The AFFIRM theorem prover: Proof forests and management of large proofs

  • Roddy W. Erickson
  • David R. Musser
Thursday Afternoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)

Abstract

The AFFIRM theorem prover is an interative, natural-deduction system centered around abstract data types. Since long proofs are often required to verity algorithms, we describe a model (called the "proof forest") which helps the user to visualize and manage the potentially large number of theorems and subgoals that can arise.

References

  1. 1.
    Burstall, R. M. and Goguen, J. A., "Putting Theories Together to Make Specifications," in Proceedings of the Fifth International Joint Conference on Artificial Intelligence, pp. 1045–1058, IEEE, August 1977.Google Scholar
  2. 2.
    Gerhart, S. L. et al., An Overview of AFFIRM: A Specification and Verification System, USC Information Sciences Institute, Technical Report RR-9-81, 1980. Also to appear in Proc. IFIP 80Google Scholar
  3. 3.
    Goguen, J. A., Thatcher, J. W., and Wagner, E. G., "Abstract Data Types as Initial Algebras and the Correctness of Data Representations," in Yeh, R. T. (ed.), Current Trends in Programming Methodology, Volume IV, Prentice-Hall, 1978.Google Scholar
  4. 4.
    Guttag, J. V., "Abstract Data Types and the Development of Data Structures," CACM 20, June 1977, 397–404.Google Scholar
  5. 5.
    Guttag, J. V., Horowitz, E., and Musser, D. R., "Abstract Data Types and Software Validation," CACM 21, December 1978, 1048–1064. (Also USC Information Sciences Institute RR-76/48, August 1976.)Google Scholar
  6. 6.
    Guttag, J. V., "Notes on Type Abstraction," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 13–23.Google Scholar
  7. 7.
    Huet, G., Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, IRIA — LABORIA, Technical Report LABORIA Report No. 250, 1978.Google Scholar
  8. 8.
    Knuth, D. E., and Bendix, P. B., "Simple Word Problems in Universal Algebras," in Leech, J. (ed.), Computational Problems in Abstract Algebra, pp. 263–297, Pergamon Press, New York, 1970.Google Scholar
  9. 9.
    Lankford, D. S. and Musser, D. R., On Semi-deciding First-Order Validity and Invalidity, 1978. unpublished manuscriptGoogle Scholar
  10. 10.
    McCarthy, J., "A Basis for a Mathematical Theory of Computation," in Braffort and Hirschberg (eds.), Computer Programming and Formal Systems, pp. 33–70, North-Holland, 1963.Google Scholar
  11. 11.
    Musser, D. R., "Abstract Data Type Specification in the AFFIRM System," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 24–32.Google Scholar
  12. 12.
    Spitzen, J., and Wegbreit, B., "The Verification and Synthesis of Data Structures," Acta Informatica 4, 1975, 127–144.Google Scholar
  13. 13.
    Thompson, D. H., ed., AFFIRM Reference Manual, USC Information Sciences Institute, 1979.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Roddy W. Erickson
    • 1
  • David R. Musser
    • 2
  1. 1.USC Information Sciences InstituteMarina del ReyUS
  2. 2.Computer Science BranchgGeneral Electric Research and Development CenterSchenectadyUS

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