Abstract
We describe a new representation for first-order terms which is amenable to simple and fast traversal and matching operations. In addition, we describe some efficient discrimination net indexing algorithms which use the new term representation. We have implemented these ideas in a term rewriting system called HIPER, and have obtained substantial speedups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boyer, Bob, ‘Rewrite rule compilation’, Technical Report AI-194-86-P, Micro-electronics and Computer Technology Corporation (MCC) (June 1986).
Christian, Jim, ‘High-performance permutative completion’, Ph.D. thesis, University of Texas at Austin (1989). Available as MCC Technical Report ACT-AI-303-89.
Christian, Jim, ‘Fast Knuth-Bendix completion: Summary’, inProceedings of the Conference on Rewriting Techniques and Applications, Chapel Hill, North Carolina (1989).
Knuth, Donald, and Bendix, Peter, ‘Simple word problems in universal algebra’, in J. Leech (ed.),Computational Problems in Abstract Algebra, Pergamon Press, Oxford, U.K. (1970).
Geser, Alfons, Hussman, Heinrich, and Mück, Andreas, ‘A compiler for a class of conditional term rewriting systems’, inProceedings of the 1st Intl. Workshop on Conditional Term Rewriting Systems, pp. 84–90, Orsay, France (1987).
Grau, A., ‘Ternary Boolean algebra’,Bull. Amer. Math. Soc.,53, 567–572 (1947).
Greenbaum, Steven, ‘Input transformations and resolution implementation techniques for theorem proving in first-order logic’, Ph.D. thesis, University of Illinois at Urbana-Champaign (1986).
Heuillard, Thierry, ‘Compiling conditional rewriting systems’, inProceedings of the 1st Intl. Workshop on Conditional Term Rewriting Systems, pp. 111–128, Orsay, France (1987).
Hsiang, Jieh, and Rusinowitch, Michael, ‘On word problems in equational theories’, Technical Report 86/29, Dept. of Computer Science, SUNY Stonybrook (1986).
Jouannaud, Jean-Pierre, and Kirchner, Helene, ‘Completion of a set of rules modulo a set of equations’,SIAM. J. Computing (November 1986).
Kaplan, Stéphane, ‘A compiler for conditional term rewriting systems’, inProceedings of the Conference on Rewriting Techniques and Applications, pp. 25–41, Bordeaux, France (1987).
Knuth, Donald,Searching and Sorting, Addison-Wesley, Reading, Massachusetts (1973).
Lincoln, Pat, and Christian, Jim, ‘Adventures in associative-commutative unification: A summary’, inProceedings of the Ninth International Conference on Automated Deduction, pp. 358–367, Argonne, Illinois (1988).
Lincoln, Pat, and Christian, Jim, ‘Adventures in associative-commutative unification’,J. Symbolic Computation,8, 217–240 (1989).
McCune, Bill, ‘Discrimination tree indexing and FPA/path indexing for large sets of formulaes’. Notes from a presentation at the AAAI Symposium on Compilation and Representation in High Performance Theorem Proving, Stanford University (1989).
Rush, Tony, and Coleman, Derek, ‘Architecture for conditional term rewriting’, inProceedings of the 1st Intl. Workshop on Conditional Term Rewriting Systems, pp. 266–278, Orsay, France (1987).
Stickel, Mark, ‘The path-indexing method for indexing terms’, Draft (August 1989).
Toyama, Yoshihito, ‘Fast Knuth-Bendix completion with a term rewriting system compiler’, Technical Report COMP88, Institute of Electronics, Information, and Communication Engineers (Tokyo) (February 1989).
Warren, David H. D., ‘An abstract Prolog instruction set’, Technical Report 309, SRI, 1983.
Zhang, Hantao, ‘Avoiding unnecessary unifiers in AC completion’, presentation at the AAAI Symposium on Compilation and Representation in High Performance Theorem Proving, Stanford University (1989).
Author information
Authors and Affiliations
Additional information
The work reported here was conducted at MCC and at the University of Texas at Austin.
Rights and permissions
About this article
Cite this article
Christian, J. Flatterms, discrimination nets, and fast term rewriting. J Autom Reasoning 10, 95–113 (1993). https://doi.org/10.1007/BF00881866
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00881866