Calculational Relation-Algebraic Proofs in Isabelle/Isar

  • Wolfram Kahl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)

Abstract

We propose a collection of theories in the proof assistant Isabelle/Isar that support calculational reasoning in and about heterogeneous relational algebras and Kleene algebras.

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References

  1. [Asp00]
    Aspinall, D.: Proof General: A generic tool for proof development. In: Schwartzbach, M.I., Graf, S. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 38–42. Springer, Heidelberg (2000), See also http://www.proofgeneral.org CrossRefGoogle Scholar
  2. [BBS97]
    Behnke, R., Berghammer, R., Schneider, P.: Machine support of relational computations: The Kiel RELVIEW system. Technical Report 9711, Institut für Informatik und Praktische Mathematik, Christian- Albrechts- Universität Kiel (June 1997)Google Scholar
  3. [BH94]
    Berghammer, R., Hattensperger, C.: Computer-aided manipulation of relational expressions and formulae using RALF. In: Buth, B., Berghammer, R. (eds.) Systems for Computer-Aided Specification, Development and Verification, Bericht Nr. 9416, pp. 62–78. Universit ät Kiel (1994)Google Scholar
  4. [BHL99]
    Berghammer, R., Hoffmann, T., Leoniuk, B.: Rechnergest ützte Erstellung von Prototypen für Programme auf relationalen Strukturen. Technical Report 9905, Institut für Informatik und praktische Mathematik, Christian-Albrechts-Universität Kiel (July 1999)Google Scholar
  5. [BW01]
    Bauer, G., Wenzel, M.: Calculational reasoning revisited, an Isabelle/Isar experience. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 75–90. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. [Des03]
    Desharnais, J.: Kleene algebras with relations. In: Berghammer, R., Möller, B. (eds.) Proc. RelMiCS 7, International Seminar on Relational Methods in Computer Science, in combination with the 2nd Intl. Workshop on Applications of Kleene Algebra. LNCS, Springer, Heidelberg (2003) (Invited Talk)Google Scholar
  7. [DG00]
    Dougherty, D., Gutiérrez, C.: Normal forms and reduction for theories of binary relations. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 95–109. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. [DM01]
    Desharnais, J., Möller, B.: Characterizing determinacy in Kleene algebras. Information Sciences 139, 253–273 (2001)MATHCrossRefMathSciNetGoogle Scholar
  9. [DMS03]
    Desharnais, J., Möller, B., Struth, G.: Kleene algebra with domain. Technical Report 2003-7, Universität Augsburg, Institut für Informatik (2003)Google Scholar
  10. [dS02]
    de Swart, H.C.M. (ed.): RelMiCS 2001. LNCS, vol. 2561. Springer, Heidelberg (2002)MATHGoogle Scholar
  11. [FS90]
    Freyd, P.J., Scedrov, A.: Categories, Allegories. North-Holland Mathematical Library, vol. 39. North-Holland, Amsterdam (1990)MATHGoogle Scholar
  12. [Fur98]
    Furusawa, H.: Algebraic Formalisations of Fuzzy Relations and Their Representation Theorems. PhD thesis, Department of Informatics, Kyushu University (March 1998)Google Scholar
  13. [HBS94]
    Hattensperger, C., Berghammer, R., Schmidt, G.: RALF – A relation-algebraic formula manipulation system and proof checker. Notes to a system demonstration. In: Nivat, M., Rattray, C., Rus, T., Scollo, G. (eds.) AMAST 1993, Workshops in Computing, pp. 405–406. Springer, Heidelberg (1994)Google Scholar
  14. [Jip01]
    Jipsen, P.: Implementing quasi-equational logic on the web. In: Talk given at the AMS Sectional Meeting, University of South Carolina, March 16-18 (2001), http://www.chapman.edu/~jipsen/PCP/usctalk.html
  15. [Jip03]
    Jipsen, P.: PCP: Point and click proofs (2003), Web-based system at http://www.chapman.edu/~jipsen/PCP/PCPhome.html
  16. [Kah01]
    Kahl, W.: A relation-algebraic approach to graph structure transformation, Habil. Thesis, Fakultät für Informatik, Univ. der Bundeswehr München, Techn. Bericht 2002-03 (2001)Google Scholar
  17. [Kah02]
    Kahl, W.: A relation-algebraic approach to graph structure transformation. In: de Swart [dS02], pp. 1–14 (Invited Talk)Google Scholar
  18. [KH98]
    Kahl, W., Hattensperger, C.: Second-order syntax in HOPS and in RALF. In: Buth, B., Berghammer, R., Peleska, J. (eds.) Tools for System Development and Verification. BISS Monographs, vol. 1, pp. 140–164. Shaker Verlag, Aachen (1998) ISBN: 3-8265- 3806-4Google Scholar
  19. [Koz91]
    Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inform. and Comput. 110(2), 366–390 (1991)CrossRefMathSciNetGoogle Scholar
  20. [Koz94]
    Kozen, D.: On action algebras. In: van Eijck, J., Visser, A. (eds.) Logic and Information Flow, pp. 78–88. MIT Press, Cambridge (1994)Google Scholar
  21. [Koz97]
    Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems, 427–443 (May 1997)Google Scholar
  22. [Koz98]
    Kozen, D.: Typed Kleene algebra. Technical Report 98-1669, Computer Science Department, Cornell University (March 1998)Google Scholar
  23. [KS00]
    Kahl, W., Schmidt, G.: Exploring (finite) Relation Algebras using Tools written in Haskell. Technical Report 2000-02, Fakultät für Informatik, Universität der Bundeswehr München (October 2000), see also the RATH page http://ist.unibw-muenchen.de/relmics/tools/RATH/
  24. [KWP99]
    Kammüller, F., Wenzel, M., Paulson, L.C.: Locales - a sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–166. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  25. [Nip03]
    Nipkow, T.: Structured proofs in Isar/HOL. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 259–278. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  26. [NPW02]
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)MATHCrossRefGoogle Scholar
  27. [SHW97]
    Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous relation algebra. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, Advances in Computing Science, ch. 3, pp. 39–53. Springer, New York (1997)Google Scholar
  28. [SS93]
    Schmidt, G., Ströhlein, T.: Relations and Graphs, Discrete Mathematics for Computer Scientists. EATCS-Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)MATHGoogle Scholar
  29. [Str02]
    Struth, G.: Calculating Church-Rosser proofs in Kleene algebra. In: de Swart [dS02], pp. 276–290Google Scholar
  30. [VB99]
    Verhoeven, R., Backhouse, R.: Towards tool support for program verification and construction. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1128–1146. Springer, Heidelberg (1999)Google Scholar
  31. [vOG97]
    von Oheimb, D., Gritzner, T.F.: RALL: Machine-supported proofs for relation algebra. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 380–394. Springer, Heidelberg (1997)Google Scholar
  32. [Wen97]
    Wenzel, M.: Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 307–322. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  33. [Wen02]
    Wenzel, M.M.: Isabelle/Isar - A Versatile Environment for Human- Readable Formal Proof Documents. PhD thesis, Technische Universität München, Fakultät für Informatik (February 2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Wolfram Kahl
    • 1
  1. 1.Department of Computing and SoftwareMcMaster University 

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