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2022　Topics in Algebra

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Tsuchioka Shunsuke 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(W832)  Thr7-8(W832)  
Group
-
Course number
MCS.T417
Credits
2
Academic year
2022
Offered quarter
4Q
Syllabus updated
2022/11/1
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Understanding dependent types and formal proofs via an implementation of a verifier

Student learning outcomes

(1) implementation of a verifier in the textbook "Type Theory and Formal Proof An Introduction by R. Nederpelt and G. Geuvers" in a programming language such as C, python, etc.
(2) formal proof by using your verifier of simple propositions
(3) theoretical background will not be explained because I put emphasis on implementation in the course

Keywords

lambda cube, formal proof, dependent types

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Thursdays will be for explaining the textbook. Mondays will be exercise-style implementation time.

Course schedule/Required learning

  Course schedule Required learning
Class 1 introduction Understand the content of the class
Class 2 implementation (alpha equivalence) Understand the content of the class
Class 3 lambda cube Understand the content of the class
Class 4 implementation (beta reduction) Understand the content of the class
Class 5 descriptive definitions (alias) Understand the content of the class
Class 6 implementation (delta conversion) Understand the content of the class
Class 7 primitive definitions (axioms) Understand the content of the class
Class 8 implementation (type inference) Understand the content of the class
Class 9 implementation (complexity) Understand the content of the class
Class 10 de Bruijn index Understand the content of the class
Class 11 implementation (optimization) Understand the content of the class
Class 12 propositions-as-types (proofs-as-terms) correspondence (PAT) Understand the content of the class
Class 13 proof assistant (Lean) Understand the content of the class
Class 14 A future of mathematics?（IMHO） Understand the content of the class

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

「Type Theory and Formal Proof An Introduction（by R.Nederpelt and H.Geuvers）」, Cambridge University Press（viewable at Tokyo Tech）

Reference books, course materials, etc.

I will open a course webpage and upload supplementing materials

Assessment criteria and methods

Based on your implementation (source code) and comprehension checks

Related courses

  • MTH.A301 ： Algebra I
  • MTH.A302 ： Algebra II
  • MTH.A331 ： Algebra III

Prerequisites (i.e., required knowledge, skills, courses, etc.)

(1) I require that you can write a simple code in one or more programming languages (mandatory)
(2) You can execute my binary for reference if you have a C++ compiler (not mandatory)
(3) I only require that you are familiar with elementary mathematics (high school level, not undergraduate level)

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