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Table of contents (11 chapters)
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Front Matter
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Introduction
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The Evolution of Type Theory until the 1940s
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Front Matter
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Propositions as Types, Pure Type Systems, AUTOMATH
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Front Matter
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Extensions of Pure Type Systems
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Front Matter
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Back Matter
Keywords
About this book
- 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
Reviews
"This book has evolved from a number of projects by the authors … into aspects of the evolution of calculus and type theory in Logic, Mathematics and Computation. … The crown of this collaboration is this very rich and well written book … . This book not only gives a nice and concise overview … but also a mathematically precise and faithful reconstruction of the different type theories … . I expect the book will be a major work of reference … ." H.C.M. De Swart, Journal of Logic, Language and Information, Vol. 15, 2006
Authors and Affiliations
Bibliographic Information
Book Title: A Modern Perspective on Type Theory
Book Subtitle: From its Origins until Today
Authors: Fairouz Kamareddine, Twan Laan, Rob Nederpelt
Series Title: Applied Logic Series
DOI: https://doi.org/10.1007/1-4020-2335-9
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2005
Hardcover ISBN: 978-1-4020-2334-7Published: 09 June 2004
Softcover ISBN: 978-90-481-6639-8Published: 22 October 2010
eBook ISBN: 978-1-4020-2335-4Published: 10 March 2006
Series ISSN: 1386-2790
Edition Number: 1
Number of Pages: XIV, 360
Topics: Mathematical Logic and Foundations, Mathematics of Computing, Logic