide existence of solutions. For this, we assume that the equational theory is specified by a confluent and constructor-based rewrite system, and that four additional restrictions are satisfied. The procedure represents the possibly infinite set of solutions thanks to a grammar, and decides existence of solutions thanks to an emptiness test. As a consequence, checking whether a linear equality is an inductive theorem is decidable, if assuming moreover sufficient completeness.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Antoy, R. Echahed, and M. Hanus. A Needed Narrowing Strategy. In Proceedings 21st ACM Symposium on Principle of Programming Languages, Portland, pages 268–279, 1994.
H. Comon. Disunification: a Survey. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson. MIT Press, 1991.
H. Comon. Complete Axiomatizations of some Quotient Term Algebras. Theoretical Computer Science, 118(2), 1993.
H. Comon, M. Haberstrau, and J.-P. Jouannaud. Syntacticness, Cycle-Syntacticness and Shallow Theories. Information and Computation, 111(1):154–191, 1994.
N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J. Van Leuven, editor, Handbook of Theoretical Computer Science. Elsevier Science Publishers, 1990.
M. Fernández. Narrowing Based Procedures for Equational Disunification. Applicable Algebra in Engineering Communication and Computing, 3:1–26, 1992.
E. Giovannetti, G. Levi, C. Moiso, and C. Palamidessi. Kernel LEAF: a Logic plus Functional Language. The Journal of Computer and System Sciences, 42(3):139–185, 1991.
J.-M. Hullot. Canonical Forms and Unification. In W. Bibel and R. Kowalski, editors, Proceedings 5th International Conference on Automated Deduction, Les Arcs (France), volume 87 of LNCS, pages 318–334. Springer-Verlag, 1980.
S. Limet and P. Réty. E-Unification by Means of Tree Tuple Synchronized Grammars. Discrete Mathematics and Theoritical Computer Science (http://www.chapmanhall.com/dm), 1:69–98, 1997.
J.J. Moreno-Navarro and M. Rodriguez-Artalejo. Logic Programming with Functions and Predicates:The Language BABEL. Journal of Logic Programming, 12(3):191–223, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag
About this paper
Cite this paper
Limet, S., Réty, P. (1998). Solving disequations modulo some class of rewrite systems. In: Nipkow, T. (eds) Rewriting Techniques and Applications. RTA 1998. Lecture Notes in Computer Science, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052365
Download citation
DOI: https://doi.org/10.1007/BFb0052365
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64301-2
Online ISBN: 978-3-540-69721-3
eBook Packages: Springer Book Archive