content: -----------------------------------------------------------------------------
  -- |
  -- Module      :  Control.Applicative
  -- Copyright   :  Conor McBride and Ross Paterson 2005
  -- License     :  BSD-style (see the LICENSE file in the distribution)
  --
  -- Maintainer  :  ross@soi.city.ac.uk
  -- Stability   :  experimental
  -- Portability :  portable
  --
  -- This module describes a structure intermediate between a functor and
  -- a monad: it provides pure expressions and sequencing, but no binding.
  -- (Technically, a strong lax monoidal functor.)  For more details, see
  -- /Applicative Programming with Effects/,
  -- by Conor McBride and Ross Paterson, online at
  -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
  --
  -- This interface was introduced for parsers by Niklas R&#xF6;jemo, because
  -- it admits more sharing than the monadic interface.  The names here are
  -- mostly based on recent parsing work by Doaitse Swierstra.
  --
  -- This class is also useful with instances of the
  -- 'Data.Traversable.Traversable' class.
  
  module Control.Applicative (
          -- * Applicative functors
          Applicative(..),
          -- * Alternatives
          Alternative(..),
          -- * Instances
          Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
          -- * Utility functions
          (<$>), (<$), (*>), (<*), (<**>),
          liftA, liftA2, liftA3,
          optional, some, many
          ) where
  
  import Prelude hiding (id,(.))
  import qualified Prelude
  
  import Data.Functor
  import Control.Category
  import Control.Arrow
          (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
  import Control.Monad (liftM, ap, MonadPlus(..))
  import Control.Monad.Instances ()
  import Data.Monoid (Monoid(..))
  
  infixl 3 <|>
  infixl 4 <$>, <$
  infixl 4 <*>, <*, *>, <**>
  
  -- | A functor with application.
  --
  -- Instances should satisfy the following laws:
  --
  -- [/identity/]
  --      @'pure' 'id' '<*>' v = v@
  --
  -- [/composition/]
  --      @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
  --
  -- [/homomorphism/]
  --      @'pure' f '<*>' 'pure' x = 'pure' (f x)@
  --
  -- [/interchange/]
  --      @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
  --
  -- The 'Functor' instance should satisfy
  --
  -- @
  --      'fmap' f x = 'pure' f '<*>' x
  -- @
  --
  -- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
  
  class Functor f => Applicative f where
          -- | Lift a value.
          pure :: a -> f a
  
          -- | Sequential application.
          (<*>) :: f (a -> b) -> f a -> f b
  
  -- | A monoid on applicative functors.
  class Applicative f => Alternative f where
          -- | The identity of '<|>'
          empty :: f a
          -- | An associative binary operation
          (<|>) :: f a -> f a -> f a
  
  -- instances for Prelude types
  
  instance Applicative Maybe where
          pure = return
          (<*>) = ap
  
  instance Alternative Maybe where
          empty = Nothing
          Nothing <|> p = p
          Just x <|> _ = Just x
  
  instance Applicative [] where
          pure = return
          (<*>) = ap
  
  instance Alternative [] where
          empty = []
          (<|>) = (++)
  
  instance Applicative IO where
          pure = return
          (<*>) = ap
  
  instance Applicative ((->) a) where
          pure = const
          (<*>) f g x = f x (g x)
  
  instance Monoid a => Applicative ((,) a) where
          pure x = (mempty, x)
          (u, f) <*> (v, x) = (u `mappend` v, f x)
  
  -- new instances
  
  newtype Const a b = Const { getConst :: a }
  
  instance Functor (Const m) where
          fmap _ (Const v) = Const v
  
  instance Monoid m => Applicative (Const m) where
          pure _ = Const mempty
          Const f <*> Const v = Const (f `mappend` v)
  
  newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
  
  instance Monad m => Functor (WrappedMonad m) where
          fmap f (WrapMonad v) = WrapMonad (liftM f v)
  
  instance Monad m => Applicative (WrappedMonad m) where
          pure = WrapMonad . return
          WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
  
  instance MonadPlus m => Alternative (WrappedMonad m) where
          empty = WrapMonad mzero
          WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
  
  newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
  
  instance Arrow a => Functor (WrappedArrow a b) where
          fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
  
  instance Arrow a => Applicative (WrappedArrow a b) where
          pure x = WrapArrow (arr (const x))
          WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
  
  instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
          empty = WrapArrow zeroArrow
          WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
  
  -- | Lists, but with an 'Applicative' functor based on zipping, so that
  --
  -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
  --
  newtype ZipList a = ZipList { getZipList :: [a] }
  
  instance Functor ZipList where
          fmap f (ZipList xs) = ZipList (map f xs)
  
  instance Applicative ZipList where
          pure x = ZipList (repeat x)
          ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
  
  -- extra functions
  
  -- | A synonym for 'fmap'.
  --(<$>) :: Functor f => (a -> b) -> f a -> f b
  --f <$> a = fmap f a
  
  -- | Replace the value.
  --(<$) :: Functor f => a -> f b -> f a
  --(<$) = (<$>) . const
  
  -- | Sequence actions, discarding the value of the first argument.
  (*>) :: Applicative f => f a -> f b -> f b
  (*>) = liftA2 (const id)
  
  -- | Sequence actions, discarding the value of the second argument.
  (<*) :: Applicative f => f a -> f b -> f a
  (<*) = liftA2 const
  
  -- | A variant of '<*>' with the arguments reversed.
  (<**>) :: Applicative f => f a -> f (a -> b) -> f b
  (<**>) = liftA2 (flip ($))
  
  -- | Lift a function to actions.
  -- This function may be used as a value for `fmap` in a `Functor` instance.
  liftA :: Applicative f => (a -> b) -> f a -> f b
  liftA f a = pure f <*> a
  
  -- | Lift a binary function to actions.
  liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
  liftA2 f a b = f <$> a <*> b
  
  -- | Lift a ternary function to actions.
  liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
  liftA3 f a b c = f <$> a <*> b <*> c
  
  -- | One or none.
  optional :: Alternative f => f a -> f (Maybe a)
  optional v = Just <$> v <|> pure Nothing
  
  -- | One or more.
  some :: Alternative f => f a -> f [a]
  some v = some_v
    where many_v = some_v <|> pure []
          some_v = (:) <$> v <*> many_v
  
  -- | Zero or more.
  many :: Alternative f => f a -> f [a]
  many v = many_v
    where many_v = some_v <|> pure []
          some_v = (:) <$> v <*> many_v
  