[ostso]

That's a fixed-point combinator, but it's not actually the Y combinator; in fact, it defeats much of the purpose of Y, since it's defined using explicit recursion, which Y is designed to avoid.

If you just want a clear definition of a fixed-point combinator, you might as well use a non-strict language like Haskell, which doesn't require you to eta-expand g. Here's one recursive definition of fix in Haskell:

    fix f = f (fix f)

This is probably the clearest definition you could ask for of what a fixed-point combinator actually is (other than something like "fix f = f (f (f (f (f ...", which is more difficult to give to a computer).

Here's another one, which closer to what you gave in JavaScript (this is what you'll actually find in the Haskell standard libraries):

    fix f = let x = f x in x

(Of course, due to type-checking, it's non-trivial to define the actual non-recursive Y in Haskell; you usually have to resort to using some type-level recursion. But in an untyped non-strict language you could define it easily enough.)