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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 481 (20 self)
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Least fixpoints as meanings of recursive definitions.
Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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Cited by 10 (2 self)
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
Domain Theory  Corrected and expanded version
"... bases were introduced in [Smy77] where they are called "Rstructures". Examples of abstract bases are concrete bases of continuous domains, of course, where the relation is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have ..."
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bases were introduced in [Smy77] where they are called "Rstructures". Examples of abstract bases are concrete bases of continuous domains, of course, where the relation is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element.
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"... I wish to thank my parents for their continuing support, encouragement and understanding. Medda, Toto, Fiete, Anemone: Thanks for visiting me in the States! My friend Vidya was always on my side and helped me out on more than one occasion. Thanks for everything! Special thanks to Professor Karl H. H ..."
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I wish to thank my parents for their continuing support, encouragement and understanding. Medda, Toto, Fiete, Anemone: Thanks for visiting me in the States! My friend Vidya was always on my side and helped me out on more than one occasion. Thanks for everything! Special thanks to Professor Karl H. Hofmann, who taught my first course in mathematical analysis. He introduced me to mathematics, teaching with a rigour and style which motivated me throughout my career. I would like to express my thanks to all members of the department of mathematics at Tulane, most notably my fellow graduate students, for making my stay here such a pleasant one. Martin Laubinger gave me hints regarding the requirements of the Graduate School. I used a modified version of Dmitri Alexeev's Tulane University Thesis LATEX class; the diagrams were drawn using Paul Taylor's diagrams package [22].
This text is based on the chapter Domain Theory in the Handbook for Logic in
"... E. Maibaum, published by Clarendon Press, Oxford in 1994. While the numbering of all theorems and definitions has been kept the same, we have included comments and corrections which we have received over the years. For ease of reading, small typographical errors have simply been corrected. Where we ..."
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E. Maibaum, published by Clarendon Press, Oxford in 1994. While the numbering of all theorems and definitions has been kept the same, we have included comments and corrections which we have received over the years. For ease of reading, small typographical errors have simply been corrected. Where we felt the original text gave a misleading impression, we have included additional explanations, clearly marked as such. If you wish to refer to this text, then please cite the published original version where possible, or otherwise this online version which we try to keep available from the page