An upper power domain construction in terms of strongly compact sets. (English) Zbl 1518.68200
Brookes, Stephen (ed.) et al., Mathematical foundations of programming semantics. 7th international conference, Pittsburgh, PA, USA, March 25–28, 1991. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 598, 272-293 (1992).
Summary: A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power construction, and its commutation with the lower construction.
For the entire collection see [Zbl 1517.68006].
For the entire collection see [Zbl 1517.68006].
References:
| [1] | K.E. Flannery and J.J. Martin. The Hoare and Smyth power domain constructors commute under composition. Journal of Computer and System Sciences, 40:125-135, 1990. · Zbl 0699.06008 · doi:10.1016/0022-0000(90)90008-9 |
| [2] | G. Gierz, K.H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. A Compendium of Continuous Lattices. Springer-Verlag, 1980. · Zbl 0452.06001 |
| [3] | G. Gierz, J.D. Lawson, and A. Stralka. Quasicontinuous posets. Houston Journal of Mathematics, 9:191-208, 1983. · Zbl 0529.06002 |
| [4] | R. Heckmann. Power Domain Constructions. PhD thesis, Universität des Saarlandes, 1990. |
| [5] | R. Heckmann. Lower and upper power domain constructions commute on all cpos. Information Processing Letters, 40(1):7-11, 1991. · Zbl 0748.68038 |
| [6] | R. Heckmann. Power domain constructions. Science of Computer Programming, 1991. to appear. |
| [7] | M.C.B Hennessy and G.D. Plotkin. Pull abstraction for a simple parallel programming language. In J. Becvar, editor, Foundations of Computer Science, pages 108-120. Lecture Notes in Computer Science 74, Springer-Verlag, 1979. · Zbl 0457.68006 |
| [8] | P. Johnstone. Scott is not always sober. In Banaschewski and Hoffmann, editors, Continuous Lattices, Bremen 1979. Lecture Notes in Mathematics 871, Springer-Verlag, 1981. · Zbl 0469.06002 |
| [9] | A. Jung. Cartesian Closed Categories of Domains. PhD thesis, PB Mathematik, Technische Hochschule Darmstadt, 1988. · Zbl 0663.18004 |
| [10] | J.D. Lawson. The versatile continuous order. In Michael G. Main, A. Melton, Michael Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Language Semantics (MFPLS ’87), pages 565-622. Lecture Notes in Computer Science 298, Springer-Verlag, 1988. · Zbl 0662.06002 |
| [11] | G.D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5(3):452-487, 1976. · Zbl 0355.68015 · doi:10.1137/0205035 |
| [12] | Mary E. Rudin. Directed sets which converge. In McAuley and Rao, editors, General Topology and Modern Analysis (Riverside), pages 305-307, 1980. · Zbl 0457.04007 |
| [13] | M.B. Smyth. Power domains. Journal of Computer and System Sciences, 16:23-36, 1978. · Zbl 0391.68011 · doi:10.1016/0022-0000(78)90048-X |
| [14] | M.B. Smyth. Power domains and predicate transformers: A topological view. In J. Diaz, editor, ICALP ’83, pages 662-676. Lecture Notes in Computer Science 154, Springer-Verlag, 1983. · Zbl 0533.68018 |
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