Skip to main content

Using Decision Procedures to Accelerate Domain-Specific Deductive Synthesis Systems

  • Conference paper
  • First Online:
Logic-Based Program Synthesis and Transformation (LOPSTR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1559))

Abstract

This paper describes a class of decision procedures that we have found useful for efficient, domain-specific deductive synthesis, and a method for integrating this type of procedure into a general-purpose refutation-based theorem prover. We suggest that this is a large and interesting class of procedures and show how to integrate these procedures to accelerate a general-purpose theorem prover doing deductive synthesis. While much existing research on decision procedures has been either in isolation or in the context of interfacing procedures to non-refutation-based theorem provers, this appears to be the first reported work on decision procedures in the context of refutation based deductive synthesis where witnesses must be found.

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.

Reference

  1. Baader, F. & Tinelli, C, “A New Approach for Combining Decision Procedures for the Word Problem, and its Connection to the Nelson-Oppen Combination Method,” CADE14, pp. 19–33, 1997.

    Google Scholar 

  2. R. Boyer and Moore, J, Integrating Decision Procedures into Heuristic Theorem Provers: A Case Study of Linear Arithmetic, Institute for Computing Science and Computer Applications, University of Texas as Austin, 1988.

    Google Scholar 

  3. Burckert, H. J., “A Resolution Principle for a Logic With Restricted Quantifiers,” Lecture Notes in Artificial Intelligence, Vol. 568, Springer-Verlag, 1991.

    Google Scholar 

  4. Chang, C & Lee, R.C., Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.

    MATH  Google Scholar 

  5. Cyrluk, D., Lincoln, P., Shankar, N. “On Shostak’s decision procedures for combinations of theories,” Automated Deduction—CADE-13 in Lecture Notes in AI 1104, (M. A. McRobbie and J. K. Slaney Eds), Springer, pp. 463–477, 1996.

    Google Scholar 

  6. Deville, Y. and Lau, K., “Logic Program Synthesis,” Journal of Logic Programming, 19,20: 321–350, 1994.

    Article  MathSciNet  Google Scholar 

  7. Dunham, B. and North, J., “Theorem Testing by Computer,” Proceedings of the Symposium on Mathematical Theory of Automata, Polytechnic Press, Brooklyn, N.Y., pp. 173–177, 1963.

    Google Scholar 

  8. Gallier, J.H., Logic for Computer Science: Foundations of Automatic Theorem Proving, Harper and Row, 1986.

    Google Scholar 

  9. C.A.R. Hoare, “Proof of Correctness of Data Representations,” Acta Infomatica, Vol. 1, pp. 271–281, 1973.

    Article  Google Scholar 

  10. M. Lowry and J. Van Baalen, “META-Amphion: Synthesis of Efficient Domain-Specific Program Synthesis Systems”, Automated Software Engineering, vol 4, pp. 199–241, 1997.

    Article  Google Scholar 

  11. Nelson, G., and Oppen, D., “Simplification By Cooperating Decision Procedures,” ACM Transactions on Programming Languages and Systems, No. 1, pp. 245–257, 1979.

    Google Scholar 

  12. Nelson, G., and Oppen, D., “Fast decision procedures based on congruence closure,” Journal of the ACM, 27, 2, pp. 356–364, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  13. Owre, S., Rushby, M., and Shankar, N., “PVS: A Prototype Verification System,” CADE-11, LNAI Vol. 607, pp. 748–752, 1992.

    Google Scholar 

  14. Roach, S., “TOPS: Theory Operationalization for Program Synthesis,” Ph.D. Thesis at University of Wyoming, 1997.

    Google Scholar 

  15. Shostak, R., “A practical decision procedure for arithmetic with function symbols,” Journal of the ACM, Vol. 26, pp. 351–360, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  16. Shostak, R., “Deciding Combinations of Theories,” Journal of the ACM, Vol. 31, pp. 1–12, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Stickel, R. Waldinger, M. Lowry, T. Pressburger, and I. Underwood, “Deductive Composition of Astronomical Software from Subroutine Libraries,” CADE-12, 1994. See http://ic-www.arc.nasa.gov/ic/projects/amphion/docs/amphion.html

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Van Baalen, J., Roach, S. (1999). Using Decision Procedures to Accelerate Domain-Specific Deductive Synthesis Systems. In: Flener, P. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 1998. Lecture Notes in Computer Science, vol 1559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48958-4_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-48958-4_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65765-1

  • Online ISBN: 978-3-540-48958-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics