Basic Simple Type Theory

by J. Roger Hindley

• ISBN13: 9780521054225
• ISBN10: 0521054222
• Edition: 1st
• Format: Paperback
• Copyright: 2008-01-21
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction

The type-free -calculus

Assigning types to terms

The principal-type algorithm

Type assignment with equality

A version using typed terms

The correspondence with implication

The converse principal-type algorithm

Counting a type's inhabitants

Technical details

Answers to starred exercises

Bibliography

Table of principal types

Index

Table of Contents provided by Publisher. All Rights Reserved.