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proof verificationhttps://nforum.ncatlab.org/discussion/4409/2012-10-18T16:19:01+00:002012-10-24T05:16:51+00:00jim_stasheffhttps://nforum.ncatlab.org/account/12/
From a colleague Subject: [Math-visitors] remarkable achievement in proof verification Date: Wed, 17 Oct 2012 13:22:57 -0400 From: Jean Gallier <jean@cis.upenn.edu> To: ...
From a colleague Subject: [Math-visitors] remarkable achievement in proof verification Date: Wed, 17 Oct 2012 13:22:57 -0400 From: Jean Gallier <jean@cis.upenn.edu> To: faculty@math.upenn.edu, grad@math.upenn.edu, visitors@math.upenn.edu
Dear all,
I learned from the "Types Forum" that a group of researchers at MSR/INRIA led by Georges Gonthier completed a formal verification (in Coq) of the "Odd order theorem," due to Feit and Thompson (every finite group of odd order is solvable).
The task of proof verification in Coq took 6 years. The Coq development contains ~ 170 000 lines of code ~ 4200 definitions ~ 15 000 theorems.
They did find small gaps, but all could be patched.
For more details, see http://www.msr-inria.inria.fr/Projects/math-components/feit-thompson In particular, at the end of the page, look at the "final theory graph."
The question remains: how do we know (and prove) that Coq is correct? We have to verify the verifier!