-- |
-- Module      : Control.Applicative.ListF
-- Copyright   : (c) Justin Le 2019
-- License     : BSD3
--
-- Maintainer  : [email protected]
-- Stability   : experimental
-- Portability : non-portable
--
-- This module provides functor combinators that are wrappers over lists or
-- maybes of @f a@s, especially for their
-- 'Data.HFunctor.Interpret.Interpret' instances.
--
-- Each one transforms a functor into some product of itself.  For example,
-- @'NonEmptyF' f@ represents @f ':*:' f@, or @f :*: f :*: f@, or @f :*:
-- f :*: f :*: f@, etc.
module Control.Applicative.ListF (
  -- * 'ListF'
    ListF(..), mapListF
  -- * 'NonEmptyF'
  , NonEmptyF(.., ProdNonEmpty, nonEmptyProd), mapNonEmptyF
  , toListF, fromListF
  -- * 'MaybeF'
  , MaybeF(..), mapMaybeF
  , listToMaybeF, maybeToListF
  -- * 'MapF'
  , MapF(..)
  , NEMapF(..)
  ) where

import           Control.Applicative
import           Control.Natural
import           Data.Coerce
import           Data.Data
import           Data.Deriving
import           Data.Foldable
import           Data.Functor.Bind
import           Data.Functor.Classes
import           Data.Functor.Contravariant
import           Data.Functor.Contravariant.Conclude
import           Data.Functor.Contravariant.Decide
import           Data.Functor.Contravariant.Divise
import           Data.Functor.Contravariant.Divisible
import           Data.Functor.Invariant
import           Data.Functor.Plus
import           Data.List.NonEmpty                   (NonEmpty(..))
import           Data.Maybe
import           Data.Pointed
import           Data.Semigroup.Foldable
import           Data.Semigroup.Traversable
import           GHC.Generics
import qualified Data.Map                             as M
import qualified Data.Map.NonEmpty                    as NEM

-- | A list of @f a@s.  Can be used to describe a product of many different
-- values of type @f a@.
--
-- This is the Free 'Plus'.
--
-- Incidentally, if used with a 'Contravariant' @f@, this is instead the
-- free 'Divisible'.
newtype ListF f a = ListF { ListF f a -> [f a]
runListF :: [f a] }
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-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
forall k (f :: k -> *) (a :: k) r r'.
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
forall k (f :: k -> *) (a :: k) (m :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Monad m) =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
forall k (f :: k -> *) (a :: k) (m :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), MonadPlus m) =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
forall k (f :: k -> *) (a :: k) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (ListF f a)
forall k (f :: k -> *) (a :: k) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> ListF f a -> c (ListF f a)
forall k (f :: k -> *) (a :: k) (t :: * -> *) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (ListF f a))
forall k (f :: k -> *) (a :: k) (t :: * -> * -> *) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (ListF f a))
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (ListF f a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> ListF f a -> c (ListF f a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (ListF f a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (ListF f a))
$cListF :: Constr
$tListF :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
$cgmapMo :: forall k (f :: k -> *) (a :: k) (m :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), MonadPlus m) =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
gmapMp :: (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
$cgmapMp :: forall k (f :: k -> *) (a :: k) (m :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), MonadPlus m) =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
gmapM :: (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
$cgmapM :: forall k (f :: k -> *) (a :: k) (m :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Monad m) =>
(forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> ListF f a -> u
$cgmapQi :: forall k (f :: k -> *) (a :: k) u.
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
Int -> (forall d. Data d => d -> u) -> ListF f a -> u
gmapQ :: (forall d. Data d => d -> u) -> ListF f a -> [u]
$cgmapQ :: forall k (f :: k -> *) (a :: k) u.
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall d. Data d => d -> u) -> ListF f a -> [u]
gmapQr :: (r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
$cgmapQr :: forall k (f :: k -> *) (a :: k) r r'.
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
gmapQl :: (r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
$cgmapQl :: forall k (f :: k -> *) (a :: k) r r'.
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> ListF f a -> r
gmapT :: (forall b. Data b => b -> b) -> ListF f a -> ListF f a
$cgmapT :: forall k (f :: k -> *) (a :: k).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall b. Data b => b -> b) -> ListF f a -> ListF f a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (ListF f a))
$cdataCast2 :: forall k (f :: k -> *) (a :: k) (t :: * -> * -> *) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (ListF f a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (ListF f a))
$cdataCast1 :: forall k (f :: k -> *) (a :: k) (t :: * -> *) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a), Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (ListF f a))
dataTypeOf :: ListF f a -> DataType
$cdataTypeOf :: forall k (f :: k -> *) (a :: k).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
ListF f a -> DataType
toConstr :: ListF f a -> Constr
$ctoConstr :: forall k (f :: k -> *) (a :: k).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
ListF f a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (ListF f a)
$cgunfold :: forall k (f :: k -> *) (a :: k) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (ListF f a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> ListF f a -> c (ListF f a)
$cgfoldl :: forall k (f :: k -> *) (a :: k) (c :: * -> *).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> ListF f a -> c (ListF f a)
$cp1Data :: forall k (f :: k -> *) (a :: k).
(Typeable a, Typeable f, Typeable k, Data (f a)) =>
Typeable (ListF f a)
Data)

