Abstract
The broad theme of the paper is that topological concepts are basic to computer science. Such concepts as “specifications”, “predicate transformer”, and “nondeterminism” can be greatly illuminated by being formulated in topological terms. The specific tasks we undertake are: to provide a more adequate framework for power-domain constructions; and to show that the connection between (Dijkstra's) weakest preconditions and the Smyth powerdomain, established by Plotkin for the case of flat domains, actually holds in full generality.
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References
Apt, K., Plotkin, G., A Cook's tour of countable non-determinism. Proc. ICALP 1981, Springer-Verlag LNCS 115, pp. 479–494 (1981).
Berge, C., Espaces Topologiques: Fonctions Multivoques. Dunod, Paris (1959).
Continuous Lattices, Proceedings Bremen 1979, ed. Banaschewski and Hoffman, Springer LN Math. 871 (1981).
de Bakker, J., Zucker, J., Denotational semantics of concurrency, Proc. 14th ACM STOC, pp. 153–158 (1982).
de Nicola, R., Hennessy, M., Testing equivalences for processes, CSR-123-82, Dept. of Computer Science, Edinburgh (1982).
Dijkstra, E., A Discipline of Programming, Prentice-Hall (1976).
Gierz, G., Hofmann, K., Keimel, K., Lawson, J., Mislove, M., Scott, D., A Compendium of Continuous Lattices. Springer (1980).
Hennessy, M., Plotkin, G., Full abstraction for a simple parallel programming language. Proc. MFCS, Springer LNCS 74, pp. 108–120 (1979).
Hofmann, K., Mislove, M., Local compactness and continuous lattices: in [3] (pp. 209–248).
Johnstone, P., Scott is not always sober: in [3] (pp. 283–284).
Johnstone, P., Tychonoff's theorem without the axiom of choice, Fund. Math. 113, pp. 21–35 (1981).
Johnstone, P., Stone Spaces, Cambridge U.P. (198?).
Kuratowski, K., Topology. Revised edition, Academic Press and PWN (1966).
Michael, E., Topologies on spaces of subsets, Trans. AMS 71,pp.152–182 (1951).
Plotkin, G., A powerdomain construction, SIAM J. Comput. 5,pp. 452–487 (1976).
Plotkin, G., Dijkstra's predicate transformers and Smyth's powerdomains, Abstract Software Specifications (ed. D. BjØrner) LNCS 86 (1980).
Plotkin, G., A powerdomain for countable non-determinism, Proc. ICALP 1982.
Plotkin, G., Domains: notes for lecture course, Edinburgh (1981).
Rogers, H., Theory of Recursive Functions.
Smyth, M., Power domains, JCSS 16 (1978).
Smyth, M., Powerdomain and hyperspace. To appear.
Vietoris, L., Monatsh. f. Math. u. Phys. 31, pp. 173–204 (1921).
Winskel, G., Events in Computation, Thesis, Edinburgh (1980).
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© 1983 Springer-Verlag Berlin Heidelberg
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Smyth, M.B. (1983). Power domains and predicate transformers: A topological view. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036946
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DOI: https://doi.org/10.1007/BFb0036946
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