A Modern Perspective on Type Theory

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. 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. The third part proposes new systems that bring more advantages together.

"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