Overview
'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: 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
Full Product Details
Author: F.D. Kamareddine ,
T. Laan ,
Rob Nederpelt
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2004 ed.
Volume: 29
Dimensions:
Width: 15.50cm
, Height: 2.20cm
, Length: 23.50cm
Weight: 1.570kg
ISBN: 9781402023347
ISBN 10: 1402023340
Pages: 360
Publication Date: 09 June 2004
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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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
This book has evolved from a number of projects by the authors a ] into aspects of the evolution of calculus and type theory in Logic, Mathematics and Computation. a ] The crown of this collaboration is this very rich and well written book a ] . This book not only gives a nice and concise overview a ] but also a mathematically precise and faithful reconstruction of the different type theories a ] . I expect the book will be a major work of reference a ] . H.C.M. De Swart, Journal of Logic, Language and Information, Vol. 15, 2006
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
