Fix-point type. It allows to define generic recurion schemes.

Fix f = f (Fix f)

Type f should be a Functor if you want to use simple recursion schemes or Traversable if you want to use monadic recursion schemes. This style allows you to express recursive functions in non-recursive manner. You can imagine that a non-recursive function holds values of the previous iteration.

Little example:

type List a = Fix (L a)

data L a b = Nil | Cons a b

instance Functor (L a) where
   fmap f x = case x of
       Nil      -> Nil
       Cons a b -> Cons a (f b)

length :: List a -> Int
length = cata $ \x -> case x of
   Nil      -> 0
   Cons _ n -> n + 1

sum :: Num a => List a -> a
sum = cata $ \x -> case x of
   Nil      -> 0
   Cons a s -> a + s

Type f should be a Functor. They transform non-recursive functions to recursive ones.

Type f should be a Traversable.