Theory and Applications of Computability

Higher-Order Computability

Authors: Longley, John, Normann, Dag

  • Valuable for researchers in mathematical logic and theoretical computer science
  • Consolidates work carried out in this domain since the 1950s
  • Asks what ‘computability’ means for data more complex than natural numbers
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eBook $109.00
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  • ISBN 978-3-662-47992-6
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Hardcover $139.99
price for USA in USD
  • ISBN 978-3-662-47991-9
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Softcover $149.00
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  • ISBN 978-3-662-51711-6
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About this book

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages.

 

In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them.

 

The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers

Reviews

“This book is a true tour de force. The content is both mathematics and computer science; it is simultaneously an introductory textbook for students, a tutorial for seasoned researchers, a reference work, and a research monograph; ... The references to the literature are thorough. The writing is technical mathematics, and is good by that standard: there is ample intuitive explanation, and it is overall readable.” (Robert S. Lubarsky, Mathematical Reviews, April 2018)

Table of contents (13 chapters)

  • Introduction and Motivations

    Longley, John (et al.)

    Pages 3-34

  • Historical Survey

    Longley, John (et al.)

    Pages 35-50

  • Theory of Computability Models

    Longley, John (et al.)

    Pages 51-114

  • Theory of λ-Algebras

    Longley, John (et al.)

    Pages 115-164

  • Kleene Computability in a Total Setting

    Longley, John (et al.)

    Pages 167-210

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-662-47992-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-662-47991-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA in USD
  • ISBN 978-3-662-51711-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Higher-Order Computability
Authors
Series Title
Theory and Applications of Computability
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-47992-6
DOI
10.1007/978-3-662-47992-6
Hardcover ISBN
978-3-662-47991-9
Softcover ISBN
978-3-662-51711-6
Series ISSN
2190-619X
Edition Number
1
Number of Pages
XVI, 571
Number of Illustrations and Tables
2 illustrations in colour
Topics