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'
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  3. Solver friendly finite element methods

  4. Brownian motion and energy minimizing measure in negative curvature

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  7. Weyl character formula and Kac-Wakimoto conjecture

  8. Nonlocal generators of jump type Markov processes

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

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

  13. The classification of fusion categories and operator algebras

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

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

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  18. Zeros of the derivatives of the Riemann zeta function

  19. Geometry, algebra and computation in moduli theory

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

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