An experiment with the Boyer-Moore theorem prover: A proof of the correctness of a simple parser of expressions

  • Paul Y Gloess
Thursday Morning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)


The objective of this report is to convey the essential idea of a proof by the Boyer-Moore theorem prover of the correctness of a parser. The proof required a total of 147 functions and lemmas — all of which have been listed in the appendix of [4].

Included in the following text are a description of the original problem submitted to the theorem prover and a sketch of the resultant proof, together with a discussion of the reasons that induced us to introduce some auxiliary functions. The report also contains the computer-generated proof of one of the main lemmas: INIT.SEG. The complete proof is available from the author.

We conclude with some remarks on our experiment and comments on the use of the theorem prover.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Robert S. Boyer, J Strother Moore. A Computer Proof of the Correctness of a Simple Optimizing Compiler of Expressions. Technical Report N00014-75-C-0816-SRI-4079, SRI International, Menlo-Park, California 94025, January, 1977.Google Scholar
  2. 2.
    Robert S. Boyer, J Strother Moore. A Theorem Prover for Recursive Functions: a User's Manual. CSL-91, NR 049-378, SRI International, Menlo-Park, California 94025, June, 1979.Google Scholar
  3. 3.
    R. S. Boyer and J S. Moore. A Computational Logic. Academic Press Inc., New York, 1979.Google Scholar
  4. 4.
    P. Y Gloess. A Proof of the Correctness of a Simple Parser of Expressions by the Boyer-Moore System. Technical Report N00014-75-C-0816-SRI-7, SRI International, Menlo Park, California 94025, August, 1978.Google Scholar
  5. 5.
    Ps, J-P Laurent. Adding Dynamic Paramodulation to Rewrite Algorithms. Technical Report CSL-102, SRI International, Menlo Park, CA94025, December, 1979.Google Scholar
  6. 6.
    G. Huet. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Rapport Laboria no250, IRIA-LABORIA, Domaine de Voluceau, 78150 Le Chesnay, France, August, 1977.Google Scholar
  7. 7.
    G. Huet. Equations and Rewrite Rules: a Survey. CSL-111, SRI International, Menlo Park, California 94025, January, 1980.Google Scholar
  8. 8.
    D. E. Knuth and P. G. Bendix. Simple Word Problems in Universal Algebras. In J. Leech, Ed., Computational Problems in Abstract Algebra, Pergamon Press, New York, 1970, pp. 263–297.Google Scholar
  9. 9.
    D. S. Lankford. Canonical Inference. Automatic Theorem Proving Project Report ATP-32, University of Texas, December, 1975.Google Scholar
  10. 10.
    J S. Moore. A Mechanical Proof of Takeuchi's Function. Information Processing Letters 9, 4 (November 1980), 176–181.Google Scholar
  11. 11.
    D. R. Musser. Convergent Sets of Rewrite Rules for Abstract Data Types. USC Information Sciences Institute, 4676 Admiralty Way, Marina del Rey, California 90291, December, 1978. Extended AbstractGoogle Scholar
  12. 12.
    R. E. Shostak. An Algorithm for Reasoning About Equality. Communications of the ACM 21, 7 (July 1978), 583–585.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Paul Y Gloess
    • 1
    • 2
  1. 1.International Fellow, SRI InternationalMenlo ParkU.S.A.
  2. 2.Boursier de Recherche I.R.I.A.Le ChesnayFrance

Personalised recommendations