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
34 liftA, liftA2, liftA3,
38 import Prelude hiding (id,(.))
40 import Control.Category
42 (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
43 import Control.Monad (liftM, ap, MonadPlus(..))
44 import Control.Monad.Instances ()
45 import Data.Functor ((<$>), (<$))
46 import Data.Monoid (Monoid(..))
48 #ifdef __GLASGOW_HASKELL__
49 import GHC.Conc (STM, retry, orElse)
53 infixl 4 <*>, <*, *>, <**>
55 -- | A functor with application.
57 -- Instances should satisfy the following laws:
60 -- @'pure' 'id' '<*>' v = v@
63 -- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
66 -- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
69 -- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
71 -- [/ignore left value/]
72 -- @u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v@
74 -- [/ignore right value/]
75 -- @u '<*' v = 'pure' 'const' '<*>' u '<*>' v@
77 -- The 'Functor' instance should satisfy
80 -- 'fmap' f x = 'pure' f '<*>' x
83 -- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
85 -- Minimal complete definition: 'pure' and '<*>'.
87 class Functor f => Applicative f where
91 -- | Sequential application.
92 (<*>) :: f (a -> b) -> f a -> f b
94 -- | Sequence actions, discarding the value of the first argument.
95 (*>) :: f a -> f b -> f b
96 (*>) = liftA2 (const id)
98 -- | Sequence actions, discarding the value of the second argument.
99 (<*) :: f a -> f b -> f a
102 -- | A monoid on applicative functors.
104 -- Minimal complete definition: 'empty' and '<|>'.
106 -- 'some' and 'many' should be the least solutions of the equations:
108 -- * @some v = (:) '<$>' v '<*>' many v@
110 -- * @many v = some v '<|>' 'pure' []@
111 class Applicative f => Alternative f where
112 -- | The identity of '<|>'
114 -- | An associative binary operation
115 (<|>) :: f a -> f a -> f a
120 where many_v = some_v <|> pure []
121 some_v = (:) <$> v <*> many_v
126 where many_v = some_v <|> pure []
127 some_v = (:) <$> v <*> many_v
129 -- instances for Prelude types
131 instance Applicative Maybe where
135 instance Alternative Maybe where
138 Just x <|> _ = Just x
140 instance Applicative [] where
144 instance Alternative [] where
148 instance Applicative IO where
152 #ifdef __GLASGOW_HASKELL__
153 instance Applicative STM where
157 instance Alternative STM where
162 instance Applicative ((->) a) where
164 (<*>) f g x = f x (g x)
166 instance Monoid a => Applicative ((,) a) where
168 (u, f) <*> (v, x) = (u `mappend` v, f x)
170 instance Applicative (Either e) where
172 Left e <*> _ = Left e
173 Right f <*> r = fmap f r
177 newtype Const a b = Const { getConst :: a }
179 instance Functor (Const m) where
180 fmap _ (Const v) = Const v
182 instance Monoid m => Applicative (Const m) where
183 pure _ = Const mempty
184 Const f <*> Const v = Const (f `mappend` v)
186 newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
188 instance Monad m => Functor (WrappedMonad m) where
189 fmap f (WrapMonad v) = WrapMonad (liftM f v)
191 instance Monad m => Applicative (WrappedMonad m) where
192 pure = WrapMonad . return
193 WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
195 instance MonadPlus m => Alternative (WrappedMonad m) where
196 empty = WrapMonad mzero
197 WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
199 newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
201 instance Arrow a => Functor (WrappedArrow a b) where
202 fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
204 instance Arrow a => Applicative (WrappedArrow a b) where
205 pure x = WrapArrow (arr (const x))
206 WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
208 instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
209 empty = WrapArrow zeroArrow
210 WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
212 -- | Lists, but with an 'Applicative' functor based on zipping, so that
214 -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
216 newtype ZipList a = ZipList { getZipList :: [a] }
218 instance Functor ZipList where
219 fmap f (ZipList xs) = ZipList (map f xs)
221 instance Applicative ZipList where
222 pure x = ZipList (repeat x)
223 ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
227 -- | A variant of '<*>' with the arguments reversed.
228 (<**>) :: Applicative f => f a -> f (a -> b) -> f b
229 (<**>) = liftA2 (flip ($))
231 -- | Lift a function to actions.
232 -- This function may be used as a value for `fmap` in a `Functor` instance.
233 liftA :: Applicative f => (a -> b) -> f a -> f b
234 liftA f a = pure f <*> a
236 -- | Lift a binary function to actions.
237 liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
238 liftA2 f a b = f <$> a <*> b
240 -- | Lift a ternary function to actions.
241 liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
242 liftA3 f a b c = f <$> a <*> b <*> c
245 optional :: Alternative f => f a -> f (Maybe a)
246 optional v = Just <$> v <|> pure Nothing