Library function to compose a function with itself n times

Question

Is there a library function available in Haskell to compose a function with itself n times?

For example I have this function:

func :: a ->         


        

Answer 1

The iterate solution is fine, or you might like this one: the composition of n copies of f is foldr (.) id (replicate n f).

Answer 2

Here's a version that has complexity O(log n) instead of O(n) (to build the function, not to apply it):

composeN 0 f = id
composeN n f
    | even n = g
    | odd  n = f . g
    where g = g' . g'
          g' = composeN (n `div` 2) f

Answer 3

I do not know why you say that iterate is not appropriate. It is perfectly suitable for this purpose. (!! n) . iterate func is the composition of n copies of func.

(Someone had posted an answer similar to the above code, but he/she seems to have deleted it.)

Answer 4

(\n -> appEndo . mconcat . replicate n . Endo) n f x

Answer 5

\n -> appEndo . foldMap Endo . replicate n

Answer 6

iterate (f .) id !! n

or

iterate (f .) f !! (n-1)

depending on if n == 0 is allowed.