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Enrichment and Representation Theorems for Categories of Domains and Continuous Functions
, 1996
"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported b ..."
Abstract

Cited by 7 (5 self)
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This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported by SERC grant RR30735 and EC project Programming Language Semantics and Program Logics grant SC1000 795 they explain the ordertheoretic structure). Our aim is 1. to provide a justification of Scott's original consideration of ordered structures, and 2. to deepen our understanding of the notion of passage to the limit
Program Verification in Synthetic Domain Theory
, 1995
"... Synthetic Domain Theory provides a setting to consider domains as sets with certain closure properties for computing suprema of ascending chains. As a consequence the notion of domain can be internalized which allows one to construct and reason about solutions of recursive domain equations. Moreover ..."
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Synthetic Domain Theory provides a setting to consider domains as sets with certain closure properties for computing suprema of ascending chains. As a consequence the notion of domain can be internalized which allows one to construct and reason about solutions of recursive domain equations. Moreover, one can derive that all functions are continuous. In this thesis such a synthetic theory of domains (#domains) is developed based on a few axioms formulated in an adequate intuitionistic higherorder logic. This leads to an elegant theory of domains. It integrates the positive features of several approaches in the literature. In contrast to those, however, it is model independent and can therefore be formalized. A complete formalization of the whole theory of #domains has been coded into a proofchecker (Lego) for impredicative type theory. There one can exploit dependent types in order to express program modules and modular specifications. As an application of this theory an entirely fo...