Partiality and Nondeterminacy in Program Proofs

Formal Aspects of Computing

Volumn 10, Issue 1, 1998, Pages 76-96

  Morris, Joseph M ^a   Bunkenburg, Alexander ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Equational reasoning; Many valued logic; Nondeterminacy; Partial expressions; Program refinement

Indexed keywords

EID: 0007125513     PISSN: 09345043     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00003927     Document Type: Article

References (17)

1. Avron, A.: Foundations and proof theory of 3-valued logics. LFCS report series ECS-LFCS-88-48, Laboratory for the Foundations of Computer Science, Edinburgh University, 1988.
2. Avron, A.: Natural 3-valued logics - characterisation and proof theory. Journal of Symbolic Logic, 56:276-294, 1991.
3. Blikle, A.: Three-valued predicates for software specification and development. In R. et al. Bloomfield, editor, VDM - the way ahead, volume 328 of Lecture Notes in Computer Science, pages 243-266. Springer Verlag, 1988.
4. Dijkstra, E. W. and Scholten, C. S.: Predicate Calculus and Program Semantics. Springer Verlag, New York, 1990.
5. Gries, D. and Schneider, F. B.: A Logical Approach to Discrete Math. Springer Verlag, New York, 1993.
6. Jones, C B. and Middelburg, C. A.: A typed logic of partial functions reconstructed classically. Acta Informatica, 31(5):399-430, 1994.
7. Larsen, P. G. and Hansen, B. S.: Semantics of under-determined expressions. Formal Aspects of Computing, 8(1):47-66, 1996.
8. Morris, J. M. and Bunkenburg, A.: E3: A logic for reasoning equationally in the presence of partiality. To be published., 1998.
9. Milne, R. E.: The semantic foundations of the Raise specification language. RAISE/STC/REM/11, STC/STL, Harlow, UK, 1990. Technical Report.
10. Monteiro, A.: Construction des algèbres de Lukasiewicz trivalentes dans les algèbres de Boole monadiques I. Mathematica Japonica, 12:1-23, 1967.
11. NASA Office of Safety and Mission Assurance. Formal Methods Specification and Analysis Guidebook for the Verification of Software and Computer Systems, Vol. II. A Practicioner's Companion, release 1.0, May 1997. NASA-GB-001-97.
12. Norvell, T. S. and Hehner, E. C. R.: Logical specifications for functional programs. In Proceedings of the Second International Conference on Mathematics of Program Construction, Oxford, 29 June - 3 July 1992, volume 669 of Lecture Notes in Computer Science, pages 269-290. Springer Verlag, 1993.
13. Partsch, H. A.: Specification and Transformation of Programs. Springer Verlag, New York, 1990.
14. The Raise Language Group. The RAISE Specification Language. Prentice-Hall, London, 1992.
15. The RAISE Method Group. The RAISE Development Method. Prentice-Hall, London, 1995.
16. Ward, N.: A Refinement Calculus for Nondeterministic Expressions. PhD thesis, University of Queensland, 1994.
17. Walicki, M. and Meldal, S.: A complete calculus for the multialgebraic and functional semantics of nondeterminism. ACM Transactions on Programming Languages and Systems, 17:366-393, 1995.