Implement Trait for a specific function

Hello,

I wanted to know if I could implement a Trait for a specific function (not a signature, as here)?
E.g., I would like to be able to define a derivative for an existing function so that I can later call function.diff to produce the derivative.

fn affine(x: isize) -> isize {
    x * 4 + 2
}

pub trait Differentiable<Args> {
    type Output;
    fn diff(&self, args: Args) -> Self::Output;
}

impl Differentiable<()> for affine { // expected type, found function `crate::affine`
    type Output = isize;
    fn diff(&self, _args: (isize,)) -> Self::Output {
        4
    }
}

pub fn main() {
    affine.diff((4,));
}

If Rust automatically implements Fn trait on closures / functions, shouldn't there be some hidden type for each closure / function?

It's true that the function has its own type, but its not possible to implement traits for it.

Ok, thanks for the fast reply!