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The lattice of data refinement

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Abstract

We define a general notion of data refinement that comprises the traditional notion of data refinement as a special case. Using the concepts of duals and adjoints, we define converse commands and find a symmetry between ordinary data refinement and a dual (backward) data refinement. We show how ordinary and backward data refinement are interpreted as simulation, and we derive rules for the piecewise data refinement of programs. Our results are valid for a general language, including demonic and angelic nondeterminism as well as nontermination and miracles.

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References

  1. Abadi, M., Lamport, L.: The existence of refinement mappings. In: Proc 3rd Annual IEEE Symp. on Logic in Computer Science, pp. 165–175, Edinburgh 1988

  2. Back, R.J.R.: Correctness Preserving Program Refinements: Proof Theory and Applications, vol. 131 of Mathematical Center Tracts. Amsterdam: Mathematical Centre 1980

    Google Scholar 

  3. Back, R.J.R.: A calculus of refinements for program derivations. Acta Inf.25, 593–624 (1988)

    Google Scholar 

  4. Back, R.J.R.: Changing data representation in the refinement calculus. In: 21st Hawaii International Conference on System Sciences 1989

  5. Back, R.J.R.: Refinement calculus, part II: parallel and reactive programs. In: Bakker, J.W. de, Roever, W.P., Rozenberg, G. (eds.) Stepwise refinement of distributed systems. Models, formalisms, correctness. REX Workshop, Mook, The Netherlands (Lect. Notes Comput. Sci., vol. 430, pp. 67–93) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  6. Back, R.J.R.: Refining atomicity in parallel algorithms. In: Odijk, E., Rem, M., Syre, J.C. (eds.) PARLE'89. Conference on Parallel Architectures and Languages Europe, Eindhoven, The Netherlands (Lect. Notes Comput. Sci., vol. 366, pp. 199–216) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  7. Back, R.J.R., Wright, J. von: Refinement calculus, part I: Sequential non deterministic programs. In: Bakker, J.W. de, Roever, W.P., Rozenberg, G. (eds.) Stepwise refinement of distributed systems. Models, formalisms, correctness. REX Workshop, Mook, The Netherlands (Lect. Notes Comput. Sci., vol. 430, pp. 42–66) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  8. Back, R.J.R., Wright, J. von: Duality in specification languages: a lattice-theoretical approach. Acta Inf.27, 583–625 (1990)

    Google Scholar 

  9. Back, R.J.R., Wright, J. von: Statement inversion and strongest postcondition. Sci. Comput. Program.20, 223–251 (1993)

    Google Scholar 

  10. Chen, W., Udding, J.T.: Towards a calculus of data refinement. In: Shepscheut, J.L. van de (ed.) Mathematics of program construction. International Conference, Groningen, The Netherlands (Lect. Notes Comput. Sci., vol. 375, pp. 197–218) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  11. Dijkstra, E.W.: A discipline of programming. Englewood Cliffs, NJ: Prentice-Hall 1976

    Google Scholar 

  12. Dijkstra, E.W., Scholten, C.S.: Predicate calculus and program semantics (Texts Monogr. Comput. Sci.) Berlin, Heidelberg, New York: Springer 1990

    Google Scholar 

  13. Gardiner, P.H., Morgan, C.C.: A single complete rule for data refinement. Manuscript, 1991

  14. Gardiner, P.H., Morgan, C.C.: Data refinement of predicate transformers. Theor. Comput. Sci.87(1), 143–162 (1991)

    Google Scholar 

  15. He, J., Hoare, C.A.R., Sanders, J.W.: Prespecification in data refinement. Inf. Process. Lett.25, 71–76 (1987)

    Google Scholar 

  16. Hoare, C.A.R.: Proofs of correctness of data representation. Acta Inf.1(4), 271–281 (1972)

    Google Scholar 

  17. Jonsson, B.: On decomposing and refining specifications of distributed systems. In: Bakker, J.W. de, Roever, W.P., Rozenberg, G. (eds.) Stepwise refinement of distributed systems. Models, formalisms, correctness. REX Workshop, Mook, The Netherlands (Lect. Notes Comput. Sci., vol. 430, pp. 361–385) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  18. Jonsson, B.: Simulations between specifications of distributed systems. In: Baeten, J.C., Groote, J.F. (eds.) CONCUR'91. Proceedings of 2nd International Conference on Concurrency Theory (Lect. Notes Comput Sci., vol. 527, pp. 346–360) Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  19. Morgan, C.C., Gardiner, P.H.: Data refinement by calculation. Acta Inf.27, 481–503 (1990)

    Google Scholar 

  20. Morgan, C.C.: Data refinement by miracles. Inf. Process. Lett.26, 243–246 (1988)

    Google Scholar 

  21. Morgan, C.C.: The specification statement. ACM Trans. Program. Lang. Syst.10(3), 403–419 (1988)

    Google Scholar 

  22. Morgan, C.C., Woodcock, J.: Of wp and CSP. In: Proceedings of VDM-91, 1991

  23. Morris, J.M.: A theoretical basis for stepwise refinement and the programming calculus. Sci. Comput. Programm.9, 287–306 (1987)

    Google Scholar 

  24. Morris, J.M.: Laws of data refinement. Acta Inf.26, 287–308 (1989)

    Google Scholar 

  25. Nelson, G.: A generalization of Dijkstra's calculus. ACM Trans. Program. Lang. Syst.11 (4), 517–562 (1989)

    Google Scholar 

  26. Wright, J. von: A lattice-theoretical basis for program refinement. PhD thesis, Åbo Akademi University, Turku, Finland 1990

    Google Scholar 

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Authors and Affiliations

  1. Swedish School of Economics and Business Administration, Box 287, FIN-65101, Vasa, Finland

    J. von Wright

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von Wright, J. The lattice of data refinement. Acta Informatica 31, 105–135 (1994). https://doi.org/10.1007/BF01192157

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