Abstract
Some specification languages, such as VDM-SL, allow expressions whose values are not fully determined. This may be convenient in cases where the choice of value should be left to a later stage of development.
We consider a simple functional language including such under-determined expressions and present a denotational semantics for the language along with a set of proof rules for reasoning about properties of under-determined expressions. One of the specific problems considered is the combination of under-determinedness and a least fixed point semantics of recursion. Soundness of the proof rules is also discussed.
Similar content being viewed by others
References
Backhouse, R., Chisholm, P., Malcolm, G. and Saaman E.: Do-it-Yourself Type Theory.Formal Aspects of Computing, 1(1):19–84, January 1989.
Bicarregui, J., Fitzgerald, J.S., Lindsay, P., Moore, R. and Ritchie B.:Proof in VDM: A Practitioner's Guide. Springer-Verlag, 1994.
Broy, M.: A fixed point approach to applicative multiprogramming. In M. Broy and G. Schmidt, editors,Theoretical Foundations of Programming Methodology, pages 565–622. Reidel, 1982.
British Standards Institution. Z base standard, November 1992. Version 1.0.
The RAISE Language Group.:The RAISE Specification Language. Prentice-Hall, 1992.
Hoare, C.A.R.:Communication Sequential Processes. Prentice-Hall, 1985.
Information Technology Programming Languages — VDM-SL. ISO/IEC JTC1/SC22/WG19 N-20, November 1993. CD 13817-1.
Jones, C.B.:Systematic Software Development Using VDM. Prentice-Hall, 1990.
Larsen, P.G.: Towards Proof Rules for Looseness in Explicit Definitions from VDM-SL. InProceedings of the “International Workshop on Semantics of Specification Languages (SoSL)”, pages 118–134, October 1993, Utrecht, Springer-Verlag 1994.
Larsen, P.G.: Towards Proof Rules for the Full Standard VDM Specification Language. Ph.D. thesis, Department of Computer Science, Technical University of Denmark, March 1995. Technical Report ID-TR: 1995–160.
Leisenring, A.C.:Mathematical Logic and Hubert's ε-Symbol. Gordon and Breach Science Publishers, New York, 1969.
Larsen, P.G. and Hansen B.S.: Semantics for Under-determined Expressions. Technical Report ID-TR: 1994-151, Department of Computer Science, Technical University of Denmark, December 1994.
Nipkow T.: Non-deterministic Data Types: Models and Implementations.Acta Informatica, 22:629–661, 1986.
Schmidt D.A.:Denotational Semantics — A Methodology for Language Development. Allyn and Bacon, Inc. 1986.
Søndergaard, H. and Sestoft P.: Referential Transparency, Definiteness and Unfoldability.Acta Informatica, 27:505–517, 1990.
Søndergaard, H. and Sestoft P.: Non-determinism in Functional Languages.The Computer Journal, 35(5):514–523, October 1992.
Tarlecki, A. and Wieth, M.: A Naive Domain Universe for VDM. In Dines Bjørner, C.A.R. Hoare, and Hans Langmaack, editors,VDM '90 VDM and Z — Formal Methods in Software Development, pages 552–579. Springer-Verlag, 1990.
Walicki, M.: Algebraic Specifications of Nondeterminism. Ph.D. thesis, University of Bergen, Department of Informatics, 1993.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Larsen, P.G., Hansen, B.S. Semantics of under-determined expressions. Formal Aspects of Computing 8, 47–66 (1996). https://doi.org/10.1007/BF01211050
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01211050