Why is the type of this function (a -> a) -> a?

Question

Why is the type of this function (a -> a) -> a?

Prelude> let y f = f (y f)
Prelude> :t y
y :: (t -> t) -> t

Shouldn't it be an infinite/recursive type? I was going to try and put into words what I think it's type should be, but I just can't do it for some reason.

y :: (t -> t) -> ?WTFIsGoingOnOnTheRHS?

I don't get how f (y f) resolves to a value. The following makes a little more sense to me:

Prelude> let y f x = f (y f) x
Prelude> :t y
y :: ((a -> b) -> a -> b) -> a -> b

But it's still ridiculously confusing. What's going on?