Summary
In this paper we give countably infinitely many extensions of Huet and Hullot's inductive completion procedure. Also we try and throw some light on the problem of functions which are only partially defined by some set of rewrite rules. We also give a procedure which attempts to show that two derived F-algebras are isomorphic when both of the algebras are realised as retracts.
Similar content being viewed by others
References
Dershowitz, N.: Applications of the Knuth-Bendix completion procedure. Laboratory Operation Aerospace Corporation, Aerospace Report No. ATR-83 (8478)-2, May 15, 1983
Dershowitz, N.: Completion and its applications. In: Proceedings of Colliquium on Resolution of Equations in Algebraic Structures. MCC 3500 West Balconies Center Drive, Austin. Texas 78759–6509. May 4–6 1987
Fribourg, F.: A strong restriction of the completion procedure for theories with constructors. In: Kott, L. (ed.) International Colloquium on Automata, Languages and Programming. (Lect. Notes Comput. Sci., vol.) Berlin Heidelberg New York: Springer 1986
Huet, G., Oppen, D.: Equations and rewrite rules: a survey. In: Book, R. (ed.). Formal languages: Perspectives and Open Problems. New York: Academic Press 1980
Huet, G., Hullot, J.M.: Proof by induction in equational theories with constructors. JCCS 25, 2 (1982)
Jouannaud, J.P., Kounalis, E.: Proofs by induction in equational theories without constructors. In: Proceedings of the first IEEE Symposium on Logic in Computer Science, IEEE, Cambridge, Massachusetts 1986
Kapur, D., Narendran, P., Zhang, H.: Proof by induction using test sets. In: 8th International Conference on Automated Deduction (Lect. Notes Comput. Sci., vol. 230, pp. 99–117). Berlin Heidelberg New York: Springer 1986
Kirchner, H.: A general inductive completion algorithm and application to abstract data types. In: 7th International Conference on Automated Deduction (Lect. Notes Comput. Sci., vol. 170). Berlin Heidelberg New York: Springer 1984
Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational problems in abstract algebra. pp. 263–297. New York: Pergamon Press 1970
Lescanne, P.: Term rewriting systems and algebra. In: 7th International Conference on Automated Deduction (Lect. Notes Comput. Sci., Vol. 170). Berlin Heidelberg New York: Springer 1984
Musser, D.R.: On proving inductive properties of abstract data types. In: Proceedings of the seventh ACM Symposium on Principals of Programming Languages, Las Vegas, Nevada, Jan 1980, pp. 154–162
Musser, D.R., Kapur, D.: Proof by consistency. Artif. Intell. 31(2), 125–157 (1987)
Plaisted, D.A.: Semantic confluence tests and completion methods. Inform. Control 65, 182–215 (1985)
Tyama, Y.: How to prove equivalence of term rewriting systems without induction. In: 8th International Conference on Automated Deduction (Lect. Notes Comput. Sci., vol.230, pp. 118–127). Berlin Heidelberg New York: Springer 1986
Author information
Authors and Affiliations
Additional information
Supported by Science and Engineering Research Council under grant GR/D/81718. Whilst the paper was under revision the author was supported by S.E.R.C grant GR/D/57942
Rights and permissions
About this article
Cite this article
Mitchell, W.P.R. Inductive completion with retracts. Acta Informatica 25, 497–514 (1988). https://doi.org/10.1007/BF00279951
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00279951