
Proof Market: Submit Coq proof, get paid with Bitcoin - waffle_ss
https://proofmarket.org/
======
Bakkot
Hm. Seems like it would make more sense for 'buyers' to submit btc along with
the problem, which the market could then hold in escrow and release as soon as
a proof passing the verifier was submitted. No need to trust anyone but the
escrow service, between btc and machine proofs.

~~~
gwern
Depends on who you want to put the burden onto, the buyers or the sellers. If
a buyer has to pay up front, especially with a marginal service like this,
they're exposed to opportunity cost (maybe they were going to do something
else with that money, although interest rates don't really exist for Bitcoin
yet) and counterparty risk (why do you trust this website to hold onto your
bitcoins and not be hacked?). If this market never takes off - as is one's
default expectation - it'd not be pleasant for buyers to have paid up front.

~~~
pirapira
I can mix both approaches. The buyer and other people can stash up bounty,
which the first prover gets. I have not implemented this lest "bitcoin stolen
from Coq proof exchange".

~~~
tsewlliw
Way to avoid arbitrary risks and complications!

~~~
pirapira
I added risks and complications. A feature called "bounty" is now available.
Anyone can add bounty for a problem. The sum goes to the next solver.

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djhworld
I like the idea, however it appears as if the buyer has to wait until the
seller has done the work before sending them payment.

How much confidence could the seller (i.e. the person doing the proof) have
about the buyers ability to pay before they embark on completing the work?

A much better approach would be the buyer puts up the problem they want a
proof for and then pays an escrow service, that way you can have more
confidence that payment will be completed.

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yetanotherphd
This is a bit ordinary, since it is fundamentally just an escrow service.

What would be really cool is to find a way to "lock" the bitcoins so that only
a correct proof in Coq of the given theorem could unlock them. Kind of like
holomorphic encryption.

~~~
paulgb
Bitcoin does have a (non-turing-complete) scripting language built in for
ensuring that transactions meet arbitrary requirements. I wonder what subset
of proofs could be verified in that environment.

~~~
velis_vel
The language doesn't support loops; in terms of flow control, you get if
statements and that's it. So probably not much of interest.

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kordless
Escrow implementation details aside, I love the idea of paying for information
with a system that provides a method for communicating information securely
between two parties. One of the more overlooked features of Bitcoin allows for
message signing: [http://bitcoin.stackexchange.com/questions/3337/what-are-
the...](http://bitcoin.stackexchange.com/questions/3337/what-are-the-safety-
guidelines-for-using-the-sign-message-feature/3339#3339)

With a signing method, you can simultaneously prove someone created
information containing a solution to a problem and the fact someone else paid
them for the information.

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platypii
This seems like a cool idea. What I like about it is the way that it assigns a
quantifiable value to mathematical proofs, and incentives their production.

Assuming proofs are valuable (which I believe they are), then by creating a
market we can learn an approximation of what they are really worth to people.

Also I like that it is another outlet for mathematicians to profit from their
skills. The options for pure math as a career are fairly bleek right now (fuck
the nsa, academia maybe, not many research jobs in industry). I could see this
market as a way to incentive more pure math research.

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tel
I don't know if Coq with nested universes is known to be inconsistent yet, but
I suppose that for this to work someone must always bankroll `inconsistent :
forall a : Set, a` at something significantly higher than any other proof on
the market and the system should reject repeated proofs.

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elwell
This sort of 'market' could surely be used for many other use-cases.

~~~
bronty
It actually can't -- a fundamental characteristic of this marketplace is that
the work can be automatically verified [1].

As part of my PhD work, I created a service for crowdsourcing the verification
of Java programs which relied on the same characteristic:
[http://homes.cs.washington.edu/~mernst/pubs/veriweb-
oopsla20...](http://homes.cs.washington.edu/~mernst/pubs/veriweb-
oopsla2012-abstract.html).

One limitation of these crowd-sourcing approaches is that, in practice,
validation ("are we trying to build/prove the right thing?") is as important,
if not more important, than verification.

[1] this might not be quite true yet, since a solution of "admitted." would
pass the Coq checker.

~~~
tel
Is that something a grep couldn't fix?

~~~
bronty
Yes, a grep could locate that.

