Specification and integration of theorem provers and computer algebra systems

  • P. G. Bertoli
  • J. Calmet
  • F. Giunchiglia
  • K. Homann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1476)


Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domain-specific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each class alone. However, most experiments conducted so far followed an ad-hoc approach, resulting in tailored solutions to specific problems. A structured and principled approach is necessary to allow for the sound integration of systems in a modular way. The Open Mechanized Reasoning Systems (OMRS) framework was introduced for the specification and implementation of mechanized reasoning systems, e.g. ATPs. The approach was recasted to the domain of computer algebra systems. In this paper, we introduce a generalization of OMRS, named OMSCS (Open Mechanized Symbolic Computation Systems). We show how OMSCS can be used to soundly express CASs, ATPs, and their integration, by formalizing a combination between the Isabelle prover and the Maple algebra system. We show how the integrated system solves a problem which could not be tackled by each single system alone.


Integration of Logical Reasoning and Computer Algebra Computer Algebra Systems and Automated Theorem Provers 


Computer Algebra Systems Theorem Provers Integration Formal Frameworks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abbott, J. PossoXDR specifications. Internal Posso technical report, 1994.Google Scholar
  2. 2.
    Armando, A., and Ranise, S. From Integrated Reasoning Specialists to “Plug-and-Play≓ Reasoning Components. In Proceedings of AISC’98, Springer Verlag.Google Scholar
  3. 3.
    Bertoli, P.Using OMRS for real: a case study withAcl2. PhD thesis, Computer Science Dept., University Rome 3, Rome, 1997. Forthcoming.Google Scholar
  4. 4.
    C. Ballarin, K. Homann, J. C. Theorems and Algorithms: An interface between Isabelle and Maple. In International Symposium on Symbolic and Agebraic Computation, ISSAC ’95 (1995), H. M. Levelt, Ed., ACM Press, pp. 150–157.Google Scholar
  5. 5.
    Calmet, J., and Homann, K. Structures for symbolic mathematical reasoning and computation. In Proceedings of DISCO ’96 — Design and Implementation of Symbolic Computation Systems (1996), J. Calmet and C. Limongelli, Eds.Google Scholar
  6. 6.
    Coglio, A. Definizione di un formalismo per la specifica delle strategie di inferenza dei sistemi di ragionamento meccanizzato e sua applicazione ad un sistema allo stato dell’arte. Master’s thesis, University of Genoa, Italy, 1996.Google Scholar
  7. 7.
    E. Clarke, X. Z. Analytica — a theorem prover in mathematica. In Proc. of the 10th Conference on Automated Deduction (1992), Springer-Verlag, pp. 761–765.Google Scholar
  8. 8.
    Giunchiglia, F., Pecchiari, P., and Talcott, C. Reasoning Theories: Towards an Architecture for Open Mechanized Reasoning Systems. Tech. Rep. 9409-15, IRST, Trento, Italy, 1994. Short version in Proc. of the First International Workshop on Frontiers of Combining Systems (FroCoS’96), Munich, Germany, 1996.Google Scholar
  9. 9.
    J. Harrison, L. T. Extending the HOL prover with a Computer Algebra System to reason about the Reals. In Higher Order Logic Theorem proving and its Applications, J. J. Joyce and J. H. Seger, Eds. Springer-Verlag, 1993, pp. 174–184.Google Scholar
  10. 10.
    Homann, K. Symbolisches Loesen mathematischer Probleme durch Kooperation algorithmischer und logischer Systeme. PhD thesis, Univ. of Karlsruhe, 1996.Google Scholar
  11. 11.
    Prawitz, D. Natural Deduction: A Proof-theoretical Study., 1965.Google Scholar
  12. 12.
    Vorkoetter, S. OpenMath specifications: March 1994, March 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • P. G. Bertoli
    • 1
  • J. Calmet
    • 2
  • F. Giunchiglia
    • 3
  • K. Homann
    • 4
  1. 1.ITC-IRSTTrentoItaly
  2. 2.University of KarlsruheGermany
  3. 3.ITC-IRST - Trento and DISAUniversity of TrentoItaly
  4. 4.Siemens CorporationMunichGermany

Personalised recommendations