Domains and Lambda-Calculi

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Overview

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 modeling of various families of typed lambda calculi considered as core programming languages and as meta-languages for denotational semantics. This theory is now 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.

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Editorial Reviews

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"...the book is well written and will be clear to readers with sufficient mathematical maturity." Computing Reviews

"...fills a gap in the literature, giving us a wide perspective of the development of domain theory...self-contained and amazingly clear in many respects...an excellent survey, and recommended reading, for those who have been exposed to the subject and seek a good technical introduction to advanced topics..." Mathematical Reviews

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Product Details

Table of Contents

Preface; Notation; 1. Continuity and computability; 2. Syntactic theory of λ-calculus; 3. D∞ models and intersection types; 4. Interpretation of λ-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.

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