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Lightweight Program Construction and Verification Tools in Isabelle/HOL

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Software Engineering and Formal Methods (SEFM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8702))

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Abstract

We present a principled approach to the development of construction and verification tools for while-programs. Our verification tool uses Kleene algebra with tests to capture the control flow of programs and its relational semantics for their data flow. It is extended to a Morgan-style program construction tool by adding one single axiom to the algebra. Our formalisation in Isabelle/HOL makes these tools themselves correct by construction. Verification condition generation and program construction steps are based on simple equational reasoning and supported by powerful Isabelle tactics. Two case studies on program construction and verification show our tools at work.

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References

  1. Angus, A., Kozen, D.: Kleene algebra with tests and program schematology. Technical Report TR2001-1844, Cornell University (2001)

    Google Scholar 

  2. Armstrong, A., Gomes, V.B.F., Struth, G.: Algebraic principles for rely-guarantee style concurrency verification tools. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 78–93. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Armstrong, A., Gomes, V.B.F., Struth, G.: Algebras for program correctness in Isabelle/HOL. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds.) RAMiCS 2014. LNCS, vol. 8428, pp. 49–64. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  4. Armstrong, A., Gomes, V.B.F., Struth, G.: Kleene algebras with tests and demonic refinement algebras. Archive of Formal Proofs (2014)

    Google Scholar 

  5. Armstrong, A., Struth, G., Weber, T.: Kleene algebra. Archive of Formal Proofs (2013)

    Google Scholar 

  6. Armstrong, A., Struth, G., Weber, T.: Program analysis and verification based on Kleene algebra in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 197–212. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Cavalcanti, A., Sampaio, A., Woodcock, J.: A refinement strategy for circus. Formal Aspects of Computing 15(2-3), 146–181 (2003)

    Article  MATH  Google Scholar 

  8. Desharnais, J., Struth, G.: Internal axioms for domain semirings. Science of Computer Programming 76(3), 181–203 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Filliâtre, J.-C., Marché, C.: The Why/Krakatoa/Caduceus platform for deductive program verification. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 173–177. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Haftmann, F., Krauss, A., Kunčar, O., Nipkow, T.: Data refinement in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 100–115. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Kozen, D.: Kleene algebra with tests. ACM TOPLAS 19(3), 427–443 (1997)

    Article  Google Scholar 

  12. Kozen, D.: On Hoare logic and Kleene algebra with tests. ACM TOCL 1(1), 60–76 (2000)

    Article  MathSciNet  Google Scholar 

  13. Kozen, D.: Kleene algebras with tests and the static analysis of programs. Technical Report TR2003-1915, Cornell University (2003)

    Google Scholar 

  14. Kozen, D., Patron, M.-C.: Certification of compiler optimizations using Kleene algebra with tests. In: Lloyd, J., et al. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 568–582. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Möller, B., Struth, G.: Algebras of modal operators and partial correctness. Theoretical Computer Science 351(2), 221–239 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Möller, B., Struth, G.: wp is wlp. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929, pp. 200–211. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Morgan, C.: Programming from specifications, 2nd edn. Prentice Hall (1994)

    Google Scholar 

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

    MATH  Google Scholar 

  19. Nipkow, T.: Winskel is (almost) right: Towards a mechanized semantics. Formal Aspects of Computing 10(2), 171–186 (1998)

    Article  MATH  Google Scholar 

  20. Pous, D.: Kleene algebra with tests and Coq tools for while programs. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 180–196. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. Sternagel, C., Thiemann, R.: Certification of nontermination proofs. In: Beringer, L., Felty, A. (eds.) ITP 2012. LNCS, vol. 7406, pp. 266–282. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Sheffield, UK

    Alasdair Armstrong, Victor B. F. Gomes & Georg Struth

Authors
  1. Alasdair Armstrong
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  2. Victor B. F. Gomes
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  3. Georg Struth
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Editor information

Editors and Affiliations

  1. NASA Ames Research Center, Mail Stop 269-2, Moffett Field, 94035, CA, USA

    Dimitra Giannakopoulou

  2. Inria Grenoble-Rhône-Alpes, 655, Avenue de l’Europe, Montbonnot Saint-Martin, 38330, France

    Gwen Salaün

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© 2014 Springer International Publishing Switzerland

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Armstrong, A., Gomes, V.B.F., Struth, G. (2014). Lightweight Program Construction and Verification Tools in Isabelle/HOL. In: Giannakopoulou, D., Salaün, G. (eds) Software Engineering and Formal Methods. SEFM 2014. Lecture Notes in Computer Science, vol 8702. Springer, Cham. https://doi.org/10.1007/978-3-319-10431-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-10431-7_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10430-0

  • Online ISBN: 978-3-319-10431-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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