1 -----------------------------------------------------------------------------
3 -- Module : Control.Applicative
4 -- Copyright : Conor McBride and Ross Paterson 2005
5 -- License : BSD-style (see the LICENSE file in the distribution)
7 -- Maintainer : libraries@haskell.org
8 -- Stability : experimental
9 -- Portability : portable
11 -- This module describes a structure intermediate between a functor and
12 -- a monad: it provides pure expressions and sequencing, but no binding.
13 -- (Technically, a strong lax monoidal functor.) For more details, see
14 -- /Applicative Programming with Effects/,
15 -- by Conor McBride and Ross Paterson, online at
16 -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
18 -- This interface was introduced for parsers by Niklas Röjemo, because
19 -- it admits more sharing than the monadic interface. The names here are
20 -- mostly based on recent parsing work by Doaitse Swierstra.
22 -- This class is also useful with instances of the
23 -- 'Data.Traversable.Traversable' class.
25 module Control.Applicative (
26 -- * Applicative functors
31 Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
32 -- * Utility functions
33 (<$>), (<$), (*>), (<*), (<**>),
34 liftA, liftA2, liftA3,
38 import Prelude hiding (id,(.))
39 import qualified Prelude
41 import Control.Category
43 (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
44 import Control.Monad (liftM, ap, MonadPlus(..))
45 import Control.Monad.Instances ()
46 import Data.Monoid (Monoid(..))
50 infixl 4 <*>, <*, *>, <**>
52 -- | A functor with application.
54 -- Instances should satisfy the following laws:
57 -- @'pure' 'id' '<*>' v = v@
60 -- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
63 -- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
66 -- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
68 -- The 'Functor' instance should satisfy
71 -- 'fmap' f x = 'pure' f '<*>' x
74 -- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
76 class Functor f => Applicative f where
80 -- | Sequential application.
81 (<*>) :: f (a -> b) -> f a -> f b
83 -- | A monoid on applicative functors.
84 class Applicative f => Alternative f where
85 -- | The identity of '<|>'
87 -- | An associative binary operation
88 (<|>) :: f a -> f a -> f a
90 -- instances for Prelude types
92 instance Applicative Maybe where
96 instance Alternative Maybe where
101 instance Applicative [] where
105 instance Alternative [] where
109 instance Applicative IO where
113 instance Applicative ((->) a) where
115 (<*>) f g x = f x (g x)
117 instance Monoid a => Applicative ((,) a) where
119 (u, f) <*> (v, x) = (u `mappend` v, f x)
123 newtype Const a b = Const { getConst :: a }
125 instance Functor (Const m) where
126 fmap _ (Const v) = Const v
128 instance Monoid m => Applicative (Const m) where
129 pure _ = Const mempty
130 Const f <*> Const v = Const (f `mappend` v)
132 newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
134 instance Monad m => Functor (WrappedMonad m) where
135 fmap f (WrapMonad v) = WrapMonad (liftM f v)
137 instance Monad m => Applicative (WrappedMonad m) where
138 pure = WrapMonad . return
139 WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
141 instance MonadPlus m => Alternative (WrappedMonad m) where
142 empty = WrapMonad mzero
143 WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
145 newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
147 instance Arrow a => Functor (WrappedArrow a b) where
148 fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
150 instance Arrow a => Applicative (WrappedArrow a b) where
151 pure x = WrapArrow (arr (const x))
152 WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
154 instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
155 empty = WrapArrow zeroArrow
156 WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
158 -- | Lists, but with an 'Applicative' functor based on zipping, so that
160 -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
162 newtype ZipList a = ZipList { getZipList :: [a] }
164 instance Functor ZipList where
165 fmap f (ZipList xs) = ZipList (map f xs)
167 instance Applicative ZipList where
168 pure x = ZipList (repeat x)
169 ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
173 -- | A synonym for 'fmap'.
174 (<$>) :: Functor f => (a -> b) -> f a -> f b
177 -- | Replace the value.
178 (<$) :: Functor f => a -> f b -> f a
181 -- | Sequence actions, discarding the value of the first argument.
182 (*>) :: Applicative f => f a -> f b -> f b
183 (*>) = liftA2 (const id)
185 -- | Sequence actions, discarding the value of the second argument.
186 (<*) :: Applicative f => f a -> f b -> f a
189 -- | A variant of '<*>' with the arguments reversed.
190 (<**>) :: Applicative f => f a -> f (a -> b) -> f b
191 (<**>) = liftA2 (flip ($))
193 -- | Lift a function to actions.
194 -- This function may be used as a value for `fmap` in a `Functor` instance.
195 liftA :: Applicative f => (a -> b) -> f a -> f b
196 liftA f a = pure f <*> a
198 -- | Lift a binary function to actions.
199 liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
200 liftA2 f a b = f <$> a <*> b
202 -- | Lift a ternary function to actions.
203 liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
204 liftA3 f a b c = f <$> a <*> b <*> c
207 optional :: Alternative f => f a -> f (Maybe a)
208 optional v = Just <$> v <|> pure Nothing
211 some :: Alternative f => f a -> f [a]
213 where many_v = some_v <|> pure []
214 some_v = (:) <$> v <*> many_v
217 many :: Alternative f => f a -> f [a]
219 where many_v = some_v <|> pure []
220 some_v = (:) <$> v <*> many_v