Higher-Order Computability

  • John Longley
  • Dag Normann

Part of the Theory and Applications of Computability book series (THEOAPPLCOM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Background and General Theory

    1. Front Matter
      Pages 1-2
    2. John Longley, Dag Normann
      Pages 3-34
    3. John Longley, Dag Normann
      Pages 35-50
    4. John Longley, Dag Normann
      Pages 51-114
    5. John Longley, Dag Normann
      Pages 115-164
  3. Particular Models

    1. Front Matter
      Pages 165-166
    2. John Longley, Dag Normann
      Pages 167-210
    3. John Longley, Dag Normann
      Pages 211-278
    4. John Longley, Dag Normann
      Pages 279-348
    5. John Longley, Dag Normann
      Pages 349-430
    6. John Longley, Dag Normann
      Pages 431-462
    7. John Longley, Dag Normann
      Pages 463-488
    8. John Longley, Dag Normann
      Pages 489-504
    9. John Longley, Dag Normann
      Pages 505-534
    10. John Longley, Dag Normann
      Pages 535-546
  4. Back Matter
    Pages 547-571

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.



Computability Models Computability Theory Intensional Models Kleene Computability Lambda Algebras

Authors and affiliations

  • John Longley
    • 1
  • Dag Normann
    • 2
  1. 1.Informatics ForumSchool of InformaticsEdinburghUnited Kingdom
  2. 2.Dept. of MathematicsThe University of OsloOsloNorway

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science Computer Science (R0)
  • Print ISBN 978-3-662-47991-9
  • Online ISBN 978-3-662-47992-6
  • Series Print ISSN 2190-619X
  • Series Online ISSN 2190-6203
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
IT & Software
Consumer Packaged Goods