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Basic Simple Type Theory (Cambridge Tracts in Theoretical Computer Science)
 
 
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Basic Simple Type Theory (Cambridge Tracts in Theoretical Computer Science) [Hardcover]

J. Roger Hindley (Author)

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Book Description

0521465184 978-0521465182 August 28, 1997
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. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. 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 that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.

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Editorial Reviews

Review

"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

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 focussing 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. The mathematical presentation is rigorous but clear, making it the first book at this level which can be used as introduction to type theory for computer scientists.

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Inside This Book (learn more)
First Sentence:
The -calculus is a family of prototype programming languages invented by a logician, Alonzo Church, in the 1930's. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
applicative combination, condensed detachment, condensed tree, implicational logic, typable term, principal deduction, shrinking lemma, leftmost reduction, intuitionist logic, typed terms, implicational fragment, provable formulae, combinatory logic, alphabetic variant, strong normalization, assigning types, counting algorithm, unification algorithm, occurs negatively, normal inhabitants, closed terms, extra node, logic deduction, occurs positively, natural deduction
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Proof Let, Lemma Every, Proof Straightforward, David Meredith, Definition Hilbert-style, Carew Meredith, Proof Induction, Proof Suppose
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This book cites 38 books:
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