[Haskell-cafe] GPT & Haskell

[Viktor Dukhovni]

On Sat, Apr 01, 2023 at 08:18:08AM +0200, Aloïs Cochard wrote:

> How can this be useful when you have to anyway review everything is doing
> as he might to just randomly insert a bug or a security flaw???
> I prefer to read poems by my human friends.
> 
> I highly recommend starting reading this paper at page 128 instead of
> wasting your time on that prompt:
> https://arxiv.org/pdf/2303.12712.pdf
> 
> Be ready for a good laugh

Part of the good laugh is on page 136:

    Let P be a point on the hyperbola

        x^2 + 3xy + 4x − 5y = −9y^2 − 133.

    Find the shortest possible distance from the origin to P.

The authors of the paper say that "GPT-4 produces a sound argument",
I beg to differ.

    Let u = 3y, then

        x^2 + xu + u^2 + 4x − (5/3)u = − 133.

    The degree-two part of which is positive-definite.  The linear terms
    just shift the origin. So the equation is actually:

        r^2 + rs + s^2 = RHS

    For a straight-forward to compute choice of r = x - a, s = u - b.

There are then two issues (just the first one is enough) with the prompt:

    * The equation can't represent a hyperbola, it would be an ellipse.
    * The ellipse doesn't exist, because the RHS constant is actually negative. 

THe authors are just as prone to autopilot nonsense reasoning as GPT-4.

This rather reminds me of:

    https://math.stackexchange.com/questions/1594740/v-i-arnold-says-russian-students-cant-solve-this-problem-but-american-student

-- 
    Viktor.