Date:August 27, 2014

Time: 4:30PM-5:30PM

Location: NIMS, CAMP seminar room (국가수리과학연구소 수학원리응용센터 세미나실)

[Title]

Mechanization of Proof: From 4-Color Theorem to Compiler Verification.

[Abstract]

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.

[Speaker]

Chung-Kil Hur (허충길)

[Short-Bio]

Chung-Kil Hur is an assistant professor in Department of Computer Science and Engineering at Seoul National University.  Previously he worked as a postdoctoral researcher at Microsoft Research Cambridge, Max Planck Institute for Software Systems (MPI-SWS) and Laboratoire PPS. He obtained a Ph.D. from University of Cambridge and a B.Sc. in Mathematics and in Computer Science from KAIST. He also received a bronze medal in the 35th International Mathematical Olympiad (IMO) in 1994.  His research interests are in software verification, interactive theorem proving, probabilistic programming and Beyesian inference.