Abstract
In this paper, we use the concept of normal subsets in abstract bases to study continuous sub-domains and solving continuous domain equations. Firstly, the problem of definition and characterization of sub-domains in the category of continuous domains will be discussed. Then a dcpo class of abstract bases will be introduced and a fixed point theorem of continuous mappings on the class will be addressed. Finally, connections with other approaches to domain equations will be discussed briefly.
This work is supported by China National Natural Science Foundations
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References
S. Abramsky, A. Jung, Domain Theory, in: Handbook of Logic in Computer Science, Vol.2, edited by S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, pp.1–168, Oxford University Press, 1994.
A. Edalat, Domains for Computation in Mathematics, Physics and Exact Real Arithmetic, Bulletin of Symbolic Logic, Vol.3(1997), pp.401–452.
C.A. Gunter, Universal profinite domains, Information and Computation, Vol.72 (1987), pp.1–30.
C. Gunter. D. Scott, Semantic domains, in Handbook of Theoretical Computer Science, Vol.B, edited by J.van Leeuwen, pp.633–674, North Holland, 1990.
R. Hoofman, Continuous Information Systems, Information and Computation, Vol.105 (1993), pp.42–71.
A. Jung, Catesian Closed Categories of Domains, CWI Tracts, Centrum voor Wiskunde en Informatica, Vol.66, Amsterdam, 1989.
A. Jung, The classification of continuous domains, In Logic in Computer Science, pp.35–40, IEEE Computer Society Press, 1990.
K. Larsen, G. Winskel, Using information systems to solve recursive domain equations effectively, in G. Kahn, D.B. MacQueen and G. Plotkin, eds, Semantics of Data Types, Lecture Notes in Computer Science 173, Springer-Verlag, Berlin, 1984, pp.109–129.
M.W. Mislove, Using Duality to Solve Domain Equations, Electronic Notes in Theoretical Computer Science, Vol.6 (1997).
G.D. Plotkin, Postgraduate lecture notes in advanced domain theory, Dept. of Computer Science, Univ. of Edingburgh, 1981.
D.S. Scott, Domains for denotational semantics, inM.Nielsen and E .M. Schmidteds, Automata,Languages and Programming, Lecture Notes in Computer Science140, Springer-Verlag, Berlin, 1982, pp.577
G.Q. Zhang, DI-domains as Prime information systems, Information and Computation, Vol.100 (1992), pp.151–177.
C.Y. Zheng, L. Fan, H.B. Cui, Frames and Continuous Lattices (2nd edition), Capital Normal University 2000 (in Chinese)
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Fan, L., Zheng, CY. (2001). Normal Subsets in Abstract Bases. In: Keimel, K., Zhang, GQ., Liu, YM., Chen, YX. (eds) Domains and Processes. Semantic Structures in Computation, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0654-5_8
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DOI: https://doi.org/10.1007/978-94-010-0654-5_8
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