Abstract
Data refinements are refinement steps in which a program’s local data structures are changed. Data refinement proof obligations require the software designer to find an abstraction relation that relates the states of the original and new program. In this paper we describe an algorithm that helps a designer find an abstraction relation for a proposed refinement. Given sufficient time and space, the algorithm can find a minimal abstraction relation, and thus show that the refinement holds. As it executes, the algorithm displays mappings that cannot be in any abstraction relation. When the algorithm is not given sufficient resources to terminate, these mappings can help the designer find a suitable abstraction relation. The same algorithm can be used to test an abstraction relation supplied by the designer.
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
Back, R.-J.R.: Refinement of parallel and reactive programs. Technical Report Caltech-CS-TR-92-93, Computer Science Department, California Institute of Technology (1992)
Back, R.-J.R., von Wright, J.: Trace refinement of action systems. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 367–384. Springer, Heidelberg (1994)
Back, R.-J.R., von Wright, J.: Contracts, games and refinement. Information and Computation 156, 25–45 (2000)
Back, R.-J.R., von Wright, J.: Encoding, decoding and data refinement. Formal Aspects of Computing 12, 313–349 (2000)
Bensalem, S., Lakhnech, Y., Owre, S.: Computing abstractions of infinite state systems compositionally and automatically. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 319–331. Springer, Heidelberg (1998)
Butler, M.: On the use of data refinement in the development of secure communications systems. Formal Aspects of Computing 14(1), 2–34 (2002)
Doche, M., Gravell, A.: Extraction of abstraction invariants for data refinement. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 120–139. Springer, Heidelberg (2002)
Lange, M., Stirling, C.: Model checking games for branching time logics. Journal of Logic and Computation 12, 623–639 (2002)
Morgan, C., Gardiner, P.H.B.: Data refinement by calculation. Acta Informatica 27(6), 481–503 (1989)
Robinson, N.J.: Checking Z data refinements using an animation tool. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) B 2002 and ZB 2002. LNCS, vol. 2272, pp. 62–81. Springer, Heidelberg (2002)
Robinson, N.J.: Finding abstraction relations for data refinement. Technical Report TR03-03, Software Verification Research Centre, School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane 4072, Australia (February 2003), http://www.itee.uq.edu.au/~njr/tr0303.pdf
Robinson, N.J., Fidge, C.: Animation of data refinements. In: Proceedings of the Asia-Pacific Software Engineering Conference, APSEC 2002, Gold Coast, Australia, December 2002, pp. 137–146. IEEE Computer Society Press, Los Alamitos (2002)
von Wright, J.: Data refinement and the simulation method. Technical Report Ser. A, No. 137, Abo Akademi (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Robinson, N.J. (2003). Incremental Derivation of Abstraction Relations for Data Refinement. In: Dong, J.S., Woodcock, J. (eds) Formal Methods and Software Engineering. ICFEM 2003. Lecture Notes in Computer Science, vol 2885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39893-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-39893-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20461-9
Online ISBN: 978-3-540-39893-6
eBook Packages: Springer Book Archive