Abstract
Completion can be seen as a process that transforms proofs in an initially given equational theory to rewrite proofs in final rewrite rules. Rewrite proofs are the normal forms of proofs under these proof transformations. The purpose of this paper is to provide a framework in which one may further restrict the normal forms of proofs which completion is required to construct, thereby further decreasing the complexity of reduction and goal solving in completed systems.
This work is partially supported by the ESPRIT-project PROSPECTRA, ref#390.
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5 References
Bachmair, L.: Proof methods for equational theories. PhD-Thesis, U. of Illinois, Urbana Champaign, 1987.
Bachmair, L., Dershowitz, N. and Hsiang, J.: Proof orderings for equational proofs. Proc. LICS 86, 346–357.
Bertling, H. and Ganzinger, H.: Completion of Application-Restricted Equations. Report 289, FB Informatik, U. Dortmund, 1989.
Bosco, P.G., Giovannetti, E. and Moiso, C.: Refined Strategies for Semantic Unification. TAP-SOFT 87, Springer LNCS 250, 276–290, 1987.
Bertling, H., Ganzinger, H. and Schäfers, R.: CEC: A system for conditional equational completion. User Manual Version 1.4, PROSPECTRA-Report M.1.3-R-7.0, U. Dortmund, 1988.
Bergstra, J. and Klop, J.W.: Conditional Rewrite Rules: Confluence and Termination. Report IW198/82, Mathematisch Centrum, Amsterdam, 1982.
Dershowitz, N., Okada, M. and Sivakumar, G.: Confluence of conditional rewrite systems. Proc. 1st Int'l Workshop on Conditional Term Rewriting, Orsay, 1987, Springer LNCS 308, 1988, 31–44.
Dershowitz, N. and Plaisted, D.A.: Logic Programming cum Applicative Programming. Proc. IEEE Symp. on Logic Programming, Boston 1985, 54–67, 1985.
Dershowitz, N. and Sivakumar, G.: Solving Goals in Equational Languages. Proc. 1st Int'l Workshop on Conditional Term Rewriting, Orsay, 1987, Springer LNCS 308, 1988, 45–55.
Fribourg, L.: SLOG: A Logic Programming Language Interpreter Based on Clausal Superposition. Proc. IEEE Symp. on Logic Programming, Boston 1985, 172–184, 1985.
Ganzinger, H.: A Completion procedure for conditional equations. Report 234, U. Dortmund, 1987, also in: Proc. 1st Int'l Workshop on Conditional Term Rewriting, Orsay, 1987, Springer LNCS 308, 1988, 62–83 (revised version to appear in J. Symb. Computation).
Ganzinger, H.: Completion with History-Dependent Complexities for Generated Equations. In Sannella, Tarlecki (eds.): Recent Trends in Data Type Specifications. Springer LNCS 332, 1988, 73–91.
Ganzinger, H.: Order-Sorted Completion: The Many-Sorted Way. Report 274, FB Informatik, Univ. Dortmund, 1988, Extended abstract to appear in Proc. TAPSOFT(CAAP) '89, Barcelona.
Giovannetti, E. and Moiso, C.: A Completeness Result for E-Unification Algorithms Based on Narrowing. Proc. Workshop on Foundations of Logic and Functional Programming, Springer LNCS 306, 157–167, 1988.
Gouen, J.A. and Meseguer, J.: Eqlog: Equality, Types, and Generic Modules for Logic Programming. J. Logic Programming, 1,2, 179–210, 1984.
Hölldobler, St.: From Paramodulation to Narrowing. Univ. der Bundeswehr, München, 1987.
Hullot, J.M.: Canonical Forms and Unification. Proc. CADE 1980, 318–334, 1980.
Hussmann, H.: Unification in Conditional-Equational Theories. Proc. EUROCAL, Springer LNCS 204, 543–553, 1985.
Jouannaud, J.P. and Waldmann, B.: Reductive conditional term rewriting systems. Proc. 3rd TC2 Working Conference on the Formal Description of Programming Concepts, Ebberup, Denmark, Aug. 1986, North-Holland.
Kaplan, St.: Fair conditional term rewrite systems: unification, termination and confluence. Report 194, U. de Paris-Sud, Centre d'Orsay, Nov. 1984.
Kaplan, St.: A compiler for conditional term rewriting. Proc. RTA 1987, LNCS 256, 1987, 25–41.
Kounalis, E. and Rusinowitch, M.: On word problems in Horn theories. Proc. 1st Int'l Workshop on Conditional Term Rewriting, Orsay, 1987, Springer LNCS 308, 1988, 144–160.
Padawitz, P.: Computing in Horn Clause Theories. EATCS Monographs in Computer Science, 16, 1988.
Robinson, G.A. and Wos, L.: Paramodulation and Theorem Proving in First-Order Theories with Equality. In: Meltzer, Mitchie (Eds): Machine Intelligence 4, 1969.
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Bertling, H., Ganzinger, H. (1989). Completion-time optimization of rewrite-time goal solving. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_99
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DOI: https://doi.org/10.1007/3-540-51081-8_99
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