Comment by smosher_

It's because the generator recurses with:

    return fself(num - 1) + fself(num - 2);

instead of calling fib (or fib_gen) explicitly. fself is passed into the generator and it will need to be passed in again and again. That's what Y gets you. You could get tracing the way you suggest from something like:

    let fib f n =
        let n' = (* compute fib for n *) in
        f n'

and supply some f that will log (and return) the computed values, but that won't work with the motivating example: memoization. This really should have been clearer in TFA.

It's worth noting the memoization in the linked gist isn't pure. memo() allocates a cache and returns a function that references it. The cache is updated by mutating in place. After all the hoops we've jumped thorugh it's a bit of a let-down to end up here. (It's doable though.)

(Edit: improve clarity.)