Abstract
The B-Method provides a collection of structuring mechanisms which support information hiding, modularisation and compositionality of module operations, although, in order to achieve compositionality and independent (parallel) refinement, sharing is restricted in B. In this paper we elaborate some non-interference and compositionality assumptions that underlie structuring mechanisms such as uses, sees and imports and show how they may be violated by inducing emerging properties which alter the context of the used, seen or imported machine. We discuss how such situations can be avoided by considering necessary and sufficient conditions for logical conservativeness and modularisation. As proof obligations, these conditions ensure that the properties of the context of the seen, used or imported component are conserved, i.e. that they are preserved but not enriched. From a logical viewpoint, these proof obligations require that the uniform interpolant of the contextual extension axioms is implied by the base context.
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References
J.R. Abrial. The B-Book: Assigning Programs to Meanings. C.U.P., 1996.
B-CORE (UK) Ltd. The b-toolkit. 1999. URL: http://www.b-core.com.
J. Barwise, D. Gabbay, and C. Hartonas. On the logic of information flow. Bulletin Of The IGPL, 3(1):7–49, 1995.
D. Bert, M-L. Potet, and Y. Rouzaud. A study on Components and Assembly primitives in B. In H. Habrias, ed., First Conference on the B-Method, 1996.
J.C. Bicarregui. Non-Interference, Security and Bisimulation: explorations into the roles of Read and Write frames. CLRC-RAL, 1998.
J.C. Bicarregui and et al. Formal Methods Into Practice: case studies in the application of the B Method. I.E.E. Transactions on Software Engineering, 1997.
J.C. Bicarregui, J. Dick, B. Matthews, and E. Woods. Making the most of formal specification through animation, testing and proof. Sci. of Comp. Prog., 1997.
J. van Benthem. Modality, bisimulation and interpolation in infinitary logic. ANNALSPAL: Annals of Pure and Applied Logic, 96, 1999.
M. Buchi and B. Back. Compositional Symmetric Sharing in B. In FM’99-Formal Methods, volume I of LNCS, pages 431–451. Springer, Septermber 1999.
D. Clutterbuck, J.C. Bicarregui, and B.M. Matthews. Experiences with proof in formal development. In H. Habrias, ed., First Conference on the B-Method, 1996.
W. Craig. Three uses of the Herbrand-Getzen theorem in relating model theory and proof theory. Journal of Symbolic Logic XXII, pages 269–285, 1957.
G. D’Agostino, A. Montanari, and A. Policriti. A set-theoretic translation method for (poly)modal logics. Lecture Notes in Computer Science 900, 1995.
Th. Dimitrakos and T.S.E. Maibaum. Notes on refinement, interpolation and uniformity. In ASE’97, 12th IEEE Int. Conf., 1997.
Theodosis Dimitrakos. Formal support for specification design and implementation. PhD thesis, Imperial College, March 1998.
Theodosis Dimitrakos. Parameterising specifications on diagrams. In ASE’98, 13th IEEE Int. Conf., 1998.
Theodosis Dimitrakos and Tom Maibaum. On a generalised modularisation theorem. Information Processing Letters, 74(1–2):65–71, 2000.
S. Dunne. The Safe Machine: A New Specification Construct for B. In FM’99-Formal Methods, volume I of LNCS, pages 472–489. Springer, Septermber 1999.
H. B. Enderton. A Mathematical Introduction to Logic. Academic Press, 1972.
Cliff B. Jones. Accomodating interference in the formal design of concurrent object-based programs. Formal Methods in System Design, 8(2):105–122, March 1996.
Kevin Lano. The B Language and Method. Springer-Verlag, 1996.
P.J. Lupton. Promotin Forward Simulation. In J.E. Nicholls, editor, Z User Workshop, pages 27–49. Springer-Verlag, Oxford 1990.
B. Matthews, B. Ritchie, and J. Bicarregui. Synthesising structure from flat specifications. In 2nd International B Conference, LNCS, 1998.
M.C. Mere and P.A.S. Veloso. Definition-like extensions by sorts Bulletin of the IGPL, 3:579–595, 1995.
B. Meyer. Object Oriented Construction. Prentice-Hall, 1988.
M-L. Potet and Y. Rouzaud. Composition and Refinement in the B-Method. In D. Bert, editor, Second B International Conference, pages 46–65, 1998.
Yann Rouzaud. Interpreting the B-Method in the Refinement Calculus. In J. Wing, J. Woodcock, and J. Davies, editors, FM’99-Formal Methods, vol. I, 1999.
P.Y.A Ryan and S.A. Schneider. Process algebra and non-interference. In PCSFW: Proc. of The 12th Computer Security Foundations Workshop. IEEE Comp. Soc. Press, 1999.
Ketil Stølen. Development of Parallel Programs on Shared Data-Structures. PhD thesis, University of Manchester, 1990. Available as a technical report UMCS-91-1-1.
Wladyslaw M. Turski and Thomas S. E. Maibaum. The Specification of Computer Programs. Addison-Wesley, 1987.
P.A.S. Veloso and T.S.E. Maibaum. On the modularisation theorem for logical specifications. Information Processing Letters 53, pages 287–293, 1995.
P.A.S. Veloso and S.R.M. Veloso. On extensions by function symbols: coservativeness and comparison. Tech. Report. COPPE/UFRJ. 1990. (See also [23,32])
P.A.S. Veloso and S.R.M. Veloso. Some remarks on conservative extensions: a Socratic dialogue. Bulletin of the EATCS, vol. 43, 1991.
J.C.P. Woodcock. Mathematics as a Management Tool: Proof Rules for Promotion. In CSR Sixth Annual Conference on Large Sofware Systems. Bristol, 1989.
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Dimitrakos, T., Bicarregui, J., Matthews, B., Maibaum, T. (2000). Compositional Structuring in the B-Method: A Logical Viewpoint of the Static Context. In: ZB 2000: Formal Specification and Development in Z and B. ZB 2000. Lecture Notes in Computer Science, vol 1878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44525-0_8
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