A calculus for and termination of rippling

Journal of Automated Reasoning

Volumn 16, Issue 1-2, 1996, Pages 147-180

  Basin, David A ^a   Walsh, Toby ^b,c  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b DIST   (Italy)

^c ITC IRST   (Italy)

Author keywords

Inductive theorem proving; Mathematical induction; Term rewriting

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTATIONAL METHODS; FORMAL LOGIC; PROBLEM SOLVING;

CALCULUS; INDUCTIVE THEOREM PROVING; MATHEMATICAL INDUCTION; RIPPLING; TERM REWRITING; WAVE RULES;

THEOREM PROVING;

EID: 0030101909     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00244462     Document Type: Article

References (17)

1. Basin, David and Walsh, Toby: Difference unification, in Proc. 13th IJCAI, International Joint Conference on Artificial Intelligence, 1993, pp. 116-122.
2. Basin, David and Walsh, Toby: Termination orderings for rippling, in Proc. 12th Int. Conf. Automated Deduction (CADE-12), Nancy, France, June 1994, Springer-Verlag.
3. Biundo, Susanne, Hummel, Birgit, Hutter, Dieter, and Walther, Christoph: The Karlsruhe induction theorem proving system, in 8th Int. Conf. Automated Deduction, Oxford, UK, 1986.
4. Boyer, Robert S. and Moore, J Strother: A Computational Logic. Academic Press, 1979.
5. Bundy, Alan, van Harmelen, Frank, Hesketh, Jane, and Smaill, Alan: Experiments with proof plans for induction, J. Automated Reasoning 7 (1991), 303-324.
6. Bundy, Alan, Stevens, Andrew, van Harmelen, Frank, Ireland, Andrew, and Smaill, Alan: Rippling: A heuristic for guiding inductive proofs, Artificial Intelligence 62 (1993), 185-253.
7. Bundy, Alan, van Harmelen, Frank, Horn, Christian, and Smaill, Alan: The Oyster-Clam system, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 647-648.
8. Bundy, Alan, van Harmelen, Frank, Smaill, Alan, and Ireland, Andrew: Extensions to the rippling-out tactic for guiding inductive proofs, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 132-146.
9. Bundy, Alan and Welham, Bob: Using meta-level inference for selective application of multiple rewrite rules in algebraic manipulation, Artificial Intelligence 16(2) (1981), 189-212.
10. Cleve, Jürgen and Hutter, Dieter: A methodology for equational reasoning, in HICSS-27, IEEE, 1994.
11. Dershowitz, Nachum: Termination of rewriting, in J.-P. Jouannaud (ed.), Rewriting Techniques and Applications, Academic Press, 1987, pp. 69-116.
12. Dershowitz, Nachum: Orderings for term-rewriting systems, Theor. Computer Science 17(3) (March 1982), 279-301.
13. Hutter, Dieter: Colouring terms to control equational reasoning, an expanded version of PhD Thesis: Mustergesteuerte Strategien für Beweisen von Gleichheiten, Universität Karlsruhe, 1991.
14. Hutter, Dieter: Guiding inductive proofs, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 147-161.
15. Ireland, Andrew and Bundy, Alan: Productive use of failure in inductive proof, J. Automated Reasoning 16(1-2) (1996), 79-111.
16. Walsh, Toby, Nunes, Alex and Bundy, Alan: The use of proof plans to sum series, in D. Kapur (ed.), 11th Conf. Automated Deduction, Lecture Notes in Computer Science 607, Springer-Verlag, 1992, pp. 325-339.
17. Yoshida, Tetsuja, Bundy, Alan, Green, Ian, Walsh, Toby, and Basin, David: Coloured rippling: An extension of a theorem proving heuristic, in ECAI-94, Wiley, New York, 1994.