Volume 29 2005

A Modern Perspective on Type Theory

From its Origins until Today

Authors:

ISBN: 978-1-4020-2334-7 (Print) 978-1-4020-2335-4 (Online)

Table of contents (11 chapters)

  1. Introduction

    1. No Access

      Book Chapter

      Pages 1-6

      Introduction

  2. The Evolution of Type Theory until the 1940s

    1. Front Matter

      Pages 7-7

    2. No Access

      Book Chapter

      Pages 3-18

      Prehistory

    3. No Access

      Book Chapter

      Pages 19-67

      Type theory in Principia Mathematica

    4. No Access

      Book Chapter

      Pages 69-101

      Deramification

  3. Propositions as Types, Pure Type Systems, AUTOMATH

    1. Front Matter

      Pages 103-103

    2. No Access

      Book Chapter

      Pages 105-123

      Propositions as Types and Pure Type Systems

    3. No Access

      Book Chapter

      Pages 125-152

      The pre-PAT RTT and STT in PAT-style

    4. No Access

      Book Chapter

      Pages 153-177

      A Correspondence between RTT and the system Nuprl

    5. No Access

      Book Chapter

      Pages 179-230

      Automath

  4. Extensions of Pure Type Systems

    1. Front Matter

      Pages 231-231

    2. No Access

      Book Chapter

      Pages 233-241

      Pure Type Systems with definitions

    3. No Access

      Book Chapter

      Pages 243-254

      The Barendregt cube with parameters

    4. No Access

      Book Chapter

      Pages 255-310

      Pure Type Systems with parameters and definitions