General Synthetic Domain Theory - A Logical Approach.

Reus, Bernhard and Streicher, Thomas (1999) General Synthetic Domain Theory - A Logical Approach. Mathematical Structures in Computer Science, 9 (2). pp. 177-223. ISSN 0960-1295

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Abstract

Synthetic 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

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
Depositing User: Bernhard Reus
Date Deposited: 06 Feb 2012 19:54
Last Modified: 28 Mar 2012 15:02
URI: http://sro.sussex.ac.uk/id/eprint/22886
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