Abstract
In this paper, we present a formalisation of the reference semantics of Object-Z in the higher-order logic (HOL) instantiation of the generic theorem prover Isabelle, Isabelle/HOL. This formalisation has the effect of both clarifying the semantics and providing the basis for a theorem prover for Object-Z. The work builds on an earlier encoding of a value semantics for object-oriented Z in Isabelle/HOL and a denotational semantics of Object-Z based on separating the internal and external effects of class methods.
An inductive definition specifies the smallest set consistent with a given set of rules. A co-inductive definition specifies the greatest set.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Barendregt. Lambda calculi with types. In Handbook of Logic in Computer Science, Vol. 2. Oxford University Press, 1992.
J. Bowen and M. Gordon. A shallow embedding of Z in HOL. Information and Software Technology, 37(5–6):269–276, 1995.
M.J.C. Gordon and T.F. Melham, editors. Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, 1993.
A. Griffiths. A Formal Semantics to Support Modular Reasoning in Object-Z. PhD thesis, University of Queensland, 1997.
A. Griffiths. Object-oriented operations have two parts. In D.J. Duke and A.S. Evans, editors, 2nd BCS-FACS Northern Formal Methods Workshop, Electronic Workshops in Computing. Springer-Verlag, 1997.
F. Kammüller. Modular Reasoning in Isabelle. PhD thesis, Computer Laboratory, University of Cambridge, 1999. Technical Report 470.
Kolyang, T. Santen, and B. Wolff. A structure preserving encoding of Z in Isabelle/ HOL. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics (TPHOLs 96), volume 1125 of Lecture Notes in Computer Science, pages 283–298. Springer-Verlag, 1996.
L.C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.
T. Santen. A theory of structured model-based specifications in Isabelle/HOL. In E.L. Gunter and A. Felty, editors, Theorem Proving in Higher-Order Logics (TPHOLs 97), volume 1275 of Lecture Notes in Computer Science, pages 243–258. Springer-Verlag, 1997.
T. Santen. On the semantic relation of Z and HOL. In J. Bowen and A. Fett, editors, ZUM’98: The Z Formal Specification Notation, LNCS 1493, pages 96–115. Springer-Verlag, 1998.
T. Santen. Isomorphisms-a link between the shallow and the deep. In Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Théry, editors, Theorem Proving in Higher Order Logics, LNCS 1690, pages 37–54. Springer-Verlag, 1999.
T. Santen. A Mechanized Logical Model of Z and Object-Oriented Specification. Shaker-Verlag, 2000. Dissertation, Fachbereich Informatik, Technische Universität Berlin, (1999).
G. Smith. The Object-Z Specification Language. Kluwer Academic Publishers, 2000.
G. Smith. Recursive schema definitions in Object-Z. In A. Galloway J. Bowen, S. Dunne and S. King, editors, International Conference of B and Z Users (ZB 2000), volume 1878 of Lecture Notes in Computer Science, pages 42–58. Springer-Verlag, 2000.
H. Tej and B. Wolff. A corrected failure-divergence model for CSP in Isabelle/HOL. In J. Fitzgerald, C.B. Jones, and P. Lucas, editors, Formal Methods Europe (FME 97), volume 1313 of Lecture Notes in Computer Science, pages 318–337. Springer-Verlag, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Smith, G., Kammüller, F., Santen, T. (2002). Encoding Object-Z in Isabelle/HOL. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds) ZB 2002:Formal Specification and Development in Z and B. ZB 2002. Lecture Notes in Computer Science, vol 2272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45648-1_5
Download citation
DOI: https://doi.org/10.1007/3-540-45648-1_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43166-4
Online ISBN: 978-3-540-45648-3
eBook Packages: Springer Book Archive