module Data.Functor.Syntax where

import Data.Composition
import Data.Function.Apply


-- * Nested Mapping

(<$$>) :: (Functor f0, Functor f1) =>
          (a -> b)
       -> f1 (f0 a)
       -> f1 (f0 b)
(<$$>) = fmap . fmap

infixr 8 <$$>

(<$$$>) :: (Functor f0, Functor f1, Functor f2) =>
          (a -> b)
       -> f2 (f1 (f0 a))
       -> f2 (f1 (f0 b))
(<$$$>) = fmap . fmap . fmap

infixr 8 <$$$>

(<$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
          (a -> b)
       -> f3 (f2 (f1 (f0 a)))
       -> f3 (f2 (f1 (f0 b)))
(<$$$$>) = fmap . fmap . fmap . fmap

infixr 8 <$$$$>

(<$$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3, Functor f4) =>
          (a -> b)
       -> f4 (f3 (f2 (f1 (f0 a))))
       -> f4 (f3 (f2 (f1 (f0 b))))
(<$$$$$>) = fmap . fmap . fmap . fmap . fmap

infixr 8 <$$$$$>

-- * Nested Application

(<~$>) :: Functor f0 =>
          f0 (a -> b)
       -> a -> f0 b
(<~$>) f x = fmap ($ x) f

infixl 8 <~$>

(<~~$>) :: Functor f0 =>
          f0 (a -> b -> c)
       -> b -> f0 (a -> c)
(<~~$>) f x = fmap (-$ x) f

infixl 8 <~~$>

(<~~~$>) :: Functor f0 =>
          f0 (a -> b -> c -> d)
       -> c -> f0 (a -> b -> d)
(<~~~$>) f x = fmap (--$ x) f

infixl 8 <~~~$>

(<~$$>) :: (Functor f0, Functor f1) =>
           f1 (f0 (a -> b))
        -> a -> f1 (f0 b)
(<~$$>) f x = fmap (<~$> x) f

infixl 8 <~$$>

(<~~$$>) :: (Functor f0, Functor f1) =>
            f1 (f0 (a -> b -> c))
         -> b -> f1 (f0 (a -> c))
(<~~$$>) f x = fmap (<~~$> x) f

infixl 8 <~~$$>

(<~~~$$>) :: (Functor f0, Functor f1) =>
             f1 (f0 (a -> b -> c -> d))
          -> c -> f1 (f0 (a -> b -> d))
(<~~~$$>) f x = fmap (<~~~$> x) f

infixl 8 <~~~$$>


(<~$$$>) :: (Functor f0, Functor f1, Functor f2) =>
            f2 (f1 (f0 (a -> b)))
         -> a -> f2 (f1 (f0 b))
(<~$$$>) f x = fmap (<~$$> x) f

infixl 8 <~$$$>

(<~~$$$>) :: (Functor f0, Functor f1, Functor f2) =>
            f2 (f1 (f0 (a -> b -> c)))
         -> b -> f2 (f1 (f0 (a -> c)))
(<~~$$$>) f x = fmap (<~~$$> x) f

infixl 8 <~~$$$>

(<~~~$$$>) :: (Functor f0, Functor f1, Functor f2) =>
             f2 (f1 (f0 (a -> b -> c -> d)))
          -> c -> f2 (f1 (f0 (a -> b -> d)))
(<~~~$$$>) f x = fmap (<~~~$$> x) f

infixl 8 <~~~$$$>


(<~$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
             f3 (f2 (f1 (f0 (a -> b))))
          -> a -> f3 (f2 (f1 (f0 b)))
(<~$$$$>) f x = fmap (<~$$$> x) f

infixl 8 <~$$$$>

(<~~$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
            f3 (f2 (f1 (f0 (a -> b -> c))))
         -> b -> f3 (f2 (f1 (f0 (a -> c))))
(<~~$$$$>) f x = fmap (<~~$$$> x) f

infixl 8 <~~$$$$>

(<~~~$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
             f3 (f2 (f1 (f0 (a -> b -> c -> d))))
          -> c -> f3 (f2 (f1 (f0 (a -> b -> d))))
(<~~~$$$$>) f x = fmap (<~~~$$$> x) f

