- 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
Buy this book
- About this book
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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
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“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)
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Introduction and Motivations
Pages 3-34
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Historical Survey
Pages 35-50
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Theory of Computability Models
Pages 51-114
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Theory of λ-Algebras
Pages 115-164
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Kleene Computability in a Total Setting
Pages 167-210
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Table of contents (13 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Higher-Order Computability
- Authors
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- John Longley
- Dag Normann
- 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
- 2 illustrations in colour
- Topics
*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.
