Basic Simple Type Theory

An introduction to type theory for computer scientists.

J. Roger Hindley (Author)

9780521054225, Cambridge University Press

Paperback / softback, published 21 January 2008

200 pages, 10 b/w illus. 1 table
22.8 x 15.1 x 1.1 cm, 0.31 kg

The proofs in this book are given in great detail, and still the author succeeds in writing the book in a clear but not too technical style. It is easy and pleasurable to read this book." Journal of Symbolic Logic

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for computer scientists.

Introduction
1. The type-free ?-calculus
2. Assigning types to terms
3. The principal-type algorithm
4. Type assignment with equality
5. A version using typed terms
6. The correspondence with implication
7. The converse principal-type algorithm
8. Counting a type's inhabitants
9. Technical details
Answers to starred exercises
Bibliography
Table of principal types
Index.

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