Data/Bitraversable.hs

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE ScopedTypeVariables #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Bitraversable
    -- Copyright   :  (C) 2011-2016 Edward Kmett
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- @since 4.10.0.0
    ----------------------------------------------------------------------------
    module Data.Bitraversable
      ( Bitraversable(..)
      , bisequenceA
      , bisequence
      , bimapM
      , bifor
      , biforM
      , bimapAccumL
      , bimapAccumR
      , bimapDefault
      , bifoldMapDefault
      ) where

    import Control.Applicative
    import Data.Bifunctor
    import Data.Bifoldable
    import Data.Coerce
    import Data.Functor.Identity (Identity(..))
    import Data.Functor.Utils (StateL(..), StateR(..))
    import GHC.Generics (K1(..))

    -- | 'Bitraversable' identifies bifunctorial data structures whose elements can
    -- be traversed in order, performing 'Applicative' or 'Monad' actions at each
    -- element, and collecting a result structure with the same shape.
    --
    -- As opposed to 'Traversable' data structures, which have one variety of
    -- element on which an action can be performed, 'Bitraversable' data structures
    -- have two such varieties of elements.
    --
    -- A definition of 'bitraverse' must satisfy the following laws:
    --
    -- [/naturality/]
    --   @'bitraverse' (t . f) (t . g) ≡ t . 'bitraverse' f g@
    --   for every applicative transformation @t@
    --
    -- [/identity/]
    --   @'bitraverse' 'Identity' 'Identity' ≡ 'Identity'@
    --
    -- [/composition/]
    --   @'Compose' . 'fmap' ('bitraverse' g1 g2) . 'bitraverse' f1 f2
    --     ≡ 'traverse' ('Compose' . 'fmap' g1 . f1) ('Compose' . 'fmap' g2 . f2)@
    --
    -- where an /applicative transformation/ is a function
    --
    -- @t :: ('Applicative' f, 'Applicative' g) => f a -> g a@
    --
    -- preserving the 'Applicative' operations:
    --
    -- @
    -- t ('pure' x) = 'pure' x
    -- t (f '<*>' x) = t f '<*>' t x
    -- @
    --
    -- and the identity functor 'Identity' and composition functors 'Compose' are
    -- defined as
    --
    -- > newtype Identity a = Identity { runIdentity :: a }
    -- >
    -- > instance Functor Identity where
    -- >   fmap f (Identity x) = Identity (f x)
    -- >
    -- > instance Applicative Identity where
    -- >   pure = Identity
    -- >   Identity f <*> Identity x = Identity (f x)
    -- >
    -- > newtype Compose f g a = Compose (f (g a))
    -- >
    -- > instance (Functor f, Functor g) => Functor (Compose f g) where
    -- >   fmap f (Compose x) = Compose (fmap (fmap f) x)
    -- >
    -- > instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    -- >   pure = Compose . pure . pure
    -- >   Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
    --
    -- Some simple examples are 'Either' and '(,)':
    --
    -- > instance Bitraversable Either where
    -- >   bitraverse f _ (Left x) = Left <$> f x
    -- >   bitraverse _ g (Right y) = Right <$> g y
    -- >
    -- > instance Bitraversable (,) where
    -- >   bitraverse f g (x, y) = (,) <$> f x <*> g y
    --
    -- 'Bitraversable' relates to its superclasses in the following ways:
    --
    -- @
    -- 'bimap' f g ≡ 'runIdentity' . 'bitraverse' ('Identity' . f) ('Identity' . g)
    -- 'bifoldMap' f g = 'getConst' . 'bitraverse' ('Const' . f) ('Const' . g)
    -- @
    --
    -- These are available as 'bimapDefault' and 'bifoldMapDefault' respectively.
    --
    -- @since 4.10.0.0
    class (Bifunctor t, Bifoldable t) => Bitraversable t where
      -- | Evaluates the relevant functions at each element in the structure,
      -- running the action, and builds a new structure with the same shape, using
      -- the results produced from sequencing the actions.
      --
      -- @'bitraverse' f g ≡ 'bisequenceA' . 'bimap' f g@
      --
      -- For a version that ignores the results, see 'bitraverse_'.
      --
      -- @since 4.10.0.0
      bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
      bitraverse f g = bisequenceA . bimap f g

    -- | Alias for 'bisequence'.
    --
    -- @since 4.10.0.0
    bisequenceA :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
    bisequenceA = bisequence

