content: {-# LANGUAGE Trustworthy #-}
  {-# LANGUAGE AutoDeriveTypeable #-}
  {-# LANGUAGE DeriveGeneric #-}
  {-# LANGUAGE GeneralizedNewtypeDeriving #-}
  {-# LANGUAGE NoImplicitPrelude #-}
  {-# LANGUAGE ScopedTypeVariables #-}
  
  -----------------------------------------------------------------------------
  -- |
  -- Module      :  Control.Applicative
  -- Copyright   :  Conor McBride and Ross Paterson 2005
  -- License     :  BSD-style (see the LICENSE file in the distribution)
  --
  -- Maintainer  :  libraries@haskell.org
  -- Stability   :  experimental
  -- Portability :  portable
  --
  -- This module describes a structure intermediate between a functor and
  -- a monad (technically, a strong lax monoidal functor).  Compared with
  -- monads, this interface lacks the full power of the binding operation
  -- '>>=', but
  --
  -- * it has more instances.
  --
  -- * it is sufficient for many uses, e.g. context-free parsing, or the
  --   'Data.Traversable.Traversable' class.
  --
  -- * instances can perform analysis of computations before they are
  --   executed, and thus produce shared optimizations.
  --
  -- 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 parsing work by Doaitse Swierstra.
  --
  -- For more details, see
  -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html Applicative Programming with Effects>,
  -- by Conor McBride and Ross Paterson.
  
  module Control.Applicative (
      -- * Applicative functors
      Applicative(..),
      -- * Alternatives
      Alternative(..),
      -- * Instances
      Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
      -- * Utility functions
      (<$>), (<$), (<**>),
      liftA, liftA2, liftA3,
      optional,
      ) where
  
  import Control.Category hiding ((.), id)
  import Control.Arrow
  import Data.Maybe
  import Data.Tuple
  import Data.Eq
  import Data.Ord
  import Data.Foldable (Foldable(..))
  import Data.Functor ((<$>))
  
  import GHC.Base
  import GHC.Generics
  import GHC.List (repeat, zipWith)
  import GHC.Read (Read(readsPrec), readParen, lex)
  import GHC.Show (Show(showsPrec), showParen, showString)
  
  newtype Const a b = Const { getConst :: a }
                    deriving (Generic, Generic1, Monoid, Eq, Ord)
  
  instance Read a => Read (Const a b) where
      readsPrec d = readParen (d > 10)
          $ \r -> [(Const x,t) | ("Const", s) <- lex r, (x, t) <- readsPrec 11 s]
  
  instance Show a => Show (Const a b) where
      showsPrec d (Const x) = showParen (d > 10) $
                              showString "Const " . showsPrec 11 x
  
  instance Foldable (Const m) where
      foldMap _ _ = mempty
  
  instance Functor (Const m) where
      fmap _ (Const v) = Const v
  
  instance Monoid m => Applicative (Const m) where
      pure _ = Const mempty
      (<*>) = coerce (mappend :: m -> m -> m)
  -- This is pretty much the same as
  -- Const f <*> Const v = Const (f `mappend` v)
  -- but guarantees that mappend for Const a b will have the same arity
  -- as the one for a; it won't create a closure to raise the arity
  -- to 2.
  
  newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
                           deriving (Generic, Generic1, Monad)
  
  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 }
                             deriving (Generic, Generic1)
  
  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] }
                    deriving (Show, Eq, Ord, Read, Functor, Generic, Generic1)
  
  instance Applicative ZipList where
      pure x = ZipList (repeat x)
      ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
  
  -- extra functions
  
  -- | One or none.
  optional :: Alternative f => f a -> f (Maybe a)
  optional v = Just <$> v <|> pure Nothing
  