Refinement calculus, part I: Sequential nondeterministic programs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 430 LNCS, Issue , 1990, Pages 42-66

  Back, R J R ^a   Von Wright, J ^b  

^a ÅBO AKADEMI UNIVERSITY   (Finland)

^b HANKEN SCHOOL OF ECONOMICS   (Finland)

Author keywords

Angelic nondeterminism; Data refinement; Demonic nondeterminism; Inverse statements; Lattices; Miraculous statements; Specification methods; Stepwise refinement; Total correctness; Weakest preconditions

Indexed keywords

CRYSTAL LATTICES; GAME THEORY; INVERSE PROBLEMS; SPECIFICATIONS;

ANGELIC NONDETERMINISM; DATA REFINEMENTS; DEMONIC NONDETERMINISM; INVERSE STATEMENTS; MIRACULOUS STATEMENTS; STEPWISE REFINEMENT; TOTAL CORRECTNESS; WEAKEST PRECONDITION;

CALCULATIONS;

EID: 85017204677     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-52559-9_60     Document Type: Conference Paper

References (37)

1. R. J. R. Back. On the Correctness of Refinement Steps in Program, Development. PhD thesis, Department of Computer Science, University of Helsinki, Helsinki, 1978. Report A-1978-4.
2. R. J. R. Back. Correctness Preserving Program Refinements: Proof Theory and Applications, volume 131 of Mathematical Center Tracts. Mathematical Centre, Amsterdam, 1980.
3. R. J. R. Back. On correct refinement of programs. J. Computer and Systems Sciences, 23(1):49-68, August 1981.
4. R. J. R. Back. Procedural abstraction in the refinement calculus. Reports on computer science and mathematics 55, Äbo Akademi, 1987.
5. R. J. R. Back. A calculus of refinements for program derivations. Acta Informatica, 25:593-624, 1988.
6. R. J. R. Back. Changing data representation in the refinement calculus. In 21st Hawaii International Conference on System Sciences, January 1989. Also available as Abo Akademi reports on computer science and mathematics no. 68, 1988.
7. R. J. R. Back. Refining atomicity in parallel algorithms. In PARLE Conference on Parallel Architectures and Languages Europe, volume 366 of Lecture Notes in Computer Science, Eindhoven, the Netherlands, June 1989. Springer Verlag. Also available as Àbo Akademi reports on computer science and mathematics no. 57, 1988.
8. R. J. R. Back and K. Sere. Refinement of action systems. In Mathematics of Program Construction, volume 375 of Lecture Notes in Computer Science, Groningen, The Netherlands, June 1989. Springer-Verlag.
9. R. J. R. Back and J. von Wright. Combining angels, demons and miracles in program specifications. Reports on computer science and mathematics 86, Abo Akademi, 1989.
10. R. J. R. Back and J. von Wright. Command lattices, variable environments and data refinement. Reports on computer science and mathematics (in preparation), Abo Akademi, 1989.
11. R. J. R. Back and J. von Wright. Duality in specification languages: a lattice-theoretical approach. Reports on computer science and mathematics 77, Abo Akademi, 1989. To appear in Acta Informatica.
12. R. J. R. Back and J. von Wright. A lattice-theoretical basis for a specification language. In Mathematics of Program Construction, volume 375 of Lecture Notes in Computer Science, Groningen, The Netherlands, June 1989. Springer-Verlag.
13. R. J. R. Back and J. von Wright. Statement inversion and strongest postcondition. Reports on computer science and mathematics (in preparation), Abo Akademi, 1989.
14. G. Birkhoff. Lattice Theory. American Mathematical Society, Providence, 1961.
15. R. M. Burstall and J. Darlington. Some transformations for developing recursive programs. J. ACM, 24(l):44-67, 1977.
16. W. Chen and J. T. Udding. Towards a calculus of data refinement. In Mathematics of Program Construction, volume 375 of Lecture Notes in Computer Science, Groningen, The Netherlands, June 1989. Springer-Verlag.
17. J. W. de Bakker, Mathematical Theory of Program Correctness. Prentice-Hall, 1980.
18. E. W. Dijkstra. Notes on structured programming. In E. D. Dahl, O.J. and C. Hoare, editors, Structured Programming. Academic Press, 1971.
19. E. W. Dijkstra. A Discipline of Programming. Prentice-Hall International, 1976.
20. P. Gardiner and C. C. Morgan. Data refinement of predicate transformers. Manuscript (to appear in Theoretical Computer Science), 1988.
21. S. L. Gerhart. Correctness preserving program transformations. In Proc. 2nd ACM Conference of Principles of Programming Languages, pages 54-66, 1975.
22. G. Gratzer. General Lattice Theory. Birkhäuser Verlag, Basel, 1978.
23. D. Gries. The Science of Programming. Springer-Verlag, New York, 1981.
24. P. Guerreiro. Another characterization of weakest preconditions. In Lecture Notes in Computer Science 137. Springer-Verlag, 1982.
25. W. H. Hesselink. An algebraic calculus of commands. Report CS 8808, Department of Mathematics and Computer Science, University of Groningen, 1988.
26. W. H. Hesselink. Command algebras, recursion and program transformation. Report CS 8812, Department of Mathematics and Computer Science, University of Groningen, 1988.
27. C. A. R. Hoare. Proofs of correctness of data representation. Acta Informatica, 1(4):271-281, 1972.
28. C. A. R. Hoare, I. J. Hayes, J. He, C. C. Morgan, A. W. Roscoe, J. W. Sanders, I. H. Sorensen, J. Spivey, and A. Sufrin. Laws of programming. Communications of the ACM, 30(8):672-686, August 1987.
29. C. C. Morgan. Data refinement by miracles. Information Processing Letters, 26:243-246, January 1988.
30. C. C. Morgan. The specification statement. ACM Transactions on Programming Languages and Systems, 10(3):403-419, July 1988.
31. C. C. Morgan. Programming from specifications. Manuscript, 1989.
32. C. C. Morgan. Types and invariants in the refinement calculus. In Mathematics of Program Construction, volume 375 of Lecture Notes in Computer Science, Groningen, The Netherlands, June 1989. Springer-Verlag.
33. C. C. Morgan and P. Gardiner. Data refinement by calculation. Technical report, Programming Research Group, Oxford University, 1988.
34. J. M. Morris. A theoretical basis for stepwise refinement and the programming calculus. Science of Computer Programming, 9:287-306, 1987.
35. J. M. Morris. Laws of data refinement. Acta Informatica, 26:287-308, 1989.
36. G. Nelson. A generalization of Dijkstra’s calculus. Tech. Rep 16, Digital Systems Research Center, Palo Alto, Calif., April 1987.
37. N. Wirth. Program development by stepwise refinement. Communications of the ACM, 14:221-227, 1971.