F. D. Kamareddine, T. Laan, Rob Nederpelt

A Modern Perspective on Type Theory (eBook, PDF)

From its Origins until Today

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 360
• Erscheinungstermin: 10. März 2006
• Englisch
• ISBN-13: 9781402023354
• Artikelnr.: 37344534

Inhaltsangabe

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.

Rezensionen

"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