Skip to main content
SpringerLink
Log in

The clean termination of iterative programs

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

The paper is devoted to a program-correctness concept which captures partial correctness, termination (nonlooping) and clean termination (nonabortion). The underlying proof method offers a one-stage proof of all the three properties. This method is proved consistent and algebraically complete. It is first discussed for the general case of arbitrary possibly nondeterministic iterative programs. Next, this case is restricted to arbitrary deterministic iterative programs and finally to structured programs. The presented approach is compared with partial correctness, total correctness and weakest precondition methods. The concluding example shows the verification of an arithmetical program in machine-bounded arithmetics. As a side effect of the verification procedure one finds input boundary conditions which guarantee clean termination.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bakker de, J.W.: Mathematical Theory of Program Correctness, Englewoods Cliffs: Prentice-Hall Int., 1980

    Google Scholar 

  2. Bakker de, J.W., Meertens, L.G.L.T.: On the completness of the inductive assertion method. J. Comput. System Sci. II, 323–357 (1975)

    Google Scholar 

  3. Blikle, A.: An algebraic approach to mathematical theory of programs. CCPAS Reports 119 (1973)

  4. Blikle, A.: Proving programs by δ-relations. Formalization of semantics of programming languages and writing of Compilers (Proc. Symp. Frankfurt/Oder 1974). Elektron. Informationsverarbeit. Kybernetik 11, 267–274 (1975)

    Google Scholar 

  5. Blikle, A.: A comparative review of some program-verification methods. In: Mathematical Foundations of Computer Science 1977 (Proc. 6th Symp. Tatranska Lomnica 1977). (J. Gruska, ed.) Lecture Notes in Computer Sciences, Vol. 53, pp. 17–33. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  6. Blikle, A.: Assertion programming. In: Mathematical Foundations of Computer Science (Proc. 8th Symposium. Olomouc 1979) (J. Becvar ed.) Lecture Notes in Computer Sciences, Vol. 74. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  7. Blikle, A.: On correct program development. (Proc. 4th Int. Conf. on Software Engineering, Sept. 1979 Munich, pp. 164–173) IEEE Catalog No. 79 CH 1479-5 C, 1979b

  8. Blikle, A.: On the development of correct specified programs. IEEE Transactions on Software Engineering (to appear in 1981)

  9. Blikle, A., Mazurkiewicz, A.: An algebraic approach to the theory of programs, algorithms, languages and recursiveness. Math. Found. Comp. Sci. (Proc. Symp. Warsaw-Jablonna 1972) Warsaw 1972

  10. Coleman, D., Hughes, J.W.: The clean termination of PASCAL programs. Acta Informat. 11, 195–210 (1979)

    Google Scholar 

  11. Dijkstra, E.W.: Guarded commands, non-determinancy and a calculus for the derivation of programs. (Proc. 1975 Int. Conf. Reliable Software) Comm. ACM 18, 453–457 (1975)

    Google Scholar 

  12. Dijkstra, E.W.: A discipline of programming. Englewood Cliffs: Prentice Hall 1976

    Google Scholar 

  13. Floyd, R.W.: Assigning meanings to programs. Appl. Math. Comput. 19, 19–32 (1967)

    Google Scholar 

  14. Hitchcock, P., Park, D.: Induction rules and termination proofs, in: Automata, Languages and Programming (Proc. IRIA Symp. 1972, M. Nivat, ed.) Amsterdam: North Holland 1973

    Google Scholar 

  15. Hoare, C.A.R.: An axiomatic definition of the programming language PASCAL. (International Symposium on Theoretical Programming). Lecture Notes in Computer Science, Vol. 5. Springer: Berlin-Heidelberg-New York 1974

    Google Scholar 

  16. Jensen, K., Wirth, N.: PASCAL User Manual. 2nd ed. Springer: Berlin-Heidelberg-New York 1975

    Google Scholar 

  17. Manna, Z., Pnueli, A.: Axiomatic approach to total correctness of programs. Acta Informat. 3, 243–263 (1974)

    Google Scholar 

  18. Mazurkiewicz, A.: Proving algorithms by tail functions, Information and Control 18, 220–226 (1971)

    Google Scholar 

  19. Mazurkiewicz, A.: Proving properties of processes. Algorytmy 11, 5–22 (1974)

    Google Scholar 

  20. McCarthy, J.: A basis for a mathematical theory of computation. (Western Joint Computer Conference, May 1961) (P. Braffort, D. Hirschberg, eds.), Computer Programming and Formal Systems. Amsterdam, North Holland: 1967, pp. 33–70

    Google Scholar 

  21. Naur, P.: Proof of algorithms by general snapshots. BIT 6, 310–316 (1966)

    Google Scholar 

  22. Roever de, W.P.: Dijkstra's predicate transformer, nondeterminism, recursion and termination. Mathematical Foundation of Computer Science 1976 (Proc. 5th. Symp. Gdansk, September 1976) (A. Mazurkiewicz, ed.) Lecture Notes in Computer Sciences, Vol. 45, pp. 472–481. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  23. Sites, R.L.: Proving that computer programs terminate cleanly. STAN-CS-74-418, 1974

  24. Strachey, C, Wadworth, C.P.: Continuations, a mathematical semantics for handling full jumps. Technical Monograph PRG-11, Oxford 1974

  25. Turing, A.M.: On checking a large routine. Report of a Conference on High Speed Automatic Calculating Machines, pp. 67–69, University Mathematical Laboratory, Cambridge 1949

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Polish Academy of Sciences PKiN, P.O. Box 22, 00-901, Warsaw, Poland

    Andrzej Blikle

Authors
  1. Andrzej Blikle
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper was prepared when the author was visiting the Department of Computer Science of the Technical University of Denmark in Lyngby.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blikle, A. The clean termination of iterative programs. Acta Informatica 16, 199–217 (1981). https://doi.org/10.1007/BF00261259

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00261259

Keywords

Search

Navigation