2010, ISBN: 9789048166398

gebonden uitgave

[ED: Softcover], [PU: Springer / Springer Netherlands], `Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-appl… Meer...

[ED: Softcover], [PU: Springer / Springer Netherlands], `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 themodern 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 Softcover reprint of hardcover 1st ed. 2004. 2010. xiv, 360 S. XIV, 360 p. 240 mm Versandfertig in 6-10 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Offene Rechnung (Vorkasse vorbehalten)<

2010, ISBN: 9789048166398

gebonden uitgave

[ED: Softcover], [PU: Springer / Springer Netherlands], `Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-appl… Meer...

[ED: Softcover], [PU: Springer / Springer Netherlands], `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 Softcover reprint of hardcover 1st ed. 2004. 2010. xiv, 360 S. XIV, 360 p. 240 mm Versandfertig in 6-10 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Offene Rechnung (Vorkasse vorbehalten)<

2010, ISBN: 9789048166398

pocketboek, gebonden uitgave

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides an overview … Meer...

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting., DE, [SC: 0.00], Neuware, gewerbliches Angebot, Taschenbuch, 360, [GW: 526g], Softcover reprint of hardcover 1. Auflage 2004, Banküberweisung, PayPal, [CT: Naturwissenschaft/Mathematik / Sonstiges - Naturwissenschaften]<

2010, ISBN: 9789048166398

pocketboek, gebonden uitgave

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides an overview … Meer...

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting., DE, [SC: 0.00], Neuware, gewerbliches Angebot, Taschenbuch, 360, [GW: 600g], Softcover reprint of hardcover 1. Auflage 2004, Banküberweisung, PayPal<

2010, ISBN: 9789048166398

From its Origins until Today, Buch, Softcover, Softcover reprint of hardcover 1st ed. 2004, [PU: Springer], Springer, 2010