Advertisement

Towards Trustworthy Specification I: Consistency Checks

  • Markus Roggenbach
  • Lutz Schröder
Conference paper
Part of the Lecture Notes in Computer Science book series

Abstract

As the first of two methodological devices aimed at increasing the trust in the ‘correctness’ of a specification, we develop a calculus for proving consistency of CASL Specification. It turns out to be possible to delegate large parts of the proof load to syntactical criteria by structuring consistency proofs along the given specification structure, so that only in rather few remaining focus points, actual theorem proving is required. The practical usability of the resulting calculus is demonstrated by extensive examples taken from the CASL library of basic data types.

Keywords

Consistency Check Theorem Prove Proof System Proof Obligation Development Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wolfgang Ahrendt, A basis for model computation in free data types, Proceedings of the CADE-17 Workshop on Model Computation, 2000.Google Scholar
  2. [2]
    Egidio Astesiano, Michel Bidoit, Hélène Kirchner, Bernd Krieg-Brückner, Peter D. Mosses, Donald Sannella, and Andrzej Tarlecki, Casl: The common algebraic specification language, Theoretical Computer Science (to appear).Google Scholar
  3. [3]
    S. Autexier, D. Hutter, H. Mantel, and A. Schairer, Towards an evolutionary formal software development using Casl, Recent Trends in Algebraic Development Techniques, LNCS, vol. 1827, Springer, 1999, pp. 73–88.Google Scholar
  4. [4]
    H. Baumeister, Relations between abstract datatypes modeled as abstract datatypes, Ph.D. thesis, Universität des Saarlandes, 1998.Google Scholar
  5. [5]
    M. Bidoit, M. V. Cengarle, and R. Hennicker, Proof systems for structured specifications and their refinements, Algebraic Foundations of Systems specification (E. Astesiano et al., eds.), Springer, 1999, pp. 385–433.Google Scholar
  6. [6]
    M. Cerioli, A. Haxthausen, B. Krieg-Brückner, and T. Mossakowski, Permissive subsorted partial logicin Casl, Algebraic Methodology and Software Technology, LNCS, vol. 1349, Springer, 1997, pp. 91–107.CrossRefGoogle Scholar
  7. [7]
    CoFI, The Common Framework Initiative for algebraic specification and development, electronic archives, notes and documents accessible from http://www.brics.dk/Projects/CoFI.
  8. [8]
    CoFI Language Design Task Group, Casl-The CoFI Algebraic Specification Language-Summary, version 1.0.1, Documents/CASLSummary, in [7], March 2001.Google Scholar
  9. [9]
    CoFI Semantics Task Group, Casl-The CoFI Algebraic Specification Language-Semantics, Note S-9 (version 0.96), in [7], July 1999.Google Scholar
  10. [10]
    R. Diaconescu, J. Goguen, and P. Stefaneas, Logical support for modularisation, Logical Environments, Cambridge, 1993, pp. 83–130.Google Scholar
  11. [11]
    J. Farrés-Casals, Proving correctness of constructor implementations, Mathematical Foundations of Computer Science, LNCS, vol. 379, Springer, 1989, pp. 225–236.Google Scholar
  12. [12]
    J.-Y. Girard, Locus solum, Math. Struct. Comput. Sci., To appear.Google Scholar
  13. [13]
    J. Goguen and R. Burstall, Institutions: Abstract model theory for specification and programming, J. ACM 39 (1992), 95–146.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    M. J. C. Gordon and T. M. Melham, Introduction to HOL: A theorem proving environment for higher order logics, Cambridge, 1993.Google Scholar
  15. [15]
    R. Hennicker and M. Wirsing, Proof systems for structured algebraic Specification: An overview, Fundamentals of Computation Theory, LNCS, vol. 1279, Springer, 1997, pp. 19–37.CrossRefGoogle Scholar
  16. [16]
    B. Klin, P. Hoffman, A. Tarlecki, L. Schröder, and T. Mossakowski, Checking amalgamability conditions for Casl architectural Specification, Mathematical Foundations of Computer Science, LNCS, Springer, 2001, to appear.Google Scholar
  17. [17]
    T. F. Melham, A package for inductive relation definitions in HOL, International Workshop on the HOL Theorem Proving System and its Applications, IEEE Computer Society Press, 1992, pp. 350–357.Google Scholar
  18. [18]
    T. Mossakowski, S. Autexier, and D. Hutter, Extending development graphs with hiding, Fundamental Aspects of Software Engineering, LNCS, vol. 2029, Springer, 2001, pp. 269–283.CrossRefGoogle Scholar
  19. [19]
    W. Reif, G. Schellhorn, and A. Thums, Flaw detection in formal Specification, International Joint Conference on Automated Reasoning, LNCS, vol. 2083, Springer, 2001, pp. 642–657.Google Scholar
  20. [20]
    Markus Roggenbach, Till Mossakowski, and Lutz Schröder, Basic datatypes in CASL, Note L-12 in [7], current version 0.7 available at http://www.informatik.uni-bremen.de/co./CASL/lib/basic, March 2001.
  21. [21]
    Markus Roggenbach and Lutz Schröder, Towards trustworthy Specification II: Testing by proof, work in progress.Google Scholar
  22. [22]
    L. Schröder, T. Mossakowski, and A. Tarlecki, Amalgamation in Casl via enriched signatures, International Colloquium on Automata, Languages and Programming, LNCS, vol. 2076, Springer, 2001, pp. 993–1004.CrossRefGoogle Scholar
  23. [23]
    J. R. Shoenfield, Mathematical logic, Addison-Wesley, 1967.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Markus Roggenbach
    • 1
  • Lutz Schröder
    • 1
  1. 1.BISS, Department of Computer ScienceBremen UniversityBremen

Personalised recommendations