# Domain theory

@inproceedings{Abramsky1995DomainT, title={Domain theory}, author={Samson Abramsky and Achim Jung}, booktitle={Logic in Computer Science}, year={1995} }

bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element. Other examples are partially ordered sets, where (INT) is satisfied because of reflexivity. We will shortly identify posets as…

## 1,261 Citations

### A foundation for computation

- Computer Science
- 2000

This thesis is the study and application of domains with measurements and seeks to develop a mathematical setting in which the question “Does this program work, and if so, how does it compare to others which solve the same problem?” may be sensibly formalized and answered.

### On Some Constructions in Quantitative Domain Theory (Extended Abstract)

- Mathematics
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Domains introduced by Dana Scott [11] and independently by Yuri L. Ershov [3] are a structure modelling the notion of approximation and of computation. A computation performed using an algorithm…

### TOWARDS A FORMAL THEORY OF COMPUTABILITY

- Computer Science
- 2010

The present work can be seen as an attempt to develop a constructive theory of formal neighborhoods for continuous functionals, in a direct and intuitive style, to replace abstract domain theory by a more concrete, finitary theory of representations.

### On Domain Theory over Girard Quantales

- Computer ScienceFundam. Informaticae
- 2009

This paper demonstrates that the domain-theoretic construction of the Hoare, Smyth and Plotkin powerdomains of a continuous dcpo can be straightforwardly adapted to yield corresponding constructions for continuous Q-domains.

### Topology in Computer Science Problems

- Mathematics
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We pose the problem of whether every FS-domain is a retract of a bifinite domain purely in terms of quasi-uniform spaces. 6.1 The problem and its history Ever since domains were introduced by Dana…

### Coalgebraic Theories of Sequences in PVS

- Computer ScienceJ. Log. Comput.
- 1999

This paper explains the setting of an extensive formalisation of the theory of sequences in the Prototype Veriication System based on the characterisation of sequences as a nal coalgebra, which is used as an axiom.

### From Objects to Diagrams for Ranges of Functors

- Mathematics
- 2011

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for ''many'' objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general…

### Absolute retractness of automata on directed complete posets

- Mathematics
- 2017

The notion of retractness, which is about having left inverses (reflection) for monomorphisms, is crucial in most branches of mathematics. One very important notion related to it is injectivity,…

### A Cook's Tour of the Finitary Non-Well-Founded Sets

- MathematicsWe Will Show Them!
- 2005

A topological universe of finitary sets, which can be seen as a natural limit completion of the hereditarily finite sets, is given, which contains non-well founded sets and a universal set and is closed under positive versions of the usual axioms of set theory.

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