Higher-Order Computability by John LongleyHigher-Order Computability by John Longley

Higher-Order Computability

byJohn Longley, Dag Normann

Hardcover | November 17, 2015

Pricing and Purchase Info

$166.61 online 
$193.50 list price save 13%
Earn 833 plum® points

Prices and offers may vary in store


In stock online

Ships free on orders over $25

Not available in stores


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

Title:Higher-Order ComputabilityFormat:HardcoverDimensions:571 pagesPublished:November 17, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3662479915

ISBN - 13:9783662479919

Look for similar items by category:


Table of Contents

Introduction and Motivation.- Historical Survey.- Theory of Computability Models.- Theory of Lambda Algebras.- Kleene Computability in a Total Setting.- Nested Sequential Procedures.- PCF and Its Models.- Total Continuous Functionals.- Hereditarily Effective Operations.- Partial Continuous Functionals.- Sequentially Realizable Functionals.- Some Intensional Models.- Related and Future Work.- References.- Index.