Skip to main content
SpringerLink
Log in

A sound and relatively complete Hoare-logic for a language with higher type procedures

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

Present day Hoare-like proof-systems are in general not capable of dealing with procedures with procedure parameters. Nevertheless, the fact, that the actual termination problem over finite interpretations is decidable for a language with procedures of finite modes and without global variables [15] indicates, that a relatively complete Hoare-style proof-system for such a language (Clarke's language L 4) should exist, which then necessarily has to incorporate new proof-techniques. This paper presents such a system (using a suitable oracle set) and thus essentially solves the conjecture raised by Langmaack and Olderog.

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. Goguen, J.A., Thatcher, J.W., Wagner, E.G., Wright, J.B.: Initial algebra semantics and continuous algebras. JACM 24, 68–95 (1977)

    Google Scholar 

  2. Apt, K.R.: Ten years of Hoare's logic: a survey-part I. ACM TOPLAS 3, 431–483 (1981)

    Google Scholar 

  3. Bakker, de, J.W., Klop, J.W., Meyer, J.-J.C.: Correctness of programs with function procedures. Report IW 170/81, Mathematisch Centrum, Amsterdam 1981

    Google Scholar 

  4. Barendregt, H.P.: The type free lambda calculus. Handbook of Mathematical Logic, North-Holland 1977

  5. Clarke, E.M.: Programming language constructs for which it is impossible to obtain good Hoare-like axioms. JACM 26, 129–147 (1979)

    Google Scholar 

  6. Cook, S.A.: Soundness and completeness of an axiom system for program verification. SIAM J. Comput. 7, 70–90 (1978)

    Google Scholar 

  7. Damm, W.: The IO-and OI-hierarchies. Schriften zur Informatik and Angewandten Mathematik, Nr. 41, TH Aachen (1980) and TCS 20, 95–207 (1982)

  8. Damm, W., Fehr, E.: A schematological approach to the analysis of the procedure concept in ALGOL-languages. Proc. 5ème Colloque sur les Arbres en Algèbre et en Programmation, Lille, pp. 130–134, 1980

  9. Damm, W., Josko, B.: On verifying higher type procedures. Abstract in: Formale Methoden und Mathematische Hilfsmittel für die Softwarekonstruktion. Broy, M. (ed.). Tagungsbericht 1/1982, Mathematisches Forschungsinstitut Oberwolfach

  10. Gorelick, G.A.: A complete axiomatic system for proving assertions about recursive and nonrecursive programs. Tech. Rep. 75, Dept. of Computer Sci., Univ. of Toronto 1975

  11. Hoare, C.A.R.: An axiomatic basis for computer programming. Comm. ACM 12, 576–583 (1969)

    Google Scholar 

  12. Josko, B.: On expressive interpretations of a Hoare-logic for a language with higher type procedures. Schriften zur Informatik und Angewandten Mathematik, TH Aachen 1983

    Google Scholar 

  13. Langmaack, H.: On procedures as open subroutines I, II. Acta Informat. 2, 311–333 (1973) and 3, 227–241 (1974)

    Google Scholar 

  14. Langmaack, H.: On a theory of decision problems in programming languages. Proc. Int. Conf. on Mathematical Studies of Information Processing, LNCS 75, 538–558 (1979)

    Google Scholar 

  15. Langmaack, H.: On termination problems for finitely interpreted ALGOL-like programs. Bericht Nr. 7904, Inst. f. Inform. u. Prakt. Math. Christian-Albrechts-Univ., Kiel 1979

    Google Scholar 

  16. Langmaack, H., Olderog, E.-R.: Present-day Hoare-like systems for programming languages with procedures : power, limits and most likely extensions. Proc. 7th Coll. Automata, Languages and Programming, LNCS 85, 363–373 (1980)

  17. Lipton, R.J.: A necessary and sufficient condition for the existence of Hoare logics. 18th IEEE Symp. on Foundations of Computer Science, pp. 1–6, 1977

  18. Olderog, E.-R.: Sound and complete Hoare-like calculi based on copy rules. Acta Informat. 16, 161–197 (1981)

    Google Scholar 

  19. Olderog, E.R.: Hoare-style proof and formal computations. GI-1. Jahrestagung, IFB 50, 65–71 (1981)

    Google Scholar 

  20. Olderog, E.-R.: Correctness of PASCAL-like programs without global variables. Abstract in: Formale Methoden und Mathematische Hilfsmittel für die Softwarekonstruktion. Broy, M. (ed.). Tagungsbericht 1/1982, Mathematisches Forschungsinstitut Oberwolfach

  21. Olderog, E.-R.: Correctness of programs with PASCAL-like procedures without global variables. (to appear in TCS)

  22. Wand, M.: A new incompleteness result for Hoare's system. JACM 25, 168–175 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik II, RWTH Aachen, Büchel 29-31, D-5100, Aachen, FRG

    Werner Damm & Bernhard Josko

Authors
  1. Werner Damm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernhard Josko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the DFG under grant No. In 20/2

Rights and permissions

Reprints and permissions

About this article

Cite this article

Damm, W., Josko, B. A sound and relatively complete Hoare-logic for a language with higher type procedures. Acta Informatica 20, 59–101 (1983). https://doi.org/10.1007/BF00264295

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00264295

Keywords

Search

Navigation