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GLEFATINF:A graphic framework for combining theorem provers and editing proofs for different logics

  • Ricardo Caferra
  • Michel Herment
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 722)

Abstract

A running system for combining theorem provers, editing and checking proofs in different logics is presented. It is based on a formalism similar to and developed from the Calculus of Constructions (Coquand and Huet).

Its abilities are independent of the logic and the calculus used. It is therefore possible to present and combine proofs coming from any theorem prover. The user may define the full graphic presentation of proofs, formulas,... he wishes.

Some other original features are: proofs can be viewed and browsed in different ways, (parts of) proofs can be memorized and reused, the size of inference steps for proof presentation can be fixed arbitrarily, symmetries can be handled in a natural manner, equational and non equational proofs are treated in an homogeneous way,...

The principles of the underlying formalism and the several languages used are given. The system has been implemented on Macintosh (and will soon be transported on SUN workstations).

The system should also allow an easy integration of theorem provers with symbolic computation systems.

Several running examples in classical and non-classical logics show evidence of the capabilities of the system. In particular, we present an OTTER [McC90] proof in which we handle symmetries in the proved theorem. Finally, the main lines of current and future work are given.

Keywords

Graphic Proof Presentation Proof Edition Logical Frameworks 

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Bibliography

  1. [And91] P.B. Andrews: More on the problem of finding a mapping between clause representation and natural deduction representation, Journal of Automated Reasoning 7 (1991), pp. 285–286.CrossRefGoogle Scholar
  2. [AHMP92] A. Avron, F.A. Honsell, I.A. Mason, R. Pollack: Using typed lambda calculus to implement formal systems on a machine, Journal of Automated Reasoning 9 (1992), pp. 309–354.CrossRefGoogle Scholar
  3. [Avr91] A. Avron: Simple consequence relations, Information and Computation 92 (1991), pp. 105–139.CrossRefGoogle Scholar
  4. [BC87] T. Boy de la Tour, R. Caferra: Proof analogy in interactive theorem proving: a method to use and express it via second order pattern matching, Proc. AAAI-87, Morgan & Kaufmann 1987, pp. 95–99.Google Scholar
  5. [CH88] T. Coquand, G. Huet: The calculus of constructions, Information and Computation 76 (1988), pp. 95–120.CrossRefGoogle Scholar
  6. [CH93] R. Caferra, M. Herment: GLEFATINF A graphic framework for combining provers and editing proofs for different logics, (long version). In preparation.Google Scholar
  7. [Che76] D. Chester: The translation of formal proofs into English, Artificial Intelligence 7 (1976), pp. 261–278.CrossRefGoogle Scholar
  8. [CHZ91] R. Caferra, M. Herment, N. Zabel: User-oriented theorem proving with the ATINF graphic proof editor, Proc. FAIR'91, LNAI 535, Springer-Verlag 1991, pp. 2–10.Google Scholar
  9. [CZ92] E. Clarke, X. Zhao: Analytica-An experiment in combinig theorem proving and symbolic computation, RR CMU-CS-92-117, September 1992.Google Scholar
  10. [Dyb82] P. Dybjer: Mathematical proofs in natural language, Report 5, Programming Methodology Group, University of Goteborg, April 1982.Google Scholar
  11. [HHP89] R. Harper, F. Honsell, G. Plotkin: A framework for defining logics, RR CMU-CS-89-173, Carnegie Mellon University, January 1989.Google Scholar
  12. [Hua90] X. Huang: Reference choices in mathematical proofs, Proc. ECAI'90, Pitman 1990, pp. 720–725.Google Scholar
  13. [Lin90] C. Lingenfelder: Transformation and structuring of computer generated proofs, SEKI Report SR-90-26, University of Kaiserslautern 1990.Google Scholar
  14. [LP90] C. Lingenfelder, A. Präcklein: Presentation of proofs in equational calculus, SEKI Report SR-90-15 (SFB), University of Kaiserslautern 1990.Google Scholar
  15. [McC90] W.W. McCune: OTTER 2.0 users guide, Technical Report ANL-90/9, Argonne National Laboratory, Illinois 1990.Google Scholar
  16. [Mil84] D.A. Miller: Expansion tree proofs and their conversion to natural deduction, Proc. CADE-7, LNCS 170, Springer-Verlag 1984, pp. 375–393.Google Scholar
  17. [Pau89] L.C. Paulson: The foundation of a generic theorem prover, Journal of Automated Reasoning 5 (1989), pp. 363–397.CrossRefGoogle Scholar
  18. [Qui87] V. Quint: Une approche de l'Edition Structurée des documents, Ph.D Thesis, Université Sc. Tech. et Méd. de Grenoble (1987).Google Scholar
  19. [Wang93] D.M. Wang: An elimination method based on Seidenberg's theory and its applications in computational algebraic geometry In Progress in Mathematics 109, pp. 301–328, Birkhäuser, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ricardo Caferra
    • 1
  • Michel Herment
    • 1
  1. 1.LIFIA-IMAGGrenoble CedexFrance

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