Abstract
The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect to four schema operations for three notions of operation refinement. The mathematical connection between the equational schema logic and monotonicity is discussed and evaluated.
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References
C. Bolton, J. Davies, and J. C. P. Woodcock. On the refinement and simulation of data types and processes. In K. Araki, A. Galloway, and K. Taguchi, editors, Integrated Formal Methods (IFM’99). Springer, 1999.
A. Cavalcanti. A Refinement Calculus for Z. PhD thesis, University of Oxford, 1997.
A. Cavalcanti and J. C. P. Woodcock. ZRC — a refinement calculus for Z. Formal Aspects of Computing, 10(3):267–289, 1998.
J. Derrick and E. Boiten. Refinement in Z and Object-Z: Foundations and Advanced Applications. Formal Approaches to Computing and Information Technology — FACIT. Springer, May 2001.
M. Deutsch, M. C. Henson, and S. Reeves. An analysis of total correctness refinement models for partial relation semantics I. University of Essex, technical report CSM-362, 2001. To appear in the Logic Journal of the IGPL.
M. Deutsch, M. C. Henson, and S. Reeves. Results on formal stepwise design in Z. In 9th Asia Pacific Software Engineering Conference (APSEC 2002), pages 33–42. IEEE Computer Society Press, December 2002.
M. Deutsch, M. C. Henson, and S. Reeves. Operation refinement and monotonicity in the schema calculus. University of Essex, technical report CSM-381, February 2003.
A. Diller. Z: An Introduction to Formal Methods. J. Wiley and Sons, 2nd edition, 1994.
L. Groves. Evolutionary Software Development in the Refinement Calculus. PhD thesis, Victoria University, 2000.
L. Groves. Refinement and the Z schema calculus. In REFINE 2002: Refinement Workshop. BCS FACS, July 2002.
J. Grundy. A Method of Program Refinement. PhD thesis, University of Cambridge, 1993.
I. Hayes. Specification Case Studies. Prentice Hall, 2nd edition, 1993.
M. C. Henson and S. Reeves. Investigating Z. Logic and Computation, 10(1):43–73, 2000.
M. C. Henson and S. Reeves. Program development and specification refinement in the schema calculus. In J. P. Bowen, S. Dunne, A. Galloway, and S. King, editors, ZB 2000: Formal Speci.cation and Development in Z and B, volume 1878 of Lecture Notes in Computer Science, pages 344–362. Springer, 2000.
M. C. Henson and S. Reeves. A logic for schema-based program development. University of Essex, technical report CSM-361, 2001. To appear in the Journal of Formal Aspects of Computing.
J. Jacky. Formal specification of control software for a radiation therapy machine. Radiation Oncology Department, University of Washington, technical report 94-07-01, 1994.
S. King. Z and the Refinement Calculus. In D. Bjørner, C. A. R. Hoare, and H. Langmaack, editors, VDM’ 90 VDM and Z — Formal Methods in Software Development, volume 428 of Lecture Notes in Computer Science, pages 164–188. Springer-Verlag, April 1990.
B. P. Mahony. The least conjunctive refinement and promotion in the refinement calculus. Formal Aspects of Computing, 11:75–105, 1999.
B. Potter, J. Sinclair, and D. Till. An Introduction to Formal Specification and Z. Prentice Hall, 2nd edition, 1996.
J. M. Spivey. The Z Notation: A Reference Manual. Prentice Hall, 2nd edition, 1992.
B. Strulo. How firing conditions help inheritance. In J. P. Bowen and M. G. Hinchey, editors, ZUM’ 95: The Z Formal Specification Notation, volume 967 of Lecture Notes in Computer Science, pages 264–275. Springer Verlag, 1995.
M. Utting. Private communication. Department of Computer Science, University of Waikato, Hamilton, New Zealand, June 2002.
N. Ward. Adding specification constructors to the refinement calculus. In J. C. P. Woodcock and P. G. Larsen, editors, Formal Methods Europe (FME’ 93), volume 670 of Lecture Notes in Computer Science, pages 652–670. Springer-Verlag, 1993.
J. C. P. Woodcock. Calculating properties of Z specifications. ACM SIGSOFT Software Engineering Notes, 14(5):43–54, 1989.
J. C. P. Woodcock. Implementing promoted operations in Z. In C. B. Jones, R. C. Shaw, and T. Denvir, editors, 5th Refinement Workshop, Workshops in Computing, pages 367–378. Springer-Verlag, 1992.
J. C. P. Woodcock and J. Davies. Using Z: Specification, Refinement and Proof. Prentice Hall, 1996.
J. B. Wordsworth. Software Development with Z — A Practical Approach to Formal Methods in Software Engineering. Internalional Computer Science Series. Addison-Wesley, 1992.
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Deutsch, M., Henson, M.C., Reeves, S. (2003). Operation Refinement and Monotonicity in the Schema Calculus. In: Bert, D., Bowen, J.P., King, S., Waldén, M. (eds) ZB 2003: Formal Specification and Development in Z and B. ZB 2003. Lecture Notes in Computer Science, vol 2651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44880-2_9
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DOI: https://doi.org/10.1007/3-540-44880-2_9
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