fix :: (a -> a) -> a
  fix f = f (fix f)

  f :: [Int] -> [Int]
  f xs = 1 : map (*2) xs

  take 7 (fix f)  ==>  [1,2,4,8,16,32,64]

Looks right to me.

Under Haskell's evaluation strategy `(fix f)` will not be evaluated until it is used, if the definition of `f` ignores its parameter under some scenario, then evaluation will terminate.

A general fixed point combinator cannot have a base case; it relies on the parameter to terminate the computation.

I think the trick is that Haskel is lazily evaluated. The Y combinator has a different formulation on strict languages.