deriveShow1 ''ListF
deriveRead1 ''ListF
deriveEq1 ''ListF
deriveOrd1 ''ListF

instance Apply f => Apply (ListF f) where
    ListF fs :: [f (a -> b)]
fs <.> :: ListF f (a -> b) -> ListF f a -> ListF f b
<.> ListF xs :: [f a]
xs = [f b] -> ListF f b
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF ([f b] -> ListF f b) -> [f b] -> ListF f b
forall a b. (a -> b) -> a -> b
$ (f (a -> b) -> f a -> f b) -> [f (a -> b)] -> [f a] -> [f b]
forall (f :: * -> *) a b c.
Apply f =>
(a -> b -> c) -> f a -> f b -> f c
liftF2 f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Apply f => f (a -> b) -> f a -> f b
(<.>) [f (a -> b)]
fs [f a]
xs
instance Applicative f => Applicative (ListF f) where
    pure :: a -> ListF f a
pure  = [f a] -> ListF f a
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF ([f a] -> ListF f a) -> (a -> [f a]) -> a -> ListF f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (f a -> [f a] -> [f a]
forall a. a -> [a] -> [a]
:[]) (f a -> [f a]) -> (a -> f a) -> a -> [f a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure
    ListF fs :: [f (a -> b)]
fs <*> :: ListF f (a -> b) -> ListF f a -> ListF f b
<*> ListF xs :: [f a]
xs = [f b] -> ListF f b
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF ([f b] -> ListF f b) -> [f b] -> ListF f b
forall a b. (a -> b) -> a -> b
$ (f (a -> b) -> f a -> f b) -> [f (a -> b)] -> [f a] -> [f b]
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>) [f (a -> b)]
fs [f a]
xs

instance Functor f => Alt (ListF f) where
    <!> :: ListF f a -> ListF f a -> ListF f a
(<!>) = ListF f a -> ListF f a -> ListF f a
forall a. Semigroup a => a -> a -> a
(<>)

instance Functor f => Plus (ListF f) where
    zero :: ListF f a
zero = ListF f a
forall a. Monoid a => a
mempty

instance Applicative f => Alternative (ListF f) where
    empty :: ListF f a
empty = ListF f a
forall (f :: * -> *) a. Plus f => f a
zero
    <|> :: ListF f a -> ListF f a -> ListF f a
(<|>) = ListF f a -> ListF f a -> ListF f a
forall (f :: * -> *) a. Alt f => f a -> f a -> f a
(<!>)

instance Semigroup (ListF f a) where
    ListF xs :: [f a]
xs <> :: ListF f a -> ListF f a -> ListF f a
<> ListF ys :: [f a]
ys = [f a] -> ListF f a
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF ([f a]
xs [f a] -> [f a] -> [f a]
forall a. [a] -> [a] -> [a]
++ [f a]
ys)

instance Monoid (ListF f a) where
    mempty :: ListF f a
mempty = [f a] -> ListF f a
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF []

instance Pointed f => Pointed (ListF f) where
    point :: a -> ListF f a
point = [f a] -> ListF f a
forall k (f :: k -> *) (a :: k). [f a] -> ListF f a
ListF ([f a] -> ListF f a) -> (a -> [f a]) -> a -> ListF f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (f a -> [f a] -> [f a]
forall a. a -> [a] -> [a]
: []) (f a -> [f a]) -> (a -> f a) -> a -> [f a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
.