Skip to main content

Analysis of the equality relations for the program terms

  • Contributed Papers
  • Conference paper
  • First Online:
Static Analysis (SAS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1145))

Included in the following conference series:

Abstract

In this article an abstract interpretation and formal language based analysis for imperative programs is presented. This analysis makes a lower approximation of the equality relations for the program terms, i.e. for a given program point our analysis produces a set of equalities t 1=t 2 where t 1 and t 2 represent program expressions such that their values are equal for any behavior of the program if this program point is reached. The results of the analysis can be used for debugging, verification, optimization and specialization of programs. An abstract semantics of Pascal-like language is described and some examples of the analysis are given.

This work performed in part while the author was in Laboratoire d'Informatique de l'école Polytechnique (Palaiseau, France). The work has been partially supported by Russian Committee on Higher Education under grant “Formal methods for program analysis and transformation∝.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.Aho, J.Ullman. The theory of parsing, translation and compilation. Vol.1-Prentice-Hall Inc., Englewood Cliffs, NJ, 1972.

    Google Scholar 

  2. B.Alpern, M.N.Wegman, F.K.Zadeck. Detecting equality of variables in programs.-Proc. of the 15 th Annual ACM Symposium Principles of Programming Languages, San Diego, USA, 1988. CA. ACM Press, New York, USA, pages 1–11, 1988.

    Google Scholar 

  3. F.Bourdoncle. Efficient chaotic iteration strategies with widenings.-Proc. of the International Conference Formal Methods in Programming and Their Applications, Novosibirsk, Russia, 1993. LNCS 735, Springer-Verlag, Berlin, Germany, pages 129–141, 1993.

    Google Scholar 

  4. M.Bruynooghe, G.Janssens. On abstracting the procedural behaviour of logic program.-Proc. of the First and Second Russian Conferences on Logic Programming, Irkutsk (1990) and St.Petersburg (1991), Russia. LNAI 592, Springer-Verlag, Berlin, Germany, pages 240–262, 1992.

    Google Scholar 

  5. A.Cortesi,B.Le Charlier,P.Van Hentenryck. Type analysis of Prolog using type graphs.-Journal of Logic Programming, 16(2), pages 179–209, 1995.

    Google Scholar 

  6. P.Cousot, R.Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction of approximation of fixpoints.-Proc. of the 4 th Annual ACM Symposium Principles of Programming Languages, Los-Angeles, USA, 1977. CA. ACM Press, New York, USA, pages 238–252, 1977.

    Google Scholar 

  7. Cousot P., Cousot R. Systematic design of program analysis frameworks.-Rec. of the 6 th ACM Symposium on Principles of Programming Languages, San Antonio, USA, 1979. TX. ACM Press, New York, USA, pages 269–282, 1979.

    Google Scholar 

  8. P.Cousot, R.Cousot. Abstract interpretation frameworks.-Journal of Logic and Computation, 2(4), pages 511–547, 1992.

    Google Scholar 

  9. P.Cousot, R.Cousot. Comparing the Galois connection and widening/narrowing approaches to abstract interpretation, invited paper.-Proc. of the 5 th International Symposium Programming Language Implementation and Logic Programming, Leuven, Belgium, 1992. LNCS 631, Springer-Verlag, Berlin, Germany, pages 269–295, 1992.

    Google Scholar 

  10. P.Cousot, R.Cousot. Formal languages, grammar and set-constraint-based program analysis by abstract interpretation.-Rec. of the Functional Programming Languages and Computer Architecture SIGPLAN-SIGARCH-WG 2.8, La Jolla, USA, 1995. CA. ACM Press, New York, USA, pages 170–181, 1995.

    Google Scholar 

  11. A.Deutsch. A storeless model of aliasing and its abstraction using finite representation of right-regular equivalence relations.-Proc. of the IEEE International Conference on Compiler Languages, pages 2–13, 1992.

    Google Scholar 

  12. A.Deutsch. Interprocedural may-alias analysis for pointers: beyond k-limiting.-Proc. of the ACM SIGPLAN'94 Conference on Program Language Design and Implementation, SIGPLAN Notices, 29(6), pages 230–241, 1994.

    Google Scholar 

  13. P.Eades, X.Lin, W.F.Smyth. A fast and effective heuristic for the feedback arc set problem.-Information Processing Letters, 47(6), pages 319–323, 1993.

    Google Scholar 

  14. P.Emelianov, V.Sabelfeld. Analyzer of semantic properties of Modula-programs.-Software intellectualization and quality, Novosibirsk, Russia, pages 13–21, 1994, in russian.

    Google Scholar 

  15. M.R.Garey, D.S.Johnson. Computers and intractability. A guide to the theory of {ie188-01}-completeness.-W.H.Freeman and company, New York, USA, 1979.

    Google Scholar 

  16. N.D.Jones. Flow analysis of lazy higher-order functional programs.-In Abstract Interpretation of Declarative Languages, (Eds.: S.Abramsky and C.Hankin), Ellis Horwood, Chichester, UK, pages 103–122, 1987.

    Google Scholar 

  17. N.Heintze. Set based program analysis.-Ph.D. Thesis, School of Computer Sciences, Carnegie Mellon University, Pittsburg, USA, 1992.

    Google Scholar 

  18. F.Masdupuy. Semantic analysis of interval congruences.-Proc. of the International Conference Formal Methods in Programming and Their Applications, Novosibirsk, Russia, 1993. LNCS 735, Springer-Verlag, Berlin, Germany, pages 142–155, 1993.

    Google Scholar 

  19. G.Nelson, D.C.Oppen. Fast decision procedures based on congruence closure.-Journal of the ACM, 27(2), pages 356–364, 1980.

    Google Scholar 

  20. V.Sabelfeld. The logic-termal equivalence is polynomial-time decidable.-Information Processing Letters, 10(2), pages 102–112, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Radhia Cousot David A. Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Emelianov, P.G. (1996). Analysis of the equality relations for the program terms. In: Cousot, R., Schmidt, D.A. (eds) Static Analysis. SAS 1996. Lecture Notes in Computer Science, vol 1145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61739-6_41

Download citation

  • DOI: https://doi.org/10.1007/3-540-61739-6_41

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61739-6

  • Online ISBN: 978-3-540-70674-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics