Control/Applicative.hs

{-# 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 Röjemo, 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
import Control.Monad (liftM, ap, MonadPlus(..))
#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(..))

import Text.ParserCombinators.ReadP
#ifndef __NHC__
 (ReadP)
#else
 (ReadPN)
#define ReadP (ReadPN b)
#endif

import Text.ParserCombinators.ReadPrec (ReadPrec)

#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 <|> r = r
 l <|> _ = l

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

instance Applicative ReadP where
 pure = return
 (<*>) = ap

instance Alternative ReadP where
 empty = mzero
 (<|>) = mplus

instance Applicative ReadPrec where
 pure = return
 (<*>) = ap

instance Alternative ReadPrec where
 empty = mzero
 (<|>) = mplus

instance Arrow a => Applicative (ArrowMonad a) where
 pure x = ArrowMonad (arr (const x))
 ArrowMonad f <*> ArrowMonad x = ArrowMonad (f &&& x >>> arr (uncurry id))

instance ArrowPlus a => Alternative (ArrowMonad a) where
 empty = ArrowMonad zeroArrow
 ArrowMonad x <|> ArrowMonad y = ArrowMonad (x <+> y)

-- 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