Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A Practical Approach to Partiality – A Proof Based Approach

  • Conference paper
Formal Methods and Software Engineering (ICFEM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5256))

Included in the following conference series:

Abstract

Partial functions are frequently used when specifying and reasoning about computer programs. Using partial functions entails reasoning about potentially ill-defined expressions. In this paper we show how to formally reason about partial functions without abandoning the well understood domain of classical two-valued predicate calculus. In order to achieve this, we extend standard predicate calculus with the notion of well-definedness which is currently used to filter out potentially ill-defined statements from proofs. The main contribution of this paper is to show how the standard predicate calculus can be extended with a new set of derived proof rules that can be used to preserve well-definedness in order to make proofs involving partial functions less tedious to perform.

This research was carried out at the ETH Zurich as part of the EU research project IST 511599 RODIN (Rigorous Open Development Environment for Complex Systems).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Rigorous Open Development Environment for Complex Systems (RODIN) official website, http://www.event-b.org/

  2. Abrial, J.-R.: The B-Book: Assigning programs to meanings. Cambridge (1996)

    Google Scholar 

  3. Abrial, J.-R.: Modeling in Event B: System and Softtware Design. Cambridge (to appear, 2007)

    Google Scholar 

  4. Abrial, J.-R., Mussat, L.: On using conditional definitions in formal theories. In: Bert, D., Bowen, J., Henson, M., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 242–269. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Barnett, M., Leino, K.R.M., Schulte, W.: The Spec# programming system: An overview. In: Construction and Analysis of Safe, Secure, and Interoperable Smart Devices, pp. 49–69 (2005)

    Google Scholar 

  6. Barringer, H., Cheng, J.H., Jones, C.B.: A logic covering undefinedness in program proofs. Acta Inf. 21, 251–269 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Behm, P., Burdy, L., Meynadier, J.-M.: Well defined B. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, pp. 29–45. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Berezin, S., Barrett, C., Shikanian, I., Chechik, M., Gurfinkel, A., Dill, D.L.: A practical approach to partial functions in CVC Lite

    Google Scholar 

  9. Chalin, P.: Logical foundations of program assertions: What do practitioners want? In: SEFM, pp. 383–393 (2005)

    Google Scholar 

  10. Darvas, Á., Mehta, F., Rudich, A.: Efficient well-definedness checking. In: International Joint Conference on Automated Reasoning (IJCAR). LNCS. Springer, Heidelberg (to appear, 2008)

    Google Scholar 

  11. Fitzgerald, J.S., Jones, C.B.: The connection between two ways of reasoning about partial functions. Technical Report CS-TR-1044, School of Computing Science. Newcastle University (August 2007)

    Google Scholar 

  12. Gordon, M.J.C., Melham, T.F.: Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, New York (1993)

    MATH  Google Scholar 

  13. Gries, D., Schneider, F.B.: Avoiding the undefined by underspecification. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 366–373. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  14. Jones, C.B.: Systematic software development using VDM, 2nd edn. Prentice-Hall, Inc., Englewood Cliffs (1990)

    MATH  Google Scholar 

  15. Jones, C.B.: Reasoning about partial functions in the formal development of programs. Electr. Notes Theor. Comput. Sci. 145, 3–25 (2006)

    Article  MATH  Google Scholar 

  16. Kleene, S.C.: Introduction to metamathematics. Bibl. Matematica. North-Holland, Amsterdam (1952)

    MATH  Google Scholar 

  17. Mehta, F.D.: Proofs for the Working Engineer. PhD thesis, ETH Zurich (2008)

    Google Scholar 

  18. Nipkow, T., Paulson, L., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  19. Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system, January 15 (2001)

    Google Scholar 

  20. Owre, S., Shankar, N.: The formal semantics of PVS (March 1999), http://www.csl.sri.com/papers/csl-97-2/

  21. Rudich, A., Darvas, Á., Müller, P.: Checking well-formedness of pure-method specifications. In: Formal Methods (FM). LNCS. Springer, Heidelberg (2008)

    Google Scholar 

  22. Sutcliffe, G., Suttner, C.B.: The TPTP (Thousands of Problems for Theorem Provers) Problem Library: CNF Release v1.2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systransis AG − Transport Information Systems, Bahnhofplatz, P.O. Box 4714, CH-6304, Zug, Switzerland

    Farhad Mehta

Authors
  1. Farhad Mehta
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Computer and Information Sciences, Hosei University, 3-7-2 Kajino-cho Koganei-shi, 184-8584, Tokoy, Japan

    Shaoying Liu

  2. Department of Computing and Software, McMaster University, 1280 Main St West, L8S 4K1, Hamilton, ON, Canada

    Tom Maibaum

  3. Department of Computer Science and Communication Engineering, , Graduate School of Information Science and Electrical Engineering, Kyushu University, 6-10-1-Hakozaki, 812-8581, Higashi-ku, Fukuoka, Japan

    Keijiro Araki

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mehta, F. (2008). A Practical Approach to Partiality – A Proof Based Approach. In: Liu, S., Maibaum, T., Araki, K. (eds) Formal Methods and Software Engineering. ICFEM 2008. Lecture Notes in Computer Science, vol 5256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88194-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88194-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88193-3

  • Online ISBN: 978-3-540-88194-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation