Extra Form
강연자 허충길
소속 서울대 컴퓨터공학부
date 2015-04-15

I will give a broad introduction to how to mechanize mathematics (or proof), which will be mainly about the proof assistant Coq. Mechanizing mathematics consists of (i) defining a set theory, (2) developing a tool that allows writing definitions and proofs in the set theory, and (3) developing an independent proof checker that checks whether a given proof is correct (ie, whether it is a valid combination of axioms and inference rules of the set theory). Such a system is called proof assistant and Coq is one of the most popular ones.

In the first half of the talk, I will introduce applications of proof assistant, ranging from mechanized proof of 4-color theorem to verification of an operating system. Also, I will talk about a project that I lead, which is to provide, using Coq, a formally guaranteed way to completely detect all bugs from compilation results of the mainstream C compiler LLVM.

In the second half, I will discuss the set theory used in Coq, called Calculus of (Inductive and Coinductive) Construction. It will give a very interesting view on set theory. For instance, in calculus of construction, the three apparently different notions coincide: (i) sets and elements, (ii) propositions and proofs, and (iii) types and programs.

If time permits, I will also briefly discuss how Von Neumann Universes are handled in Coq and how Coq is used in homotopy type theory, led by Fields medalist Vladimir Voevodsky.

첨부 '1'
  1. Weyl character formula and Kac-Wakimoto conjecture

  2. Nonlocal generators of jump type Markov processes

  3. Regularity of solutions of Hamilton-Jacobi equation on a domain

  4. What is Weak KAM Theory?

  5. 정년퇴임 기념강연: 회고

  6. <학부생을 위한 강연> 사색 정리를 포함하는 Hadwiger의 추측의 변형에 관하여

  7. The classification of fusion categories and operator algebras

  8. Green’s function for initial-boundary value problem

  9. 16Apr
    by 김수현
    in 수학강연회

    Mechanization of proof: from 4-Color theorem to compiler verification

  10. On the distributions of partition ranks and cranks

  11. Q-curvature in conformal geometry

  12. Zeros of the derivatives of the Riemann zeta function

  13. Geometry, algebra and computation in moduli theory

  14. Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology

  15. High dimensional nonlinear dynamics

  16. What is model theory?

  17. Essential dimension of simple algebras

  18. Restriction theorems for real and complex curves

  19. Recommendation system and matrix completion: SVD and its applications (학부생을 위한 강연)

  20. Deformation spaces of Kleinian groups and beyond

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