A Modern Perspective on Type Theory

From its Origins until Today
2004
ISBN: 978-1-4020-2334-7
Verlag: Springer Netherlands

Buch, Englisch, Band 29, 360 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1570 g

Reihe: Applied Logic Series

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.

Zielgruppe

Research

Autoren/Hrsg.

Kamareddine, F. D.

Nederpelt, Rob

Laan, T.

Fachgebiete

• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

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.