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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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
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)
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)
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)
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)
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)
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)
Desharnais, J., Möller, B.: Characterizing determinacy in Kleene algebras. Information Sciences 139, 253–273 (2001)
Desharnais, J., Möller, B., Struth, G.: Kleene algebra with domain. Technical Report 2003-7, Universität Augsburg, Institut für Informatik (2003)
de Swart, H.C.M. (ed.): RelMiCS 2001. LNCS, vol. 2561. Springer, Heidelberg (2002)
Freyd, P.J., Scedrov, A.: Categories, Allegories. North-Holland Mathematical Library, vol. 39. North-Holland, Amsterdam (1990)
Furusawa, H.: Algebraic Formalisations of Fuzzy Relations and Their Representation Theorems. PhD thesis, Department of Informatics, Kyushu University (March 1998)
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)
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
Jipsen, P.: PCP: Point and click proofs (2003), Web-based system at http://www.chapman.edu/~jipsen/PCP/PCPhome.html
Kahl, W.: A relation-algebraic approach to graph structure transformation, Habil. Thesis, Fakultät für Informatik, Univ. der Bundeswehr München, Techn. Bericht 2002-03 (2001)
Kahl, W.: A relation-algebraic approach to graph structure transformation. In: de Swart [dS02], pp. 1–14 (Invited Talk)
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- 3806-4
Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inform. and Comput. 110(2), 366–390 (1991)
Kozen, D.: On action algebras. In: van Eijck, J., Visser, A. (eds.) Logic and Information Flow, pp. 78–88. MIT Press, Cambridge (1994)
Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems, 427–443 (May 1997)
Kozen, D.: Typed Kleene algebra. Technical Report 98-1669, Computer Science Department, Cornell University (March 1998)
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/
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)
Nipkow, T.: Structured proofs in Isar/HOL. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 259–278. Springer, Heidelberg (2003)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
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)
Schmidt, G., Ströhlein, T.: Relations and Graphs, Discrete Mathematics for Computer Scientists. EATCS-Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)
Struth, G.: Calculating Church-Rosser proofs in Kleene algebra. In: de Swart [dS02], pp. 276–290
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)
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)
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)
Wenzel, M.M.: Isabelle/Isar - A Versatile Environment for Human- Readable Formal Proof Documents. PhD thesis, Technische Universität München, Fakultät für Informatik (February 2002)
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Kahl, W. (2004). Calculational Relation-Algebraic Proofs in Isabelle/Isar. In: Berghammer, R., Möller, B., Struth, G. (eds) Relational and Kleene-Algebraic Methods in Computer Science. RelMiCS 2003. Lecture Notes in Computer Science, vol 3051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24771-5_16
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DOI: https://doi.org/10.1007/978-3-540-24771-5_16
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