http://en.wikibooks.org/wiki/Haskell/Fix_and_recursion

fixpoint_combinator.hs

import Control.Monad.Fix

------------------------------------------------                                                                    
-- fact                                                                                                             

-- fact is a fixpoint for lambda_fact                                                                               
fact n = if n == 0 then 1 else n * fact (n-1)
lambda_fact = (\g n -> if n == 0 then 1 else n * g (n-1))

-- fixpoint combinator 'fix' "encode" recursion of fact                                                             
fixpoint_fact = fix lambda_fact

------------------------------------------------                                                                    
-- filter                                                                                                           

filter' f xs = if null xs then []
                  else let x = if f (head xs) then [head xs] else []
                           in x++ (filter' f $ tail xs)

lambda_filter = (\g f xs -> if null xs then []
                             else let x = if f (head xs) then [head xs] else []
                                      in x++ (g f $ tail xs))

fixpoint_filter = fix lambda_filter