Integrating Computer Algebra into Proof Planning

Journal of Automated Reasoning

Volumn 21, Issue 3, 1998, Pages 327-355

  Kerber, Manfred ^a   Kohlhase, Michael ^b   Sorge, Volker ^b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

Computer algebra; Hierarchical proof planning; Mechanized reasoning; Proof checking

Indexed keywords

ALGORITHMS; AUTOMATION; BOOLEAN ALGEBRA; COMPUTATIONAL METHODS; COMPUTER SYSTEMS; INTERFACES (COMPUTER); PROBLEM SOLVING; THEOREM PROVING;

COMPUTER ALGEBRA SYSTEMS; MECHANIZED REASONING SYSTEMS; PROOF PLAN;

ARTIFICIAL INTELLIGENCE;

EID: 0032287894     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006059810729     Document Type: Article

References (37)

1. Abbot, J., van Leeuwen, A., and Strotmann, A.: Objectives of OpenMath, Technical Report 12, RIACA, Eindhoven, June 1996.
2. Andrews, P. B.: Transforming matings into natural deduction proofs, in W. Bibel and R. Kowalski (eds), Proceedings of the 5th CADE, Les Arc, France, 1980, LNCS 87, Springer-Verlag, 1980, pp. 281-292.
3. Ballarin, C., Homann, K., and Calmet, J.: Theorems and algorithms: An interface between Isabelle and Maple, in A. H. M. Levelt (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'95), ACM Press, 1995, pp. 150-157.
4. Barendregt, H.: Computations and formal proofs in type theory, talk at the 2nd Meeting of the CALCULEMUS Project, Schloβ Dagstuhl, Germany, 18.11.-20.11.1996. See also The quest for correctness, available as URL: ftp://ftp.cs.kun.nl/pub/ CompMath.Found/quest.ps.Z, 1996.
5. Barendregt, H.: Computations and formal proofs in type theory, talk at the 2nd Meeting of the CALCULEMUS Project, Schloβ Dagstuhl, Germany, 18.11.-20.11.1996. See also The quest for correctness, available as URL: ftp://ftp.cs.kun.nl/pub/ CompMath.Found/quest.ps.Z, 1996.
6. Benzmüller, C., Cheikhrouhou, L., Fehrer, D., Fiedler, A., Huang, X., Kerber, M., Kohlhase, M., Melis, E., Meier, A., Schaarschmidt, W., Siekmann, J., and Sorge, V.: ΩMEGA: Towards a mathematical assistant, in W. McCune (ed.), Proceedings of the 14th CADE, Townsville Australia, 1997, LNAI 1249, Springer-Verlag, 1997, pp. 252-255.
7. Boyer, R. S. and Moore, J S.: Metafunctions, in R. S. Boyer and J S. Moore (eds), The Correctness Problem in Computer Science, Academic Press, 1981, pp. 103-184.
8. Buchberger, B.: Mathematische Software-Systeme: Drastische Erweiterung des "Intelligenzniveaus" entsprechender Programme erwartet, Informatik Spektrum 19/2 (1996), 100-101.
9. Buchberger, B.: Symbolic computation (an editorial), J. Symbolic Comput. 1 (1985), 1-6.
10. Buchberger, B.: Using Mathematica for doing simple mathematical proofs, invited talk at the 4th Tokyo Mathematica Users' Conference, November 2-3, 1996.
11. Bundy, A.: The use of explicit plans to guide inductive proofs, in E. L. Lusk and R. A. Overbeek (eds), Proceedings of the 9th CADE, Argonne, Illinois, USA, 1988, LNCS 310, Springer-Verlag, 1988, pp. 111-120.
12. Bundy, A., Stevens, A., van Harmelen, F., Ireland, A., and Smaill, A.: Rippling: A heuristic for guiding inductive proofs, Artif. Intell. 62 (1993), 185-253.
13. Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., and Watt, S. M.: First Leaves: A Tutorial Introduction to Maple V, Springer-Verlag, 1992.
14. Chou, S.-C.: Mechanical Geometry Theorem Proving, Mathematics and Its Applications, D. Reidel Publishing Company, Dordrecht, 1988.
15. Chou, S.-C., Gao, X.-S., and Zhang, J.-Z.: Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems, World Scientific, Singapore, 1994.
16. Clarke, E. and Zhao, X.: Analytica - A theorem prover in Mathematica, in Automated Deduction, 11th International Conference on Automated Deduction, Saratoga Springs, New York, 15-18 June 1992, pp. 761-763.
