Modular structuring of VDM specifications in VVSL

Abstract

Abstract

VVSL is a language for writing modularly structured VDM specifications. Its modularisation mechanism permits two modules to have parts of their state in common, including hidden parts. Firstly, this paper gives an overview of the structuring sublanguage of VVSL and a concise description of its semantic foundations: DA (a general algebraic model of modules) andλπ-calculus (a variant of classical lambda calculus). The paper also presents a variation on a “challenge problem” of Fitzgerald and Jones as an example of the use of VVSL's structuring language. Finally, their modular structuring style and the suggested language features to support it are commented upon.

References

1. [BCJ84] Barringer H.Cheng H.Jones C.B.A Logic Covering Undefinedness in Program ProofsActa Informatica198421251269
2. [Bea88] Bear, S.: Structuring for the VDM Specification Language. In:VDM '88, R. Bloomfield, L. Marshall and R. Jones (eds), LNCS 328, Springer-Verlag, pp. 2–25, 1988.
3. [Ber86] Bergstra, J.A.: Module Algebra for Relational Specifications, Technical Report LGPS 16, University of Utrecht, Logic Group, 1986.
4. [BHK90] Bergstra J.A.Heering J.Klint P.Module AlgebraJournal of the ACM199037335372
5. [Bjø82] Bjørner, D.: Formalization of Data Models. In:Formal Specification and Software Development, D. Bjørner and C.B. Jones (eds), ch. 12, Prentice-Hall, 1982.
6. [BrS81] Brodie, M.L. and Schmidt, J.W.: Final Report of the ANSI/X3/SPARC DBS-SG Relational Database Task Group, Doc. SPARC-81-690, 1981.
7. [BSI91] BSI IST/5/50: VDM Specification Language Proto-Standard (draft), BSI, 1991.
8. [Cod70] Codd E.F.A Relational Model for Large Shared Data BanksCommunications of the ACM197013377387
9. [Cod72] Codd, E.F.: Relational Completeness of Data Base Sublanguages. In:Data Base Systems, R. Rustin (ed.), pp. 65–98, Prentice-Hall, 1972.
10. [Fag81] Fagin R.A Normal Form for Relational Databases that is Based on Domains and KeysACM Transactions on Database Systems19816387415
11. [Fei89] Feijs, L.M.G., The calculusλπ. In:Algebraic Methods: Theory, Tools and Applications, M. Wirsing and J.A. Bergstra (eds), LNCS 394, Springer-Verlag, pp. 307–328, 1989.
12. [FJK89] Feijs, L.M.G., Jonkers, H.B.M., Koymans, C.P.J. and Renardel de Lavalette, G.R.: Formal Definition of the Design Language COLD-K (revised edn), Technical Report, Philips Research Laboratories Eindhoven, 1989.
13. [FiJ90] Fitzgerald, J.S. and Jones, C.B.: Modularizing the formal description of a database system. In:VDM '90, D. Bjørner, C.A.R. Hoare and H. Langmaack (eds), LNCS 428, Springer-Verlag, pp. 189–210, 1990.
14. [Jon86] Jones, C.B.:Systematic Software Development Using VDM (1st edn), Prentice-Hall, 1986.
15. [Jon90] Jones, C.B.:Systematic Software Development Using VDM (2nd edn), Prentice-Hall, 1990.
16. [Jon89a] Jonkers, H.B.M.: An introduction to COLD-K. In:Algebraic Methods: Theory, Tools and Applications, M. Wirsing and J.A. Bergstra (eds), LNCS 394, Springer-Verlag, pp. 139–205, 1989.
17. [Jon89b] Jonkers, H.B.M.: Description Algebra. In:Algebraic Methods: Theory, Tools and Applications, M. Wirsing and J.A. Bergstra (eds), LNCS 394, Springer-Verlag, pp. 283–305, 1989.
18. [Kar64] Karp, C:Languages with Expressions of Infinite Length, North-Holland, 1964.
19. [KoR89] Koymans, C.P.J. and Renardel de Lavalette, G.R.: The logic MPL_ω. In:Algebraic Methods: Theory, Tools and Applications, M. Wirsing and J.A. Bergstra (eds), LNCS 394, Springer-Verlag, pp. 247–282, 1989.
20. [Lar90] Larsen, P.G.: The Dynamic Semantics of the BSI/VDM Specification Language, Technical Report, IFAD, August 1990.
21. [Mid88] Middelburg, C.A.: The VIP VDM Specification Language. In:VDM '88, R. Bloomfield, L. Marshall and R. Jones (eds), LNCS 328, pp. 187–201, Springer-Verlag, 1988.
22. [Mid89] Middelburg C.A.VVSL: A Language for Structured VDM SpecificationsFormal Aspects of Computing19891115135
23. [Mid90] Middelburg, C.A.: Syntax and Semantics of VVSL — A Language for Structured VDM Specifications, PhD thesis, University of Amsterdam, 1990. Available from PTT Research, Dr. Neher Laboratories.
24. [Mid91] Middelburg, C.A.: Specification of Interfering Programs Based on Inter-conditions, Pub. 166/91, PTT Research, 1991.
25. [Ren89] Renardel de Lavalette, G.R.: COLD-K2, the static kernel of COLD-K, Report RP/mod-89/8, Software Engineering Research Centrum, 1989.
26. [SaT85] Sannella, D. and Tarlecki, A.: Building Specifications in an Arbitrary Institution. In:Semantics of Data Types, G. Kahn, D.B. MacQueen and G. Plotkin (eds), LNCS 173, Springer-Verlag, pp. 337–356, 1985.
27. [Tod76] Todd S.J.P.The Peterlee Relational Test Vehicle — a System OverviewIBM Systems Journal197615285308
28. [U1188] Ullman, J.D.:Principles of Database and Knowledge-base Systems, Vol. I, Computer Science Press, 1988.
29. [Wir86] Wirsing M.Structured Algebraic Specifications: A Kernel LanguageTheoretical Computer Science198642123249
30. [WiB89] Wirsing, M. and Broy, M.: A Modular Framework for Specification and Implementation. In:TAPSOFT '89, Vol. 1, J. Diaz and F. Orejas (eds), pp. 42–73, LNCS 351, Springer-Verlag, pp. 42–73, 1989.

Index Terms

• Software and its engineering

  • Software creation and management

    • Designing software

      • Requirements analysis

  • Software notations and tools

    • General programming languages

• Theory of computation

  • Formal languages and automata theory

    • Formalisms

  • Semantics and reasoning

    • Program reasoning

      • Program specifications