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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Grundlagen A Modern Perspective on Type Theory
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A Modern Perspective on Type Theory
T. Laan (Gebundene Ausgabe, Englisch)
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Beschreibung
`Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress… in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers, and the correctness of proofs and programs. The authors of this book have themselves been leading the way by providing various extensions of type theory which have been shown to bring many advantages. This book gathers much of their influential work and is highly recommended for anyone interested in type theory. The main emphasis is on: - Types: from Russell to Ramsey, to Church, to the modern Pure Type Systems and some of their extensions. - Functions: from Frege, to Russell to Church, to Automath and the use of functions in mathematics, programming languages and theorem provers. - The role of types in logic: Kripke's notion of truth, the evolution and role of the propositions as types concept and its use in logical frameworks. - The role of types in computation: extensions of type theories which can better model proof checkers and programming languages are given. The first part of the book is historical, yet at the same time, places historical systems (like Russell's RTT) in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms), but at the same time, places another historical system (the proof checker Automath) in the modern setting. The third part uses this bridging in the first two parts between historical and modern systems to propose new systems that bring more advantages together. This book has much to offer to mathematicians, logicians and to computer scientists in general. It will have considerable influence for many years to come.' - Henk Barendregt Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
09.06.2004
Sprache
Englisch
EAN
9781402023347
Herausgeber
Springer Netherland
Serien- oder Bandtitel
Applied Logic Series
Sonderedition
Nein
Autor
T. Laan
Seitenanzahl
360
Einbandart
Gebundene Ausgabe
Buch Untertitel
From its Origins until Today
Schlagwörter
Computer, calculus, computer science, logic, predicate logic, programming, programming language, proof, type theory
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
UYAM - Mathematik für Informatiker
QDTL - Philosophie: Logik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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