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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.



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List of Articles
카테고리 제목 소속 강연자
수학강연회 <학부생을 위한 ε 강연> 압축센싱과 행렬완성 file 서울대 심병효
수학강연회 <학부생을 위한 ε 강연> 수학과 예술 - 초기 컴퓨터 그래픽 file 동양대학교 진중권
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수학강연회 Nonlocal generators of jump type Markov processes file University of Bielefeld Walter Hoh
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수학강연회 정년퇴임 기념강연: 회고 file 서울대 김도한
수학강연회 <학부생을 위한 강연> 사색 정리를 포함하는 Hadwiger의 추측의 변형에 관하여 file KAIST 엄상일
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