Abstract
A decomposition procedure, called DP, operating on a ”sorted” set of equations is here used as the operational semantics of CTRS. Then, a class of CTRS called conic-flat, is defined for which DP is shown to be universally terminating when solving the equation t1=Rt2, with t1 or t2 ground.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
G. Aguzzi and M. C. Verri, ”On the Termination of a Unification Procedure”, in Proceedings of 3rd Italian Conference on Theoretical Computer Science, World Scientific, 1989.
G. Aguzzi and M. C. Verri, ”On the termination of an algorithm for unification in equational theories”, in Proceedings of IEEE TENCON '89, pp. 1034–1039
G. Aguzzi and M.C. Verri, ” A class of terminating logic programs”, R.T. 2/90, D.S.I., Univ. of Florence, 1990.
M. Baudinet, ”Proving Termination Properties of Prolog Programs: a Semantic Approach”, 3rd Annual Symp. on Logic in Computer Science, Edimburg, 1988, pp. 336–347.
N. Dershowitz, ”Orderings for Term Rewriting Systems”, Theor. Comp. Sci. vol. 17, 1982, pp. 279–301.
N. Dershowitz, ”Termination”, Lecture Notes in Computer Science, vol.202, 1985, pp. 180–224.
N. Dershowitz and G. Sivakumar, ”Solving Goals in Equational Languages”, Lecture Notes in Computer Science vol. 308, Springer Verlag, 1988, pp 45–55.
N. Dershowitz and J. P. Jouannaud, Handbook of Theoretical Computer Science chapter Rewrite Systems. Volume B, North Holland, 1990 (to appear).
M. Dincbas and P. Van Hentenryck, ”Extended Unification Algorithms for the Integration of Functional Programming into Logic Programming”, J. Logic Programming, vol. 4, 1987, pp 199–227.
J. H. Gallier and W. Snyder, ”A General Complete E-Unification Procedure”, Lecture Notes in Computer Science vol. 256, Springer Verlag, 1987, pp. 216–227.
G. Huet and D.C. Oppen, ”Equations and rewrite rules: A survey”, in Formal Language Theory: Perspectives and open problems, R. Book Ed., Academic Press, New York, 1980, pp. 349–405.
J-M. Hullot, ”Canonical Forms and Unification”, in Proceedings of the 5th Conference on Automated Deduction, 1980, pp. 318–334.
B. Jayaraman, ”Semantics of EqL”, IEEE Transactions on Software Engineering, vol. 14, n. 4, april 1988, pp 472–480.
S. Kaplan, ”Simplifying Conditional Term Rewriting Systems: Unification, Termination and Confluence”, J. Symbolic Computation, 4, 1987, pp. 295–334.
A. Martelli, C. Moiso and G. F. Rossi, ”An Algorithm for Unification in Equational Theories”, 3rd IEEE Symp. on Logic Programming, Salt Lake City, Utah, 1986, pp. 180–186.
A. Martelli and U. Montanari, ”An Efficient Unification Algorithm”, ACM Transaction on Programming Languages and Systems, 4, 2, 1982, pp 258–282.
M. Okada, ”A logical analysis on theory of conditional rewriting”, Lecture Notes in Computer Science vol. 308, Springer Verlag, 1988, pp 179–196.
U. S. Reddy, ”Narrowing as the Operational Semantics of Functional Languages”, in Proceedings on Logic Progr., IEEE, 1985, pp. 138–151.
J. A. Robinson, ”A Machine-Oriented Logic Based on the Resolution Principle”, J. ACM vol. 12, 1965, pp. 23–41.
T. Vasak and J. Potter, ”Characterization of terminating logic programs”, 3rd IEEE Symp. on Logic Programming, Salt Lake City, Utah, 1986, pp. 140–147.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aguzzi, G., Modigliani, U., Verri, M.C. (1991). An universal termination condition for solving goals in equational languages. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_110
Download citation
DOI: https://doi.org/10.1007/3-540-54317-1_110
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54317-6
Online ISBN: 978-3-540-47558-3
eBook Packages: Springer Book Archive