Type Theory (类型论) Foundations

Robert Harper 2013

Lecture 1:

Holy Trinity: A Scientific Discovery is TRUE if fulfills:

  1. Proof Theory Logic
  2. Algebraic Category Theory
  3. Program Type Theory

A Program is an ABSTRACT Mathematical Object (“M”) :

“A is true” written as “M A”,

ie M is of Type A.

Note: Program M is not about “Coding”.

Above diagram:

[Left] : Proof Theory Logic

[Right] : Category Theory

Lecture 2:

Lecture 2.1

(Video 15:30 mins)

Type Theory is the theory of construction of programming language:

Higher Order Function <=> Exponential Type

Struct, Tuple <=> Cartesian Product Type

Choices of classes of data <=> ‘Some’ Type

Logic is an application of Type Theory

Logic is a part of Math which is a part of Computer Science in which Type Theory is the ‘Theory of Construction’ of Programming Languages.

Lecture 2.2:

Lecture 3:

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