A Modern Perspective on Type Theory

1. Introduction

Part I. The Evolution of Type Theory until the 1940s

2. Prehistory

3. Type theory in Principia Mathematica

4. Deramification

Part II. Propositions as Types, Pure Type Systems, AUTOMATH

5. Propositions as Types and Pure Type Systems

6. The pre-PAT RTT and STT in PAT-style

7. A Correspondence between RTT and the system Nuprl

8. Automath

Part III. Extensions of Pure Type Systems

9. Pure Type Systems with definitions

10. The Barendregt cube with parameters

11. Pure Type Systems with parameters and definitions

Keywords: Mathematics, Mathematical Logic and Foundations, Mathematics of Computing, Logic