Abstract
In the context of the executable specification language OBJ3, an order-sorted completion procedure is implemented, providing automatically convergent specifications from user-given ones. This feature is of first importance to ensure unambiguity and termination of the rewriting execution process. We describe here how we specified a modular completion design in terms of inference rules and control language, using OBJ3 itself. On another hand, the specific problems encountered to integrate a completion process in an already reductionoriented environment are pointed out.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
L. Bachmair and N. Dershowitz. Completion for rewriting modulo a congruence. In Proceedings 2nd Conference on Rewriting Techniques and Applications, Bordeaux (France), volume 256 of Lecture Notes in Computer Science, pages 192–203, Bordeaux (France), May 1987. Springer-Verlag.
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1 & 2):69–116, 1987.
R. Forgaard and J. Guttag. Reve: A term rewriting system generator with failure-resistant Knuth-Bendix. Technical report, MIT-LCS, 1984.
H. Ganzinger and R. Giegerich. A note on termination in combinations of heterogeneous term rewriting systems. Bulletin of European Association for Theoretical Computer Science, 31, February 1987.
I. Gnaedig, C. Kirchner, and H. Kirchner. Equational completion in order-sorted algebras. In M. Dauchet and M. Nivat, editors, Proceedings of the 13th Colloquium on Trees in Algebra and Programming, volume 299 of Lecture Notes in Computer Science, pages 165–184. Springer-Verlag, 1988.
I. Gnaedig, C. Kirchner, and H. Kirchner. Equational completion in order-sorted algebras. Theoretical Computer Science, 72:169–202, 1990.
J.A. Goguen and J. Meseguer. Order-sorted algebra I: Partial and overloaded operations, errors and inheritance. Technical report, SRI International, Computer Science Lab, 1988. Given as lecture at a Seminar on Types, Carnegie-Mellon University, June 1983.
J.A. Goguen and T. Winkler. Introducing OBJ3. Technical Report SRI-CSL-88-9, SRI International, 333, Ravenswood Ave., Menlo Park, CA 94025, August 1988.
G. Huet and D. Oppen. Equations and rewrite rules: A survey. In R.V. Book, editor, Formal Language Theory: Perspectives and Open Problems, pages 349–405. Academic Press, New York, 1980.
S. Kamin and J.-J. Lévy. Attempts for generalizing the recursive path ordering. Inria, Rocquencourt, 1982.
C. Kirchner, H. Kirchner, and J. Meseguer. Operational semantics of OBJ-3. In Proceedings of 15th International Colloquium on Automata, Languages and Programming, volume 317 of Lecture Notes in Computer Science, pages 287–301. Springer-Verlag, 1988.
P. Lescanne. Computer experiments with the REVE term rewriting systems generator. In Proceedings of 10th ACM Symposium on Principles of Programming Languages, pages 99–108. Association for Computing Machinery, 1983.
P. Lescanne. Implementation of completion by transition rules + control: ORME. In H. Kirchner and W. Wechler, editors, Proceedings 2nd International Workshop on Algebraic and Logic Programming, Nancy (France), volume 463 of Lecture Notes in Computer Science, pages 262–269. Springer-Verlag, 1990.
M. Rusinowitch. On termination of the direct sum of term rewriting systems. Information Processing Letters, 26(2):65–7G, 1987.
Y. Toyama, J.W. Klop, and H.P. Barendregt. Termination for the direct sum of left-linear term rewriting systems. In N. Dershowitz, editor, Proceedings 3rd Conference on Rewriting Techniques and Applications, Chapel Hill (North Carolina, USA), volume 355 of Lecture Notes in Computer Science, pages 477–491. Springer-Verlag, April 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gnaedig, I. (1992). ELIOS-OBJ theorem proving in a specification language. In: Krieg-Brückner, B. (eds) ESOP '92. ESOP 1992. Lecture Notes in Computer Science, vol 582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55253-7_11
Download citation
DOI: https://doi.org/10.1007/3-540-55253-7_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55253-6
Online ISBN: 978-3-540-46803-5
eBook Packages: Springer Book Archive