Mathematical Theory of Domains

Introductory textbook/general reference in domain theory for professionals in computer science and logic.

V. Stoltenberg-Hansen (Author), I. Lindström (Author), E. R. Griffor (Author)

9780521064798, Cambridge University Press

Paperback / softback, published 12 June 2008

364 pages, 150 exercises
24.4 x 17 x 1.9 cm, 0.58 kg

Review of the hardback: '… can be thoroughly recommended for anyone interested in computability.' Steven Vickers, The Computer Journal

Domain theory is an established part of theoretical computer science, used in giving semantics to programming languages and logics. In mathematics and logic it has also proved to be useful in the study of algorithms. This book is devoted to providing a unified and self-contained treatment of the subject. The theory is presented in a mathematically precise manner which nevertheless is accessible to mathematicians and computer scientists alike. The authors begin with the basic theory including domain equations, various domain representations and universal domains. They then proceed to more specialized topics such as effective and power domains, models of lambda-calculus and so on. In particular, the connections with ultrametric spaces and the Kleene–Kreisel continuous functionals are made precise. Consequently the text will be useful as an introductory textbook (earlier versions have been class-tested in Uppsala, Gothenburg, Passau, Munich and Swansea), or as a general reference for professionals in computer science and logic.

Preliminaries
Part I. Basic Theory: 1. Fixed points
2. Complete partial orders
3. Domains
4. Domain equations
5. Topology
6. Representation theory
7. A universal domain
Part II. Special Topics: 8. Representability in domains
9. Basic recursion theory
10. Effective domains
11. Power domains
12. Domains as models of formal theories
References
Index of symbols
Index.

Subject Areas: Mathematical theory of computation [UYA], Mathematical logic [PBCD]