infixl 8 <~~~$$$$>


(<~$$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3, Functor f4) =>
             f4 (f3 (f2 (f1 (f0 (a -> b)))))
          -> a -> f4 (f3 (f2 (f1 (f0 b))))
(<~$$$$$>) f x = fmap (<~$$$$> x) f

infixl 8 <~$$$$$>

(<~~$$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3, Functor f4) =>
            f4 (f3 (f2 (f1 (f0 (a -> b -> c)))))
         -> b -> f4 (f3 (f2 (f1 (f0 (a -> c)))))
(<~~$$$$$>) f x = fmap (<~~$$$$> x) f

infixl 8 <~~$$$$$>

(<~~~$$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3, Functor f4) =>
             f4 (f3 (f2 (f1 (f0 (a -> b -> c -> d)))))
          -> c -> f4 (f3 (f2 (f1 (f0 (a -> b -> d)))))
(<~~~$$$$$>) f x = fmap (<~~~$$$$> x) f

infixl 8 <~~~$$$$$>


-- * Nested Compositon

(<.$>) :: Functor f0 =>
          (b -> c)
       -> f0 (a -> b)
       -> f0 (a -> c)
f <.$> g = fmap (f .) g

infixr 8 <.$>

(<.*$>) :: Functor f0 =>
           (c -> d)
        -> f0 (a -> b -> c)
        -> f0 (a -> b -> d)
f <.*$> g = fmap (f .*) g

infixr 8 <.*$>

(<.**$>) :: Functor f0 =>
           (d -> e)
        -> f0 (a -> b -> c -> d)
        -> f0 (a -> b -> c -> e)
f <.**$> g = fmap (f .**) g

infixr 8 <.**$>


(<.$$>) :: (Functor f0, Functor f1) =>
          (b -> c)
       -> f1 (f0 (a -> b))
       -> f1 (f0 (a -> c))
f <.$$> g = (f .) <$$> g

infixr 8 <.$$>

(<.*$$>) :: (Functor f0, Functor f1) =>
           (c -> d)
        -> f1 (f0 (a -> b -> c))
        -> f1 (f0 (a -> b -> d))
f <.*$$> g = (f .*) <$$> g

infixr 8 <.*$$>

(<.**$$>) :: (Functor f0, Functor f1) =>
           (d -> e)
        -> f1 (f0 (a -> b -> c -> d))
        -> f1 (f0 (a -> b -> c -> e))
f <.**$$> g = (f .**) <$$> g

infixr 8 <.**$$>


(<.$$$>) :: (Functor f0, Functor f1, Functor f2) =>
          (b -> c)
       -> f2 (f1 (f0 (a -> b)))
       -> f2 (f1 (f0 (a -> c)))
f <.$$$> g = (f .) <$$$> g

infixr 8 <.$$$>

(<.*$$$>) :: (Functor f0, Functor f1, Functor f2) =>
           (c -> d)
        -> f2 (f1 (f0 (a -> b -> c)))
        -> f2 (f1 (f0 (a -> b -> d)))
f <.*$$$> g = (f .*) <$$$> g

infixr 8 <.*$$$>

(<.**$$$>) :: (Functor f0, Functor f1, Functor f2) =>
           (d -> e)
        -> f2 (f1 (f0 (a -> b -> c -> d)))
        -> f2 (f1 (f0 (a -> b -> c -> e)))
f <.**$$$> g = (f .**) <$$$> g

infixr 8 <.**$$$>


(<.$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
          (b -> c)
       -> f3 (f2 (f1 (f0 (a -> b))))
       -> f3 (f2 (f1 (f0 (a -> c))))
f <.$$$$> g = (f .) <$$$$> g

infixr 8 <.$$$$>

(<.*$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
           (c -> d)
        -> f3 (f2 (f1 (f0 (a -> b -> c))))
        -> f3 (f2 (f1 (f0 (a -> b -> d))))
f <.*$$$$> g = (f .*) <$$$$> g

infixr 8 <.*$$$$>

(<.**$$$$>) :: (Functor f0, Functor f1, Functor f2, Functor f3) =>
           (d -> e)
        -> f3 (f2 (f1 (f0 (a -> b -> c -> d))))
        -> f3 (f2 (f1 (f0 (a -> b -> c -> e))))
f <.**$$$$> g = (f .**) <$$$$> g

infixr 8 <.**$$$$>