Two models of synthetic domain theory
Marcelo Fiore,Giuseppe Rosolini +1 more
TLDR
In this paper, two models of synthetic domain theory encompassing traditional categories of domains are introduced, and a Grothendieck topos embedding the category ω-Cpo of ωcomplete posets and ωcontinuous functions as a reflective exponential ideal is presented.About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 1997-03-28 and is currently open access. It has received 28 citations till now. The article focuses on the topics: Topos theory & Category of sets.read more
Citations
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Book ChapterDOI
Computational Adequacy in an Elementary Topos
TL;DR: It is proved that computational adequacy holds if and only if the topos is 1-consistent (i.e. its internal logic validates only true Σ\(^{\rm 0}_{\rm 1}\)-sentences).
Journal ArticleDOI
General synthetic domain theory – a logical approach
Bernhard Reus,Thomas Streicher +1 more
TL;DR: A logical and axiomatic account of a general SDT, which is special in the sense that it captures the essence of Domain Theory a la Scott but rules out, for example, Stable Domain Theory, as it requires order on function spaces to be pointwise.
General Synthetic Domain Theory - A Logical Approach
Bernhard Reus,Thomas Streicher +1 more
TL;DR: In this paper, the authors give a logical and axiomatic account of a general synthetic domain theory with the aim of grasping the structure common to all notions of domains and verify the usual induction principles of domain theory.
Journal ArticleDOI
Axioms and (counter)examples in synthetic domain theory
Jaap van Oosten,Alex Simpson +1 more
TL;DR: An axiomatic treatment of synthetic domain theory is presented, in the framework of the internal logic of an arbitrary topos, and new proofs of known facts, new equivalences between the authors' axioms and known principles, and proofs of new facts, such as the theorem that the regular complete objects are closed under lifting (and hence well-complete).
Book ChapterDOI
An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory
Marcelo Fiore,Gordon Plotkin +1 more
TL;DR: This work relates certain models of Axiomatic Domain Theory and Synthetic Domain Theory to introduce a class of non-elementary models of SDT and show that the domains in them yield models of ADT.
References
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Book
Sheaves in Geometry and Logic: A First Introduction to Topos Theory
TL;DR: Topos theory has been studied at the graduate student level for a long time, see as discussed by the authors for an overview of the main applications of topos in algebraic geometry and logic.
Book
The Formal Semantics of Programming Languages: An Introduction
TL;DR: The Formal Semantics of Programming Languages" provides the basic mathematical techniques necessary for those who are beginning a study of semantics and logics of programming languages, including the vital area of concurrency.
Book
Data Types as Lattices
TL;DR: In this article, the meaning of many kinds of expressions in programming languages can be taken as elements of certain spaces of partial objects, and these spaces are modeled in one universal domain.