Domains and Lambda-Calculi

Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.

Roberto M. Amadio (Author), Pierre-Louis Curien (Author)

9780521062923, Cambridge University Press

Paperback / softback, published 15 May 2008

504 pages, 85 b/w illus.
22.8 x 15.2 x 2.8 cm, 0.758 kg

Review of the hardback: 'This is an excellent, thorough monograph … a rich and comprehensive source of information, it is very useful as a reference to classical results in domain theory and lambda calculus.' Paula G. Severi, Zentralblatt MATH

This book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in both a language-independent and a machine-independent way, and to prove properties about programs, such as whether they terminate, or whether their result is a solution of the problem they are supposed to solve. In order to achieve this the authors first present, in an elementary and unified way, the theory of certain topological spaces that have proved of use in the modelling of various families of typed lambda calculi considered as core programming languages and as meta-languages for denotational semantics. This theory is known as Domain Theory, and was founded as a subject by Scott and Plotkin. One of the main concerns is to establish links between mathematical structures and more syntactic approaches to semantics, often referred to as operational semantics, which is also described. This dual approach has the double advantage of motivating computer scientists to do some mathematics and of interesting mathematicians in unfamiliar application areas from computer science.

Preface
Notation
1. Continuity and computability
2. Syntactic theory of ?-calculus
3. D? models and intersection types
4. Interpretation of ?-calculi in CCC's
5. CCC's of algebraic dcpo's
6. The language PCF
7. Domain equations
8. Values and computations
9. Powerdomains
10. Stone duality
11. Dependent and second order types
12. Stability
13. Towards linear logic
14. Sequentiality
15. Domains and realizability
16. Functions and processes
Appendix 1: summary of recursion theory
Appendix 2: summary of category theory
References and bibliography
Index.

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