Higher-Order Computability by John Longley (English) Hardcover Book

Description: Higher-Order Computability by John Longley, Dag Normann 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 Back Cover 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. 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. Review "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) Review Quote "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) Feature 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 Details ISBN3662479915 ISBN-10 3662479915 ISBN-13 9783662479919 Format Hardcover Series Theory and Applications of Computability Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 004.0151 Short Title HIGHER-ORDER COMPUTABILITY 201 Language English Media Book Author Dag Normann Birth 1947 Year 2015 Pages 571 Edition 1st Illustrations 2 Illustrations, color; XVI, 571 p. 2 illus. in color. DOI 10.1007/978-3-662-47992-6 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 1st ed. 2015 Publication Date 2015-11-17 Alternative 9783662517116 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:127853604;

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