~~~
tel
It's more a question of if there are any other known inconsistencies in Coq
that could be used to trivially generate proofs which are artificial under
human scrutiny but OK by an automated proof market.

~~~
bronty
You'd run into a problem if you let workers introduce assumptions (since
introducing a contradiction lets the worker prove anything).

With Coq, you don't have a problem of unsoundness. The problem you have is
that the difficulty / time it takes to write a proof is often very sensitive
to how you've written your assumptions and formulated the claim. You'd likely
want to add a mechanism to the marketplace to reward workers for suggesting
ways to improve the problem formulation.

For my Java project, we were using ESC/Java2 under the hood which is unsound
in a lot of ways. We definitely observed workers taking advantage of these
(either intentionally or not).

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shinobu
This project might be harmful because of overjustification effect. [1] If
there was some site 15 years ago that offered payment for writing an article
on a given subject, would the number of contributors to wikipedia and thus the
number of articles drop?

Also, it is unclear how to fit formalization of huge projects like
classification of simple groups or IUTech in "reward for a proof" approach.

[1]
[https://en.wikipedia.org/wiki/Overjustification_effect](https://en.wikipedia.org/wiki/Overjustification_effect)

~~~
pirapira
There is a similar site [1] without external incentives (actually Proof Market
is based on this). This site has active audience posting problems and proofs.
Possibly Proof Market ends up in another example of overjustification.

[1] [http://as305.dyndns.org/aps/](http://as305.dyndns.org/aps/)

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markeightfold
This is fascinating to me. A couple comments and links.

Here is a course on proof theory that uses Coq [1]. It is actually the course
that Vladimir Voevodsky took when he was trying to understand proof and type
theory [2], [3]. While writing the midterm paper, he discovered homotopy type
theory [4]. More details on the bitcoin scripting language can be found in the
excellent blog post by Michael Nielsen[5].

If the escrow model is implemented, you can actually imagine the mathematical
proof market maker acting like a bank, loaning out or otherwise investing
bitcoins while the world waits for a verified proof; say, of the abc
conjecture [6a] or the goldbach conjecture [6b]. This might be one small way
to disrupt Wall St [7a], [7b]. In particular, such a market, when more highly
developed, provides skilled mathematicians and scientists incentives to work
on math and ( computer ) science problems in an open source format that
benefits everyone - since everyone can look at and learn from their proofs -
rather than quantitative trading in a closed format that actually causes long
term social harm and political instability [IMHO]. I am thinking here of
Goldman Sachs and Renaissance Technology founded by James Simons. Imagine if
an incentive structure existed that encouraged all these smart folks to work
on what is essentially verifiable open source software [8].

[1]
[http://www.cs.princeton.edu/courses/archive/fall09/cos441/in...](http://www.cs.princeton.edu/courses/archive/fall09/cos441/index.php)
[2] [http://blogs.scientificamerican.com/guest-
blog/2013/10/01/vo...](http://blogs.scientificamerican.com/guest-
blog/2013/10/01/voevodskys-mathematical-revolution/) [3]
[http://www.heidelberg-laureate-forum.org/event_2013/](http://www.heidelberg-
laureate-forum.org/event_2013/) [4]
[http://homotopytypetheory.org/book/](http://homotopytypetheory.org/book/) [5]
[http://www.michaelnielsen.org/ddi/how-the-bitcoin-
protocol-a...](http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-
actually-works/) [6a] [http://www.nytimes.com/2012/09/18/science/possible-
breakthro...](http://www.nytimes.com/2012/09/18/science/possible-breakthrough-
in-maths-abc-conjecture.html) [6b]
[http://xkcd.com/1310/](http://xkcd.com/1310/) [7a]
[http://cdixon.org/2013/12/31/why-im-interested-in-
bitcoin/](http://cdixon.org/2013/12/31/why-im-interested-in-bitcoin/) [7b]
[http://cdixon.org/2010/01/23/how-to-disrupt-wall-
street/](http://cdixon.org/2010/01/23/how-to-disrupt-wall-street/) [8] This is
a pipe dream.

~~~
pirapira
This gives very broad perspective. I want to cite this comment when I talk
about the site. I have never thought about disrupting Wall St, but I do share
your pipe dream.

