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5
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0answers
57 views

What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?

Over the years, advances in machine learning has allowed us to communicate and interact, using the same natural language, more and more semantically with computers, e.g. Google, Siri, Watson, etc. On ...
22
votes
0answers
389 views

Next steps on formal proof of classification of finite simple groups

While people are steaming ahead on finessing the proof of the classification of finite simple groups (CFSG), we have a formal proof in Coq of one of the first major components: the Feit-Thompson ...
2
votes
1answer
84 views

existence of multiplicity of roots [closed]

Im confuse..I read in an article that in dealing with polynomials, a quadratic equation can have either 2 real roots, 1 equal real root or 2 complex roots...but in dealing with random polynomials only ...
53
votes
3answers
2k views

How do I verify the Coq proof of Feit-Thompson?

I probably don't have the appropriate background to even ask this question. I know next to nothing about formal or computer-aided proof, and very little even about group theory. And this question is ...
10
votes
1answer
853 views

Where can I find Gonthier's Coq code proving the four color theorem?

In a 2008 article in the Notices, Georges Gonthier announced a computer-checked proof of the four color theorem using Coq: Gonthier, Georges. Formal proof—the four-color theorem. Notices Amer. ...
0
votes
1answer
681 views

Is there any danger far from home? (Edited & Revised Version) [closed]

The notion of formal proof is defined by finite sequences ($<\omega$ - sequences) of sentences. In some sense if a sentence $\sigma$ is (finitely) provable from the theory $T$ it is very "near" to ...
1
vote
1answer
194 views

Proof of regularity for bounded elliptic problem

We consider the boundary value problem for potential in the form: $$-\Delta u(\boldsymbol{x})=0,\quad \boldsymbol{x}\in \mathbb R^3\smallsetminus S,$$ with boundary conditions $$\nabla ...
2
votes
1answer
549 views

Hilbert style axiomatic proof or sequent Calculus?

I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory? With discriminatory I mean is which proof ...
1
vote
1answer
952 views

Where is a proof of “2 is more than 1 plus 1” said by Saunders Mac Lane? [closed]

I came across this statement in the autobiography by Saunders Mac Lane. It was the interaction between solenoids and group extension that got our collaboration started, and this first work of ...
1
vote
1answer
405 views

Since an inconsistent system can prove its own consistency…

Say a proof for the consistency of a formal system (proved within the formal system) is known. There are two possible cases: 1. the formal system is consistent and it can be and has been proven to be, ...
2
votes
1answer
318 views

Sequent calculus: is there a complete linear reasoning (i.e., no trees)?

In Gentzen's sequent calculus, a formal proof is described by a tree, with each node representing the sequent obtained from the child(ren) by applying a given inference rule. If no inference rule has ...
16
votes
3answers
814 views

Finite versions of Godel' s incompleteness

Assume you have some notion of proof complexity: for instance, at the basic level, the length of a proof, or the number of symbols used, take your pick (there are more involved measures, but for sake ...
8
votes
1answer
403 views

Proving that a combinatorial sequence has no compact formula

Suppose we have a sequence $a_n$ given by some combinatorial formula, e.g. involving a sum of n terms (like ${n \choose k}^{10}3^{-k}$ etc.). Sometimes it is plausible that there is no compact ...
10
votes
2answers
2k views

Consequences of technically proving anything in Coq (on at least Linux) exploiting a bug? [closed]

Technically, it is possible to prove anything in Coq proof assistant [1] (on at least Linux) due to a programming feature (or bug). This seems tractable when validating large proofs. Human analysis ...
23
votes
6answers
4k views

How true are theorems proved by Coq?

Less tongue in cheek, is it known what the relative consistency is for theorems proved with an automatic theorem prover? Of course this depends somewhat on what assumptions one makes with respect to ...