beginner's questions - fix f

[Bob Koutsky]

Hello,

After watching members of this list discussing some for me really 
incomprehensible details of Haskell standard, I feel sort of  silly for 
asking something probably very basic, but I'd be very grateful for any answer:
Some time ago, I have decided to educate myself in functional programming, 
and I choose Haskell as a language of choice. I purchased "Haskell school 
of expression" and began to study it. Everything went well, I understood 
(at least intuitively) everything, but then, suddenly, I hit a wall:

------------------------------------------------------------
Exercise 9.9:
remainder a b = if a < b then a
                         else remainder (a-b) b

fix f = f (fix f)

Rewrite remainder using fix so that it is not recursive.
------------------------------------------------------------


Function fix left me completely puzzled. With help of hugs I found out that 
its type is "( a -> a ) -> a", but I have absolutely no idea how it could 
be used to do anything useful. It seems to me that argument to f on the 
right side of fix's definition must always evaluate to the same value, no 
matter how deep the recursion is, so there is no point to use it. I guess I 
am missing something very obvious, but what is it? Can somebody provide me 
with an example how to use fix for something just a bit useful, if possible 
to rewrite remainder?

thank you,
Bob Koutsky