    -- | Alias for 'bitraverse'.
    --
    -- @since 4.10.0.0
    bimapM :: (Bitraversable t, Applicative f)
           => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
    bimapM = bitraverse

    -- | Sequences all the actions in a structure, building a new structure with
    -- the same shape using the results of the actions. For a version that ignores
    -- the results, see 'bisequence_'.
    --
    -- @'bisequence' ≡ 'bitraverse' 'id' 'id'@
    --
    -- @since 4.10.0.0
    bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
    bisequence = bitraverse id id

    -- | @since 4.10.0.0
    instance Bitraversable (,) where
      bitraverse f g ~(a, b) = liftA2 (,) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable ((,,) x) where
      bitraverse f g ~(x, a, b) = liftA2 ((,,) x) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable ((,,,) x y) where
      bitraverse f g ~(x, y, a, b) = liftA2 ((,,,) x y) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable ((,,,,) x y z) where
      bitraverse f g ~(x, y, z, a, b) = liftA2 ((,,,,) x y z) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable ((,,,,,) x y z w) where
      bitraverse f g ~(x, y, z, w, a, b) = liftA2 ((,,,,,) x y z w) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable ((,,,,,,) x y z w v) where
      bitraverse f g ~(x, y, z, w, v, a, b) =
        liftA2 ((,,,,,,) x y z w v) (f a) (g b)

    -- | @since 4.10.0.0
    instance Bitraversable Either where
      bitraverse f _ (Left a) = Left <$> f a
      bitraverse _ g (Right b) = Right <$> g b

    -- | @since 4.10.0.0
    instance Bitraversable Const where
      bitraverse f _ (Const a) = Const <$> f a

    -- | @since 4.10.0.0
    instance Bitraversable (K1 i) where
      bitraverse f _ (K1 c) = K1 <$> f c

    -- | 'bifor' is 'bitraverse' with the structure as the first argument. For a
    -- version that ignores the results, see 'bifor_'.
    --
    -- @since 4.10.0.0
    bifor :: (Bitraversable t, Applicative f)
          => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
    bifor t f g = bitraverse f g t

    -- | Alias for 'bifor'.
    --
    -- @since 4.10.0.0
    biforM :: (Bitraversable t, Applicative f)
           => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
    biforM = bifor

    -- | The 'bimapAccumL' function behaves like a combination of 'bimap' and
    -- 'bifoldl'; it traverses a structure from left to right, threading a state
    -- of type @a@ and using the given actions to compute new elements for the
    -- structure.
    --
    -- @since 4.10.0.0
    bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e))
                -> a -> t b d -> (a, t c e)
    bimapAccumL f g s t
      = runStateL (bitraverse (StateL . flip f) (StateL . flip g) t) s

    -- | The 'bimapAccumR' function behaves like a combination of 'bimap' and
    -- 'bifoldl'; it traverses a structure from right to left, threading a state
    -- of type @a@ and using the given actions to compute new elements for the
    -- structure.
    --
    -- @since 4.10.0.0
    bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e))
                -> a -> t b d -> (a, t c e)
    bimapAccumR f g s t
      = runStateR (bitraverse (StateR . flip f) (StateR . flip g) t) s

    -- | A default definition of 'bimap' in terms of the 'Bitraversable'
    -- operations.
    --
    -- @'bimapDefault' f g ≡
    --     'runIdentity' . 'bitraverse' ('Identity' . f) ('Identity' . g)@
    --
    -- @since 4.10.0.0
    bimapDefault :: forall t a b c d . Bitraversable t
                 => (a -> b) -> (c -> d) -> t a c -> t b d
    -- See Note [Function coercion] in Data.Functor.Utils.
    bimapDefault = coerce
      (bitraverse :: (a -> Identity b)
                  -> (c -> Identity d) -> t a c -> Identity (t b d))
    {-# INLINE bimapDefault #-}

    -- | A default definition of 'bifoldMap' in terms of the 'Bitraversable'
    -- operations.
    --
    -- @'bifoldMapDefault' f g ≡
    --    'getConst' . 'bitraverse' ('Const' . f) ('Const' . g)@
    --
    -- @since 4.10.0.0
    bifoldMapDefault :: forall t m a b . (Bitraversable t, Monoid m)
                     => (a -> m) -> (b -> m) -> t a b -> m
    -- See Note [Function coercion] in Data.Functor.Utils.
    bifoldMapDefault = coerce
      (bitraverse :: (a -> Const m ())
                  -> (b -> Const m ()) -> t a b -> Const m (t () ()))
    {-# INLINE bifoldMapDefault #-}