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Higher-Order Computability [electronic resource] / by John Longley, Dag Normann.

By: Longley, John [author.].
Contributor(s): Normann, Dag [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Theory and Applications of Computability, In cooperation with the association Computability in Europe: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015Description: XVI, 571 p. 2 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783662479926.Subject(s): Computer science | Computers | Computer science -- Mathematics | Computer Science | Theory of Computation | Mathematics of ComputingAdditional physical formats: Printed edition:: No titleDDC classification: 004.0151 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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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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.

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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