The Evolution of Type Theory until the 1940s.- Prehistory.- Type theory in Principia Mathematica.- Deramification.- Propositions as Types, Pure Type Systems, AUTOMATH.- Propositions as Types and Pure Type Systems.- The pre-PAT RTT and STT in PAT-style.- A Correspondence between RTT and the system Nuprl.- Automath.- Extensions of Pure Type Systems.- Pure Type Systems with definitions.- The Barendregt cube with parameters.- Pure Type Systems with parameters and definitions.
"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
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