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Abstract: . We construct a powerdomain in a category whose objects are posets of data equipped with a cpo of "intensional" representations of the data, and whose morphisms are those monotonic functions between posets that are "realized" by continuous functions between the associated cpos. The category of cpos is contained as a full subcategory that is preserved by lifting, sums, products and function spaces. The construction of the powerdomain uses a cpo of binary trees, these being intensional... (Update)
Context of citations to this paper: More
.... be untyped, and one can perfectly well construct realizability models over typed structures (such models have been considered e.g. in [1, 29]) Indeed, in some ways it would seem ideologically preferable to work with typed structures. However, there are good reasons why...
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Realizability Models for Sequential Computation - Longley (1998) (Correct)
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BibTeX entry: (Update)
A.K. Simpson. The convex powerdomain in a category of posets realized by cpos. In Proc. Category Theory and Computer Science, pages 117--145. Springer LNCS 953, 1995. http://citeseer.ist.psu.edu/simpson95convex.html More
@inproceedings{ simpson95convex,
author = "Alex K. Simpson",
title = "The Convex Powerdomain in a Category of Posets Realized by {CPOs}",
booktitle = "Category Theory and Computer Science",
pages = "117-145",
year = "1995",
url = "citeseer.ist.psu.edu/simpson95convex.html" }
Citations (may not include all citations):156 Basic Concepts of Enriched Category Theory (context) - Kelly - 1982
146 A powerdomain construction (context) - Plotkin - 1976
144 Full abstraction for PCF - Abramsky, Jagadeesan et al. - 1994
77 Full abstraction for a simple parallel programming language (context) - Hennessy, Plotkin - 1979
66 What is a categorical model of intuitionistic linear logic - Bierman - 1995
59 Axiomatic Domain Theory in Categories of Partial Maps (context) - Fiore - 1994
46 Recursive types reduced to inductive types (context) - Freyd - 1990
36 Remarks on algebraically compact categories (context) - Freyd - 1992
31 Department of Computer Science (context) - Plotkin, notes - 1983
25 Recursive types in Kleisli categories - Simpson - 1992
23 Monads on symmetric monoidal closed categories (context) - Kock - 1970
21 Annals of Pure and Applied Logic (context) - Hyland, complete - 1988
14 Call-by-value and nondeterminism (context) - Sieber - 1993
7 Logical aspects of denotational semantics (context) - Robinson - 1987
2 A representable approach to nondeterminism (context) - Anderson, Power - 1994
2 The category theory solution of recursive domain equations (context) - Smyth, Plotkin - 1982
Documents on the same site (http://www.dcs.ed.ac.uk/home/als/Research/): More
Properties of Fixed Points in Axiomatic Domain Theory - Plotkin, Simpson (1998) (Correct)
A Uniform Approach to Domain Theory in Realizability Models - Longley, Simpson (1996) (Correct)
Lazy Functional Algorithms for Exact Real Functionals - Simpson (1998) (Correct)
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