Domains and Lambda-Calculi

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Cambridge University Press, Jul 2, 1998 - Computers - 484 pages
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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Contents

Notation ху
1
Syntactic theory of the lcalculus
22
Doo models and intersection types
43
Interpretation of lcalculi in CCCs
71
The Language PCF
124
Domain equations
144
Values and computations
168
Powerdomains
200
Stability
270
Towards linear logic
301
Sequentiality
341
Domains and realizability
388
Functions and processes
421
Summary of recursion theory
449
References and bibliography
469
Index
480

Stone duality
215
Dependent and second order types
240

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Page 470 - Blass. A game semantics for linear logic. Annals of Pure and Applied Logic, 56:183-220, 1992.

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