Skip to main content

Equational Prover of Theorema

  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2706))

Included in the following conference series:

Abstract

The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica built-in functions is allowed.

Supported by the Austrian Science Foundation (FWF) under Project SFB F1302.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Avenhaus, J. Denzinger, and M. Fuchs. Discount: a system for distributed equational deduction. In J. Hsiang, editor, Proceedings of the 6th RTA, volume 914 of LNCS, pages 397–402, Kaiserslautern, Germany, 1995. Springer.

    Google Scholar 

  2. J. Avenhaus, Th. Hillenbrand, and B. Löchner. On using ground joinable equations in equational theorem proving. J. Symbolic Computation, 2002. To appear.

    Google Scholar 

  3. L. Bachmair, N. Dershowitz, and D. Plaisted. Completion without failure. In H. Aït-Kaci and M. Nivat, editors, Resolution of Equations in Algebraic Structures, volume 2, pages 1–30. Elsevier Science, 1989.

    Google Scholar 

  4. B. Buchberger. Mathematica as a rewrite language. In T. Ida, A. Ohori, and M. Takeichi, editors, Proceedings of the 2nd Fuji Int. Workshop on Functional and Logic Programming, pages 1–13, Shonan Village Center, Japan, 1–4 November 1996. World Scientific.

    Google Scholar 

  5. B. Buchberger. Symbolic computation: Computer algebra and logic. In F. Baader and K.U. Schulz, editors, Frontiers of Combining Systems, Applied Logic Series, pages 193–220. Kluwer Academic Publishers, 1996.

    Google Scholar 

  6. B. Buchberger. Using Mathematica for doing simple mathematical proofs (invited paper). In Proceedings of the 4th Mathematica Users’ Conference, pages 80–96, Tokyo, Japan, 2 November 1996. Wolfram Media Publishing.

    Google Scholar 

  7. B. Buchberger, C. Dupré, T. Jebelean, F. Kriftner, K. Nakagawa, D. Vasaru, and W. Windsteiger. The Theorema project: A progress report. In M. Kerber and M. Kohlhase, editors, Proceedings of Calculemus’2000 Conference, pages 98–113, St. Andrews, UK, 6–7 August 2000.

    Google Scholar 

  8. R. Bündgen. Combining computer algebra and rule based reasoning. In J. Calmet and J. A. Campbell, editors, Integrating Symbolic Mathematical Computation and Artificial Intelligence. Proceedings of AISMC-2, volume 958 of LNCS, pages 209–223, Cambridge, UK, 3–5 August 1994. Springer.

    Google Scholar 

  9. J. Christian. Flatterms, discrimination trees, and fast term rewriting. J. Automated Reasoning, 10(1):95–113, 1993.

    Article  MathSciNet  Google Scholar 

  10. E. Contejean, C. Marche, B. Monate, and X. Urbain. CiME version 2, 2000. http://cime.lri.fr/.

  11. J. Denzinger and S. Schulz. Analysis and representation of equational proofs generated by a distributed completion based proof system. SEKI-report SR-94-05, University of Kaiserslautern, Germany, 1994.

    Google Scholar 

  12. H. Ganzinger, R. Nieuwenhuis, and P. Nivela. Context trees. In R. Gore, A. Leitsch, and T. Nipkow, editors, Automated Reasoning. Proceedings of the IJCAR’01, volume 2083 of LNAI, pages 242–256, Siena, Italy, June 2001. Springer.

    Google Scholar 

  13. J. C. González-Moreno. A correctness proof for Warren’s HO into FO translation. In D. Saccà, editor, Proc. of the 8th Italian Conference on Logic Programming (GULP’93), pages 569–585, Gizzeria Lido, Italy, June 1993. Mediterranean Press.

    Google Scholar 

  14. P. Graf. Substitutin tree indexing. In J. Hsiang, editor, Proceedings of the 6th RTA, volume 914 of LNCS, pages 117–131, Kaiserslautern, Germany, 1995. Springer.

    Google Scholar 

  15. T. Hillenbrand, A. Buch, R. Vogt, and B. Löchner. Waldmeister — high-performance equational deduction. J. Automated Reasoning, 18(2):265–270, 1997.

    Article  Google Scholar 

  16. J.-P. Jouannaud and A. Rubio. The higher order recursive path ordering. In Proceedings of the 14th annual IEEE symposium LICS, Trento, Italy, 1999.

    Google Scholar 

  17. T. Kutsia. Solving and proving in equational theories with sequence variables and flexible arity symbols. Technical Report 02-09, PhD Thesis. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 2002.

    Google Scholar 

  18. T. Kutsia. Theorem proving with sequence variables and flexible arity symbols. In M. Baazand A. Voronkov, editors, Logic in Programming, Artificial Intelligence and Reasoning. International Conference LPAR’02, volume 2514 of LNAI, pages 278–291, Tbilisi, Georgia, 2002. Springer.

    Google Scholar 

  19. T. Kutsia. Unification with sequence variables and flexible arity symbols and its extension with pattern-terms. In J. Calmet, B. Benhamou, O. Caprotti, L. Henocque, and V. Sorge, editors, Proceedings of Joint AISC’2002 — Calculemus’2002 conference, volume 2385 of LNAI, Marseille, France, 1–5 July 2002. Springer.

    Google Scholar 

  20. B. Löchner and Th. Hillenbrand. A phytography of Waldmeister. AI Communications, 15(2,3):127–133, 2002.

    MATH  Google Scholar 

  21. M. Marin. Introducing Sequentica, 2002. http://www.score.is.tsukuba.ac.jp/~mmarin/Sequentica/.

  22. W. W. McCune. Experiments with discrimination-tree indexing and path-indexing for term retrieval. J. Automated Reasoning, 9(2):147–167, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  23. W. W. McCune. Otter 3.0 reference manual and guide. Technical Report ANL-94/6, Argonne National Laboratory, Argonne, US, January 1994.

    Google Scholar 

  24. R. Nieuwenhuis and A. Rubio. Theorem proving with ordering and equality constrained clauses. J. Symbolic Computation, 19:321–351, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  25. I. V. Ramakrishnan, R. Sekar, and A. Voronkov. Term indexing. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume II, pages 1853–1964. Elsevier Science, 2001.

    Google Scholar 

  26. J. M. Rivero. Data structures and algorithms for automated deduction with equality. PhD Thesis. Universitat Politècnica de Catalunya, Barcelona, Spain, 2000.

    Google Scholar 

  27. M. Stickel. A Prolog Technology Theorem Prover: implementation by an extended Prolog compiler. J. Automated Reasoning, 4:353–380, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  28. M. Stickel. The path indexing method for indexing terms. Technical Report 473, Artificial Intelligence Center, SRI International, Menlo Park, CA, October 1989.

    Google Scholar 

  29. G. Sutcliffe and C. Suttner. The TPTP Problem Library for Automated Theorem Proving. http://www.cs.miami.edu/~tptp/.

  30. A. Voronkov. The anatomy of Vampire: Implementing bottom-up procedures with code trees. J. Automated Reasoning, 15(2):237–265, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  31. D. H. D. Warren. Higher-order extensions to PROLOG: are they needed? In Machine Intelligence, volume 10, pages 441–454. Edinburgh University Press, Edinburgh, UK, 1982.

    Google Scholar 

  32. S. Wolfram. The Mathematica Book. Cambridge University Press and Wolfram Research, Inc., fourth edition, 1999

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kutsia, T. (2003). Equational Prover of Theorema . In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-44881-0_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40254-1

  • Online ISBN: 978-3-540-44881-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics