{-# Language DeriveDataTypeable, FlexibleInstances, KindSignatures, MultiParamTypeClasses, RankNTypes,
StandaloneDeriving, TypeFamilies, UndecidableInstances #-}
-- | Type classes 'Functor', 'Foldable', and 'Traversable' that correspond to the standard type classes of the same
-- name, but applying the given transformation to every descendant of the given tree node. The corresponding classes
-- in the "Transformation.Shallow" module operate only on the immediate children, while those from the
-- "Transformation.Full" module include the argument node itself.
module Transformation.Deep where
import Control.Applicative (Applicative, liftA2)
import Data.Data (Data, Typeable)
import Data.Functor.Compose (Compose)
import Data.Functor.Const (Const)
import qualified Rank2
import qualified Data.Functor
import Transformation (Transformation, Domain, Codomain)
import qualified Transformation.Full as Full
import Prelude hiding (Foldable(..), Traversable(..), Functor(..), Applicative(..), (<$>), fst, snd)
-- | Like "Transformation.Shallow".'Transformation.Shallow.Functor' except it maps all descendants and not only immediate children
class (Transformation t, Rank2.Functor (g (Domain t))) => Functor t g where
(<$>) :: t -> g (Domain t) (Domain t) -> g (Codomain t) (Codomain t)
-- | Like "Transformation.Shallow".'Transformation.Shallow.Foldable' except it folds all descendants and not only immediate children
class (Transformation t, Rank2.Foldable (g (Domain t))) => Foldable t g where
foldMap :: (Codomain t ~ Const m, Monoid m) => t -> g (Domain t) (Domain t) -> m
-- | Like "Transformation.Shallow".'Transformation.Shallow.Traversable' except it folds all descendants and not only immediate children
class (Transformation t, Rank2.Traversable (g (Domain t))) => Traversable t g where
traverse :: Codomain t ~ Compose m f => t -> g (Domain t) (Domain t) -> m (g f f)
-- | Like 'Data.Functor.Product.Product' for data types with two type constructor parameters
data Product g1 g2 (p :: * -> *) (q :: * -> *) = Pair{fst :: q (g1 p p),
snd :: q (g2 p p)}
instance Rank2.Functor (Product g1 g2 p) where
f <$> ~(Pair left right) = Pair (f left) (f right)
instance Rank2.Apply (Product g h p) where
~(Pair g1 h1) <*> ~(Pair g2 h2) = Pair (Rank2.apply g1 g2) (Rank2.apply h1 h2)
liftA2 f ~(Pair g1 h1) ~(Pair g2 h2) = Pair (f g1 g2) (f h1 h2)
instance Rank2.Applicative (Product g h p) where
pure f = Pair f f
instance Rank2.Foldable (Product g h p) where
foldMap f ~(Pair g h) = f g `mappend` f h
instance Rank2.Traversable (Product g h p) where
traverse f ~(Pair g h) = liftA2 Pair (f g) (f h)
instance Rank2.DistributiveTraversable (Product g h p)
instance Rank2.Distributive (Product g h p) where
cotraverse w f = Pair{fst= w (fst Data.Functor.<$> f),
snd= w (snd Data.Functor.<$> f)}
instance (Full.Functor t g, Full.Functor t h) => Functor t (Product g h) where
t <$> Pair left right = Pair (t Full.<$> left) (t Full.<$> right)
instance (Full.Traversable t g, Full.Traversable t h, Codomain t ~ Compose m f, Applicative m) =>
Traversable t (Product g h) where
traverse t (Pair left right) = liftA2 Pair (Full.traverse t left) (Full.traverse t right)
deriving instance (Typeable p, Typeable q, Typeable g1, Typeable g2,
Data (q (g1 p p)), Data (q (g2 p p))) => Data (Product g1 g2 p q)
deriving instance (Show (q (g1 p p)), Show (q (g2 p p))) => Show (Product g1 g2 p q)
-- | Alphabetical synonym for '<$>'
fmap :: Functor t g => t -> g (Domain t) (Domain t) -> g (Codomain t) (Codomain t)
fmap = (<$>)