17. Clément, D., Montagnac, F., and Prunet, V.: Integrated software components: A paradigm for control integration, in Proceedings of the European Symposium on Software Development Environments and CASE Technology, LNCS 509, Springer-Verlag, 1991.
18. Constable, R. L. et al.: Implementing Mathematics with the Nuprl Proof Development System, Prentice-Hall, 1986.
19. Fuchssteiner, B. et al. (The MuPAD Group): MuPAD User's Manual, Wiley, 1996.
20. Giunchiglia, F., Pecchiari, P., and Talcott, C.: Reasoning theories - towards an architecture for open mechanized reasoning systems, in F. Baader and K. U. Schulz (eds), Frontiers of Combining Systems (FroCoS-1): 1st International Workshop, Munich, Germany, 1996, Kluwer Acad. Publ., 1996, pp. 157-174
21. Harrison, J. and Théry, L.: Extending the HOL theorem prover with a computer algebra system to reason about the reals, in C.-J. H. Seger and J. J. Joyce (eds), Higher Order Logic Theorem Proving and its Applications (HUG'93), LNCS 780, Springer-Verlag, 1993, pp. 174-184.
22. Harrison, J. and Théry, L.: Reasoning about the reals: The marriage of HOL and Maple, in A. Voronkov (ed.), Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), St. Petersburg, Russia, LNAI 698, Springer-Verlag, 1993, pp. 351-353.
23. Hearn, A. C.: Reduce user's manual: Version 3.6, Technical Report, Rand Corporation, Santa Monica, CA, USA, 1995.
24. Homann, K. and Calmet, J.: An open environment for doing mathematics, in M. Wester, S. Steinberg, and M. Jahn (eds), Proceedings of 1st International IMACS Conference on Applications of Computer Algebra, Albuquerque, USA, 1995.
25. Howe, D. J.: Computational metatheory in Nuprl, in E. Lusk and R. Overbeek (eds), Proceedings of the 9th CADE, Argonne, Illinois, USA, 1988, LNCS 310, Springer-Verlag, 1988, pp. 238-257.
26. Huang, X., Kerber, M., Kohlhase, M., Melis, E., Nesmith, D., Richts, J., and Siekmann, J.: Ω-MKRP: A proof development environment, in A. Bundy (ed.), Proceedings of the 12th CADE, Nancy, 1994, LNAI 814, Springer-Verlag, 1994, pp. 788-792.
27. Huang, X., Kerber, M., Kohlhase, M., and Richts, J.: Adapting methods to novel tasks in proof planning, in B. Nebel and L. Dreschler-Fischer (eds), KI-94: Advances in Artificial Intelligence - Proceedings of KI-94, 18th German Annual Conference on Artificial Intelligence, Saarbrücken, Germany, LNAI 861, Springer-Verlag, 1994, pp. 379-380.
28. Huang, X. and Fiedler, A.: Presenting machine-found proofs, in M. A. McRobbie and J. K. Slaney (eds), Proceedings of the 13th CADE, New Brunswick, NJ, USA, 1996, LNAI 1104, Springer-Verlag, 1996, pp. 221-225.
29. Jenks, R. D. and Sutor, R. S., AXIOM: The Scientific Computation System, Springer-Verlag, 1992.
30. Kapur, D.: A refutational approach to theorem proving in geometry, Artif. Intell. 37 (1988), 61-93.
31. Karatsuba, A. and Ofman, Y.: Multiplication of multidigit numbers by automata, Soviet Phys. Dokl. 7 (1963), 595-596.
32. Kowalski, R.: Algorithm = Logic + Control, Comm. Assoc. Comput. Machinery 22 (1979), 424-436.
33. McCune, W. W.: Otter 3.0 reference manual and guide, Technical Report ANL-94-6, Argonne National Laboratory, Argonne, IL, USA, 1994.
34. Universität des Saarlandes, Diplomthemen SS-89 Nr. 35, Fachschaft Wirtschaftswissenschaften, Saarbrücken, Germany, 1989.
35. Wolfram, S.: The Mathematica Book: Version 3.0, 3rd edition, Wolfram Media, Inc., Champaign, IL, 1996.
36. Wu, W.: Mechanical Theorem Proving in Geometries: Basic Principles, Texts and Monographs in Symbolic Computation, Springer, Wien, 1994.
37. Zippel, R.: Effective Polynomial Computation, Kluwer Acad. Publ., 1993.