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General Synthetic Domain Theory - A Logical Approach.
journal contribution
posted on 2023-06-08, 00:29 authored by Bernhard ReusBernhard Reus, Thomas StreicherSynthetic Domain Theory (SDT) is a version of Domain Theory where "all functions are continuous". In [14, 12] there has been developed a logical and axiomatic version of SDT which is special in the sense that it captures the essence of Domain Theory `a la Scott but rules out other important notions of domain. In this article we will give a logical and axiomatic account of General Synthetic Domain Theory (GSDT) aiming to grasp the structure common to all notions of domain as advocated by various authors. As in [14, 12] the underlying logic is a sufficiently expressive version of constructive type theory. We start with a few basic axioms giving rise to a core theory on top of which we study various notions of predomains as well-complete and replete S-spaces [9], define the appropriate notion of domain and verify the usual induction principles. 1
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Publication status
- Published
Journal
Mathematical Structures in Computer ScienceISSN
0960-1295Publisher
Mathematical Structures in Computer ScienceExternal DOI
Issue
2Volume
9Page range
177-223ISBN
0960-1295Department affiliated with
- Informatics Publications
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- No
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- Yes
Legacy Posted Date
2012-02-06Usage metrics
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