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This 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 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.
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A Modern Perspective on Type Theory APPLIED LOGIC SERIES VOLUME 29 Managing Editor Dov M. Gabbay, Department of Computer Science, King’s College, London, U.K. Co-Editor Jon Barwise† Editorial Assistant Jane Spurr, Department of Computer Science, King’s College, London, U.K. SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing so demonstrates the underlying unity and applicability of logic. The titles published in this series are listed at the end of this volume. A Modern Perspective on Type Theory From its Origins until Today by FAIROUZ KAMAREDDINE Heriot Watt University, Edinburgh, Scotland TWAN LAAN Eindhoven, The Netherlands and ROB NEDERPELT Eindhoven University of Technology, The Ne