Abstract
This paper presents a mathematical investigation of the relationships among a number of approaches for specification and refinement in two well-known paradigms based on the idea of Unifying Theories of Programming: Hoare and He’s designs and Dunne’s prescriptions. We present the technical analysis in a proof-theoretic relational framework based on two-predicate schema specifications. This enables us to demonstrate the relationships among (what prima facie seem to be) different models of refinement associated with each of these paradigms.
This is a preview of subscription content, log in via an institution to check access.
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
Azada, D., Muenchaisri, P. (eds.): APSEC 2003: Proceedings of the 10th Asia-Pacific Software Engineering Conference, Chiangmai, Thailand, December 10-12. IEEE Computer Society Press, Los Alamitos (2003)
Bjørner, D., Hoare, C.A.R., Langmaack, H.: VDM 1990. LNCS, vol. 428. Springer, Heidelberg (1990)
Bert, D., Bowen, J.P., King, S., Waldén, M. (eds.): ZB 2003. LNCS, vol. 2651. Springer, Heidelberg (2003)
Derrick, J., Boiten, E.A.: Refinement in Z and Object-Z: Foundations and Advanced Applications. In: Formal Approaches to Computing and Information Technology – FACIT. Springer, Heidelberg (2001)
Derrick, J., Boiten, E.A. (eds.): REFINE 2005 International Workshop. Electronic Notes in Theoretical Computer Science. BCS-FACS (April 2005)
Deutsch, M.: An Analysis of Total Correctness Refinement Models for Partial Relation Semantics. PhD thesis, University of Essex (2005)
Deutsch, M., Henson, M.C.: An Analysis of Backward Simulation Data-Refinement for Partial Relation Semantics. In: APSEC 2003 [1], pp. 38–48 (2003)
Deutsch, M., Henson, M.C.: An Analysis of Forward Simulation Data Refinement. In: ZB 2003 [3], pp. 148–167 (2003)
Deutsch, M., Henson, M.C.: An Analysis of Operation-Refinement in an Abortive Paradigm. In: REFINE 2005 [5] (2005)
Deutsch, M., Henson, M.C., Reeves, S.: Results on Formal Stepwise Design in Z. In: Strooper, P., Muenchaisri, P. (eds.) APSEC 2002: Proceeding of the 9th Asia-Pacific Software Engineering Conference, Gold Coast, Queensland, Australia, December 4-6, pp. 33–42. IEEE Computer Society Press, Los Alamitos (2002)
Deutsch, M., Henson, M.C., Reeves, S.: An analysis of total correctness refinement models for partial relation semantics I. Logic Journal of the IGPL 11(3), 287–317 (2003)
Deutsch, M., Henson, M.C., Reeves, S.: Modular reasoning in Z: scrutinising monotonicity and refinement. University of Essex, technical report CSM-407 (under consideration of FACJ) (December 2003)
Deutsch, M., Henson, M.C., Reeves, S.: Operation Refinement and Monotonicity in the Schema Calculus. In: ZB 2003 [3], pp. 103–126 (2003)
Diller, A.: Z: An Introduction to Formal Methods, 2nd edn. J. Wiley and Sons, Chichester (1994)
Dunne, S.E.: Recasting Hoare and He’s Unifying Theory of Programs in the Context of General Correctness. In: Butterfield, A., Strong, G., Pahl, C. (eds.) IWFM 2001: 5th Irish Workshop on Formal Methods, Dublin, Ireland, July 16-17, Workshops in Computing. BCS (2001)
Dunne, S.E.: A Predicative Model for General Correctness. Departmental Seminar, Department of Computer Science, University of Essex (March 2004)
Groves, L.J.: Evolutionary Software Development in the Refinement Calculus. PhD thesis, Victoria University (2000)
Hehner, E.C.R.: The Logic of Programming. Prentice Hall International, Englewood Cliffs (1984)
Henson, M.C., Deutsch, M., Kajtazi, B.: The Specification Logic vZ. University of Essex, technical report CSM-421 (2004)
Henson, M.C., Kajtazi, B.: The Specification Logic vZ. In: REFINE 2005 [5] (2005)
Henson, M.C., Reeves, S.: Investigating Z. Logic and Computation 10(1), 43–73 (2000)
Henson, M.C., Reeves, S.: A logic for schema-based program development. Formal Aspects of Computing 15(1), 84–99 (2003)
Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International, Englewood Cliffs (1998)
King, S.: Z and the Refinement Calculus. In: VDM 1990 [2], pp. 164–188 (1990)
Potter, B., Sinclair, J., Till, D.: An Introduction to Formal Specification and Z, 2nd edn. Prentice Hall, Englewood Cliffs (1996)
Spivey, J.M.: The Z Notation: A Reference Manual, 2nd edn. Prentice-Hall, Englewood Cliffs (1992)
Toyn, I. (ed.): Z Notation: Final Committee Draft, CD 13568.2. Z Standards Panel (1999)
Woodcock, J.C.P., Davies, J.: Using Z: Specification, Refinement and Proof. Prentice-Hall, Englewood Cliffs (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deutsch, M., Henson, M.C. (2006). A Relational Investigation of UTP Designs and Prescriptions. In: Dunne, S., Stoddart, B. (eds) Unifying Theories of Programming. UTP 2006. Lecture Notes in Computer Science, vol 4010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11768173_7
Download citation
DOI: https://doi.org/10.1007/11768173_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34750-7
Online ISBN: 978-3-540-34752-1
eBook Packages: Computer ScienceComputer Science (R0)