Fixed point combinator in Haskell

Question

The fixed point combinator doesn\'t always produce the right answer given the definition:

fix f = f (fix f)

The following code does not ter

Answer 1

Fixed point combinator finds the least-defined fixed point of a function, which is ⊥ in your case (non-termination indeed is undefined value).

You can check, that in your case

(\x -> x * x) ⊥ = ⊥

i.e. ⊥ really is fixed point of \x -> x * x.

As for why is fix defined that way: the main point of fix is to allow you use anonymous recursion and for that you do not need more sophisticated definition.