Normal Subsets in Abstract Bases
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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.
KeywordsContinuous domains abstract bases normal subsets fixed point theorem
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- 1.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.Google Scholar
- 4.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.Google Scholar
- 6.A. Jung, Catesian Closed Categories of Domains, CWI Tracts, Centrum voor Wiskunde en Informatica, Vol.66, Amsterdam, 1989.Google Scholar
- 7.A. Jung, The classification of continuous domains, In Logic in Computer Science, pp.35–40, IEEE Computer Society Press, 1990.Google Scholar
- 8.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.Google Scholar
- 9.M.W. Mislove, Using Duality to Solve Domain Equations, Electronic Notes in Theoretical Computer Science, Vol.6 (1997).Google Scholar
- 10.G.D. Plotkin, Postgraduate lecture notes in advanced domain theory, Dept. of Computer Science, Univ. of Edingburgh, 1981.Google Scholar
- 11.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.577Google Scholar
- 13.C.Y. Zheng, L. Fan, H.B. Cui, Frames and Continuous Lattices (2nd edition), Capital Normal University 2000 (in Chinese)Google Scholar