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Higher-order computability

Longley, John.

Higher-order computability

Record Type:	Electronic resources : Monograph/item
Title/Author:	Higher-order computabilityby John Longley, Dag Normann.
Author:	Longley, John.
other author:	Normann, Dag.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg :2015.
Description:	xvi, 571 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Computable functions.
Online resource:	http://dx.doi.org/10.1007/978-3-662-47992-6
ISBN:	9783662479926$q(electronic bk.)

Higher-order computability
Longley, John.

Higher-order computability[electronic resource] /by John Longley, Dag Normann. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - xvi, 571 p. :ill., digital ;24 cm. - Theory and applications of computability, in cooperation with the association computability in Europe,2190-619X. - Theory and applications of computability, in cooperation with the association computability in Europe..

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.

ISBN: 9783662479926$q(electronic bk.)

Standard No.: 10.1007/978-3-662-47992-6doiSubjects--Topical Terms:

190932
Computable functions.

LC Class. No.: QA9.59

Dewey Class. No.: 511.3

Higher-order computability
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505 0 $a 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.
520 $a 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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