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  3. Basic Simple Type Theory
  • Cited by 92
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1997
Online ISBN:
9780511608865
DOI:
https://doi.org/10.1017/CBO9780511608865
Subjects:
Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
Series:
Cambridge Tracts in Theoretical Computer Science (42)
Information

Book description

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.

Reviews

"This is an excellent introduction to type theory. It doesn't bog the reader down in any of the messy details of the proofs and yet it provides many of the most interesting results in the field....Overall, it is a great book for someone who wants to get his feet wet in type theory, but doesn't want to get in over his head." Sigact News

"...the book makes useful and stimulating reading and it will be an essential tool for computer scientists working in type theory and related areas." Mathematical Reviews

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

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