content: {-# LANGUAGE Trustworthy #-}
  {-# LANGUAGE CPP #-}
  
  -----------------------------------------------------------------------------
  -- |
  -- 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 /Applicative Programming with Effects/,
  -- by Conor McBride and Ross Paterson, online at
  -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
  
  module Control.Applicative (
      -- * Applicative functors
      Applicative(..),
      -- * Alternatives
      Alternative(..),
      -- * Instances
      Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
      -- * Utility functions
      (<$>), (<$), (<**>),
      liftA, liftA2, liftA3,
      optional,
      ) where
  
  import Prelude hiding (id,(.))
  
  import Control.Category
  import Control.Arrow (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
  import Control.Monad (liftM, ap, MonadPlus(..))
  import Control.Monad.Instances ()
  #ifndef __NHC__
  import Control.Monad.ST.Safe (ST)
  import qualified Control.Monad.ST.Lazy.Safe as Lazy (ST)
  #endif
  import Data.Functor ((<$>), (<$))
  import Data.Monoid (Monoid(..))
  
  #ifdef __GLASGOW_HASKELL__
  import GHC.Conc (STM, retry, orElse)
  #endif
  
  infixl 3 <|>
  infixl 4 <*>, <*, *>, <**>
  
  -- | A functor with application, providing operations to
  --
  -- * embed pure expressions ('pure'), and
  --
  -- * sequence computations and combine their results ('<*>').
  --
  -- A minimal complete definition must include implementations of these
  -- functions satisfying 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 other methods have the following default definitions, which may
  -- be overridden with equivalent specialized implementations:
  --
  -- @
  --      u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v
  --      u '<*' v = 'pure' 'const' '<*>' u '<*>' v
  -- @
  --
  -- As a consequence of these laws, the 'Functor' instance for @f@ will satisfy
  --
  -- @
  --      'fmap' f x = 'pure' f '<*>' x
  -- @
  --
  -- If @f@ is also a 'Monad', it should satisfy @'pure' = 'return'@ and
  -- @('<*>') = 'ap'@ (which implies that 'pure' and '<*>' satisfy the
  -- applicative functor laws).
  
  class Functor f => Applicative f where
      -- | Lift a value.
      pure :: a -> f a
  
      -- | Sequential application.
      (<*>) :: f (a -> b) -> f a -> f b
  
      -- | Sequence actions, discarding the value of the first argument.
      (*>) :: f a -> f b -> f b
      (*>) = liftA2 (const id)
  
      -- | Sequence actions, discarding the value of the second argument.
      (<*) :: f a -> f b -> f a
      (<*) = liftA2 const
  
  -- | A monoid on applicative functors.
  --
  -- Minimal complete definition: 'empty' and '<|>'.
  --
  -- If defined, 'some' and 'many' should be the least solutions
  -- of the equations:
  --
  -- * @some v = (:) '<$>' v '<*>' many v@
  --
  -- * @many v = some v '<|>' 'pure' []@
  class Applicative f => Alternative f where
      -- | The identity of '<|>'
      empty :: f a
      -- | An associative binary operation
      (<|>) :: f a -> f a -> f a
  
      -- | One or more.
      some :: f a -> f [a]
      some v = some_v
        where
          many_v = some_v <|> pure []
          some_v = (:) <$> v <*> many_v
  
      -- | Zero or more.
      many :: f a -> f [a]
      many v = many_v
        where
          many_v = some_v <|> pure []
          some_v = (:) <$> v <*> many_v
  
  -- 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
  
  #ifndef __NHC__
  instance Applicative (ST s) where
      pure = return
      (<*>) = ap
  
  instance Applicative (Lazy.ST s) where
      pure = return
      (<*>) = ap
  #endif
  
  #ifdef __GLASGOW_HASKELL__
  instance Applicative STM where
      pure = return
      (<*>) = ap
  
  instance Alternative STM where
      empty = retry
      (<|>) = orElse
  #endif
  
  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)
  
  instance Applicative (Either e) where
      pure          = Right
      Left  e <*> _ = Left e
      Right f <*> r = fmap f r
  
  -- 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 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
  