module Control.Composition
    ( -- ^ Postcomposition
      (.*)
    , (.**)
    , (.***)
    -- ^ Precomposition
    , (-.)
    , (-.*)
    -- ^ Tuple helpers
    , both
    -- ^ Reexports from Control.Arrow
    , (&&&)
    , (***)
    -- ^ Reexports from Control.Monad
    , join
    , (=<<)
    , (>=>)
    , (<=<)
    -- ^ Reexports from base
    , (&)
    , fix
    , on
    , ap
    ) where

import           Control.Arrow ((&&&), (***))
import           Control.Monad (ap, join, (<=<), (=<<), (>=>))
import           Data.Function (fix, on, (&))

infixr 8 .*
infixr 8 -.*

{-fish' :: (a -> c -> b) -> (b -> c -> c) -> a -> c -> c
fish' f g x y = g (f x y) y

fish :: (a -> c -> b) -> (b -> c -> c) -> (a -> c -> c)
fish = (>=>)-}

both :: (a -> b) -> (a, a) -> (b, b)
both = join (***)

-- | As an example:
--
-- > λ:> ((*2) .* (+)) 1 3 4
-- > 16
(.*) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(.*) f g x y = f (g x y)

(.**) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
(.**) f g x y z = f (g x y z)

(.***) :: (e -> f) -> (a -> b -> c -> d -> e) -> a -> b -> c -> d -> f
(.***) f g w x y z = f (g w x y z)

-- | The Oedipus combinator
(-.*) :: (b -> c) -> (a -> c -> d) -> a -> b -> d
(-.*) f g x y = g x (f y)

-- | Backwards function composition
(-.) :: (a -> b) -> (b -> c) -> a -> c
(-.) f g x = g (f x)