Overview
- 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
Part of the book series: Theory and Applications of Computability (THEOAPPLCOM)
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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
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Keywords
Table of contents (13 chapters)
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Front Matter
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Background and General Theory
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Front Matter
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Particular Models
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Front Matter
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Back Matter
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)
Authors and Affiliations
Bibliographic Information
Book Title: Higher-Order Computability
Authors: John Longley, Dag Normann
Series Title: Theory and Applications of Computability
DOI: https://doi.org/10.1007/978-3-662-47992-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-47991-9Published: 17 November 2015
Softcover ISBN: 978-3-662-51711-6Published: 23 August 2016
eBook ISBN: 978-3-662-47992-6Published: 06 November 2015
Series ISSN: 2190-619X
Series E-ISSN: 2190-6203
Edition Number: 1
Number of Pages: XVI, 571
Number of Illustrations: 2 illustrations in colour