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Hoare Logics for Recursive Procedures and Unbounded Nondeterminism

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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Abstract

This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounded nondeterminism only in conjunction with loops rather than procedures. We consider both single procedures and systems of mutually recursive procedures. All proofs have been checked with the theorem prover Isabelle/HOL.

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References

  1. Pierre America and Frank de Boer. Proving total correctness of recursive procedures. Information and Computation, 84:129–162, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  2. Krzysztof Apt. Ten Years of Hoare’s Logic: A Survey — Part I. ACM Trans. Programming Languages and Systems, 3(4):431–483, 1981.

    Article  MATH  Google Scholar 

  3. Krzysztof Apt. Ten Years of Hoare’s Logic: A Survey — Part II: Nondeterminism. Theoretical Computer Science, 28:83–109, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  4. Krzysztof Apt and Gordon Plotkin. Countable nondeterminism and random assignment. Journal of the ACM, 33:724–767, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  5. Robert Cartwright and Derek Oppen. The logic of aliasing. Acta Informatica, 15:365–384, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gerald Arthur Gorelick. A complete axiomatic system for proving assertions about recursive and non-recursive programs. Technical Report 75, Dept. of Computer Science, Univ. of Toronto, 1975.

    Google Scholar 

  7. Peter Hitchcock and David Park. Induction rules and termination proofs. In M. Nivat, editor, Automata, languages, and programming, pages 225–251. North-Holland, 1973.

    Google Scholar 

  8. C. A. R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12:567–580,583, 1969.

    Article  Google Scholar 

  9. C. A. R. Hoare. Procedures and parameters: An axiomatic approach. In E. En-geler, editor, Semantics of algorithmic languages, volume 188 of Lecture Notes in Mathematics, pages 102–116. Springer-Verlag, 1971.

    Google Scholar 

  10. Martin Hofmann. Semantik und Verifikation. Lecture notes, Universität Marburg. In German, 1997.

    Google Scholar 

  11. Peter V. Homeier and David F. Martin. Mechanical verification of mutually recursive procedures. In M. A. McRobbie and J. K. Slaney, editors, Automated Deduction — CADE-13, volume 1104 of Lect. Notes in Comp. Sci., pages 201–215. Springer-Verlag, 1996.

    Google Scholar 

  12. Peter V. Homeier and David F. Martin. Mechanical verification of total correctness through diversion verification conditions. In J. Grundy and M. Newey, editors, Theorem Proving in Higher Order Logics (TPHOLs’98), volume 1479 of Lect. Notes in Comp. Sci., pages 189–206. Springer-Verlag, 1998.

    Google Scholar 

  13. Thomas Kleymann. Hoare logic and auxiliary variables. Formal Aspects of Computing, 11:541–566, 1999.

    Article  MATH  Google Scholar 

  14. J. H. Morris. Comments on “procedures and parameters”. Undated and unpublished.

    Google Scholar 

  15. David Naumann. Calculating sharp adaptation rules. Information Processing Letters, 77:201–208, 2000.

    Article  MathSciNet  Google Scholar 

  16. Hanne Riis Nielson and Flemming Nielson. Semantics with Applications. Wiley, 1992.

    Google Scholar 

  17. Tobias Nipkow. Winskel is (almost) right: Towards a mechanized semantics textbook. In V. Chandru and V. Vinay, editors, Foundations of Software Technology and Theoretical Computer Science, volume 1180 of Lect. Notes in Comp. Sci., pages 180–192. Springer-Verlag, 1996.

    Google Scholar 

  18. Tobias Nipkow. Winskel is (almost) right: Towards a mechanized semantics textbook. Formal Aspects of Computing, 10:171–186, 1998.

    Article  MATH  Google Scholar 

  19. Tobias Nipkow, Lawrence Paulson, and Markus Wenzel. Isabelle/HOL —A Proof Assistant for Higher-Order Logic, volume 2283 of Lect. Notes in Comp. Sci. Springer-Verlag, 2002.

    Google Scholar 

  20. David von Oheimb. Hoare logic for mutual recursion and local variables. In C. Pandu Rangan, V. Raman, and R. Ramanujam, editors, Foundations of Software Technology and Theoretical Computer Science (FST&TCS), volume 1738 of Lect. Notes in Comp. Sci., pages 168–180. Springer-Verlag, 1999.

    Google Scholar 

  21. Ernst-Rüdiger Olderog. On the notion of expressiveness and the rule of adaptation. Theoretical Computer Science, 24:337–347, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  22. P. Pandya and M. Joseph. A structure-directed total correctness proof rule for recursive procedure calls. The Computer Journal, 29:531–537, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  23. Robert Pollack. The Theory of LEGO: A Proof Checker for the Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1994.

    Google Scholar 

  24. Thomas Schreiber. Auxiliary variables and recursive procedures. In TAP-SOFT’97: Theory and Practice of Software Development, volume 1214 of Lect. Notes in Comp. Sci., pages 697–711. Springer-Verlag, 1997.

    Google Scholar 

  25. Stefan Sokołowski. Total correctness for procedures. In Mathematical Foundations of Computer Science (MFCS), volume 53 of Lect. Notes in Comp. Sci., pages 475–483. Springer-Verlag, 1977.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität München, Germany

    Tobias Nipkow

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  1. Tobias Nipkow
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Editor information

Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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Nipkow, T. (2002). Hoare Logics for Recursive Procedures and Unbounded Nondeterminism. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_8

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  • DOI: https://doi.org/10.1007/3-540-45793-3_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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