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Basic Simple Type Theory

$129.00 (P)

Part of Cambridge Tracts in Theoretical Computer Science

  • Date Published: August 1997
  • availability: Available
  • format: Hardback
  • isbn: 9780521465182

$ 129.00 (P)
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  • 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.

    • The approach is via type-assignment, which makes it applicable to polymorphic systems and languages
    • Contains a full treatment of the type-checking algorithm by one of the pioneer developers of that algorithm
    • Contains very clear accounts of two other interesting algorithms which are otherwise buried in the technical literature
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    Reviews & endorsements

    "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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    Product details

    • Date Published: August 1997
    • format: Hardback
    • isbn: 9780521465182
    • length: 200 pages
    • dimensions: 236 x 157 x 15 mm
    • weight: 0.45kg
    • contains: 10 b/w illus. 1 table
    • availability: Available
  • Table of Contents

    Introduction
    1. The type-free λ-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.

  • Author

    J. Roger Hindley, University of Wales, Swansea

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