{-# LANGUAGE QuantifiedConstraints     #-}
{-# LANGUAGE DerivingVia               #-}
--------------------------------------------------------------------------------
-- |
-- Module      :  Data.Comp.Multi.HFunctor
-- Copyright   :  (c) 2011 Patrick Bahr
-- License     :  BSD3
-- Maintainer  :  Patrick Bahr <paba@diku.dk>
-- Stability   :  experimental
-- Portability :  non-portable (GHC Extensions)
--
-- This module defines higher-order functors (Johann, Ghani, POPL
-- '08), i.e. endofunctors on the category of endofunctors.
--
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
-- |
-- Module      :  Data.Comp.Multi.HFoldable
-- Copyright   :  (c) 2011 Patrick Bahr
-- License     :  BSD3
-- Maintainer  :  Patrick Bahr <paba@diku.dk>
-- Stability   :  experimental
-- Portability :  non-portable (GHC Extensions)
--
-- This module defines higher-order foldable functors.
--
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
-- |
-- Module      :  Data.Comp.Multi.HTraversable
-- Copyright   :  (c) 2011 Patrick Bahr
-- License     :  BSD3
-- Maintainer  :  Patrick Bahr <paba@diku.dk>
-- Stability   :  experimental
-- Portability :  non-portable (GHC Extensions)
--
-- This module defines higher-order traversable functors.
--
--------------------------------------------------------------------------------
module Data.Comp.Multi.Classes(HFunctor(..),HFoldable(..),HTraversable(..),HIdentity(..))where
import Data.Kind
import Data.Functor.Compose
import Data.Functor.Const
import Data.Maybe
import Data.Monoid
import Data.Functor.Classes
import Data.Coerce
import Data.Functor.Identity
import Data.Foldable(Foldable(..))
import GHC.Generics
-- | This class represents higher-order functors (Johann, Ghani, POPL
-- '08) which are endofunctors on the category of endofunctors.
type FTransformer = ((Type -> Type) -> Type -> Type)
type HFunctor :: FTransformer -> Constraint
class (forall f. Functor f => Functor (h f)) => HFunctor h where
    -- -- A higher-order functor @f@ maps every functor @g@ to a
    -- functor @f g@.
    --
    -- @ffmap :: (Functor g) => (a -> b) -> f g a -> f g b@
    --
    -- We omit this, as it does not work for GADTs (see Johand and
    -- Ghani 2008).

    -- | A higher-order functor @f@ also maps a natural transformation
    -- @g :-> h@ to a natural transformation @f g :-> f h@
    hfmap ::forall f g i. (f i -> g i) -> h f i -> h g i

instance (Functor f) => HFunctor (Compose f) where hfmap f (Compose xs) = Compose (fmap f xs)
type HIdentity :: FTransformer
newtype HIdentity f a = MkHIdentity {getHIdentity::f a} 
  deriving newtype (Eq,Ord,Show,Eq1,Ord1,Show1,Generic,Generic1,Functor,Foldable,Traversable)