Abstract
In previous work, based on an original idea due to Saaltink, we proposed a unifying theory of undefined expressions in logics used for formally specifying software systems. In our current paper, we instantiate these ideas in Hoare and He’s Unifying Theories of Programming, with each different treatment of undefinedness formalized as a UTP theory. In this setting, we show how to use classical logic to prove facts in a monotonic partial logic with guards, and we describe the guards for several different UTP theories. We show how classical logic can be used to prove semi-classical facts. We apply these ideas to the COMPASS Modelling Language (CML), which is an integration of VDM and CSP in the Circus tradition. We link CML, which uses McCarthy’s left-to-right expression evaluation, and to VDM, which uses Jones’s three-valued Logic of Partial Functions.
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References
Agerholm, S., Frost, J.: An Isabelle-based Theorem Prover for VDM-SL. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 1–16. Springer, Heidelberg (1997)
Bergmann, M.: An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras and Derivation Systems. Cambridge University Press (2008)
Bergstra, J.A., Bethke, I., Rodenburg, P.: A propositional logic with 4 values: true, false, divergent and meaningless. Journal of Applied NonClassical Logics 5, 199–217 (1995)
Bochvar, D.A., Bergmann, M.: On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus. History and Philosophy of Logic 2(1), 87–112 (1981)
Goldsmith, M.: FDR2 user’s manual. Technical Report Version 2.82. Formal Systems (Europe) Ltd. (2005)
Gordon, M., Wadsworth, C.P., Milner, R.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)
Hoare, C.A.R., He, J.: Unifying Theories of Programming. Series in Computer Science. Prentice Hall (1998)
Larsen, P.G., Battle, N., Ferreira, M.A., Fitzgerald, J.S., Lausdahl, K., Verhoef, M.: The Overture initiative: integrating tools for VDM. ACM SIGSOFT Software Engineering Notes 35, 1–6 (2010)
Rose, A.: A lattice-theoretic characterisation of three-valued logic. Journal of the London Mathematical Society 25, 255–259 (1950)
Saaltink, M.: The Z/EVES System. In: Bowen, J.P., Hinchey, M.G., Till, D. (eds.) ZUM 1997. LNCS, vol. 1212, pp. 72–85. Springer, Heidelberg (1997)
Woodcock, J., Saaltink, M., Freitas, L.: Unifying theories of undefinedness. In: Summer School Marktoberdorf 2008: Engineering Methods and Tools for Software Safety and Security. NATO ASI Series F. IOS Press, Amsterdam (2009)
Woodcock, J., Freitas, L.: Linking VDM and Z. In: Hinchey, M. (ed.) ICECCS, pp. 143–152. IEEE Computer Society (2008)
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Woodcock, J., Bandur, V. (2013). Unifying Theories of Undefinedness in UTP. In: Wolff, B., Gaudel, MC., Feliachi, A. (eds) Unifying Theories of Programming. UTP 2012. Lecture Notes in Computer Science, vol 7681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35705-3_1
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DOI: https://doi.org/10.1007/978-3-642-35705-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35704-6
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