A Modern Perspective on Type Theory From its Origins until Today /

A Modern Perspective on Type Theory From its Origins until Today /

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`Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century ha...

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Bibliographic Details
Main Authors: Kamareddine, Fairouz (Author), Laan, Twan (Author), Nederpelt, Rob (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Dordrecht : Springer Netherlands, 2005.
Series:Applied Logic Series, 29
Subjects:
Mathematics.
Logic.
Computer science > Mathematics.
Mathematical logic.
Mathematical Logic and Foundations.
Mathematics of Computing.
Online Access:Full Text via HEAL-Link
Table of Contents:
  • 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.

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