Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
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.
G. Gierz, K.H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. A Compendium of Continuous Lattices. Springer-Verlag, 1980.
G. Gierz, J.D. Lawson, and A. Stralka. Quasicontinuous posets. Houston Journal of Mathematics, 9:191–208, 1983.
R. Heckmann. Power Domain Constructions. PhD thesis, Universität des Saarlandes, 1990.
R. Heckmann. Lower and upper power domain constructions commute on all cpos. Information Processing Letters, 40(1):7–11, 1991.
R. Heckmann. Power domain constructions. Science of Computer Programming, 1991. to appear.
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.
P. Johnstone. Scott is not always sober. In Banaschewski and Hoffmann, editors, Continuous Lattices, Bremen 1979. Lecture Notes in Mathematics 871, Springer-Verlag, 1981.
A. Jung. Cartesian Closed Categories of Domains. PhD thesis, PB Mathematik, Technische Hochschule Darmstadt, 1988.
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.
G.D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5(3):452–487, 1976.
Mary E. Rudin. Directed sets which converge. In McAuley and Rao, editors, General Topology and Modern Analysis (Riverside), pages 305–307, 1980.
M.B. Smyth. Power domains. Journal of Computer and System Sciences, 16:23–36, 1978.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heckmann, R. (1992). An upper power domain construction in terms of strongly compact sets. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_14
Download citation
DOI: https://doi.org/10.1007/3-540-55511-0_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55511-7
Online ISBN: 978-3-540-47194-3
eBook Packages: Springer Book Archive