module Data.Composition (
  (.:),
  (.*),
  (.**),
  (.***),
  (.****),
  (.*****),
  (.******),
  (.*******),
  (.********),
  compose2,
  compose3,
  compose4,
  compose5,
  compose6,
  compose7,
  compose8,
  compose9
) where

-- | This function is defined as
-- 
-- > (.:) f g x y = f (g x y)
-- 
-- Example usage: @bind = join .: flip fmap@
-- Notice how two arguments will be given to @flip fmap@ before the result
-- is passed to @join@.
-- 
-- This is equivalent to @bind v f = join (fmap v f)@
(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(.:) f g x y = f (g x y)

-- | Equivalent to '(.:)'
-- 
-- The pattern of appending asterisks is more extensible,
-- but uncommon in practice.
(.*) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(.*) = (.) . (.)

(.**) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
(.**) = (.) . (.*)

(.***) = (.) . (.**)
(.****) = (.) . (.***)
(.*****) = (.) . (.****)
(.******) = (.) . (.*****)
(.*******) = (.) . (.******)
(.********) = (.) . (.*******)


compose2 :: (c -> d) -> (a -> b -> c) -> a -> b -> d
compose2 = (.*)

compose3 :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
compose3 = (.**)

compose4 = (.***)
compose5 = (.****)
compose6 = (.*****)
compose7 = (.******)
compose8 = (.*******)
compose9 = (.********)