6ef8bba3869c96238d65c3912d8b21fe3f97172b
[ghc.git] / libraries / base / Control / Applicative.hs
1 {-# LANGUAGE CPP #-}
2
3 -----------------------------------------------------------------------------
4 -- |
5 -- Module : Control.Applicative
6 -- Copyright : Conor McBride and Ross Paterson 2005
7 -- License : BSD-style (see the LICENSE file in the distribution)
8 --
9 -- Maintainer : libraries@haskell.org
10 -- Stability : experimental
11 -- Portability : portable
12 --
13 -- This module describes a structure intermediate between a functor and
14 -- a monad (technically, a strong lax monoidal functor). Compared with
15 -- monads, this interface lacks the full power of the binding operation
16 -- '>>=', but
17 --
18 -- * it has more instances.
19 --
20 -- * it is sufficient for many uses, e.g. context-free parsing, or the
21 -- 'Data.Traversable.Traversable' class.
22 --
23 -- * instances can perform analysis of computations before they are
24 -- executed, and thus produce shared optimizations.
25 --
26 -- This interface was introduced for parsers by Niklas Röjemo, because
27 -- it admits more sharing than the monadic interface. The names here are
28 -- mostly based on parsing work by Doaitse Swierstra.
29 --
30 -- For more details, see /Applicative Programming with Effects/,
31 -- by Conor McBride and Ross Paterson, online at
32 -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
33
34 module Control.Applicative (
35 -- * Applicative functors
36 Applicative(..),
37 -- * Alternatives
38 Alternative(..),
39 -- * Instances
40 Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
41 -- * Utility functions
42 (<$>), (<$), (<**>),
43 liftA, liftA2, liftA3,
44 optional,
45 ) where
46
47 import Prelude hiding (id,(.))
48
49 import Control.Category
50 import Control.Arrow (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
51 import Control.Monad (liftM, ap, MonadPlus(..))
52 import Control.Monad.Instances ()
53 #ifndef __NHC__
54 import Control.Monad.ST (ST)
55 import qualified Control.Monad.ST.Lazy as Lazy (ST)
56 #endif
57 import Data.Functor ((<$>), (<$))
58 import Data.Monoid (Monoid(..))
59
60 #ifdef __GLASGOW_HASKELL__
61 import GHC.Conc (STM, retry, orElse)
62 #endif
63
64 infixl 3 <|>
65 infixl 4 <*>, <*, *>, <**>
66
67 -- | A functor with application, providing operations to
68 --
69 -- * embed pure expressions ('pure'), and
70 --
71 -- * sequence computations and combine their results ('<*>').
72 --
73 -- A minimal complete definition must include implementations of these
74 -- functions satisfying the following laws:
75 --
76 -- [/identity/]
77 -- @'pure' 'id' '<*>' v = v@
78 --
79 -- [/composition/]
80 -- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
81 --
82 -- [/homomorphism/]
83 -- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
84 --
85 -- [/interchange/]
86 -- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
87 --
88 -- The other methods have the following default definitions, which may
89 -- be overridden with equivalent specialized implementations:
90 --
91 -- @
92 -- u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v
93 -- u '<*' v = 'pure' 'const' '<*>' u '<*>' v
94 -- @
95 --
96 -- As a consequence of these laws, the 'Functor' instance for @f@ will satisfy
97 --
98 -- @
99 -- 'fmap' f x = 'pure' f '<*>' x
100 -- @
101 --
102 -- If @f@ is also a 'Monad', it should satisfy @'pure' = 'return'@ and
103 -- @('<*>') = 'ap'@ (which implies that 'pure' and '<*>' satisfy the
104 -- applicative functor laws).
105
106 class Functor f => Applicative f where
107 -- | Lift a value.
108 pure :: a -> f a
109
110 -- | Sequential application.
111 (<*>) :: f (a -> b) -> f a -> f b
112
113 -- | Sequence actions, discarding the value of the first argument.
114 (*>) :: f a -> f b -> f b
115 (*>) = liftA2 (const id)
116
117 -- | Sequence actions, discarding the value of the second argument.
118 (<*) :: f a -> f b -> f a
119 (<*) = liftA2 const
120
121 -- | A monoid on applicative functors.
122 --
123 -- Minimal complete definition: 'empty' and '<|>'.
124 --
125 -- If defined, 'some' and 'many' should be the least solutions
126 -- of the equations:
127 --
128 -- * @some v = (:) '<$>' v '<*>' many v@
129 --
130 -- * @many v = some v '<|>' 'pure' []@
131 class Applicative f => Alternative f where
132 -- | The identity of '<|>'
133 empty :: f a
134 -- | An associative binary operation
135 (<|>) :: f a -> f a -> f a
136
137 -- | One or more.
138 some :: f a -> f [a]
139 some v = some_v
140 where
141 many_v = some_v <|> pure []
142 some_v = (:) <$> v <*> many_v
143
144 -- | Zero or more.
145 many :: f a -> f [a]
146 many v = many_v
147 where
148 many_v = some_v <|> pure []
149 some_v = (:) <$> v <*> many_v
150
151 -- instances for Prelude types
152
153 instance Applicative Maybe where
154 pure = return
155 (<*>) = ap
156
157 instance Alternative Maybe where
158 empty = Nothing
159 Nothing <|> p = p
160 Just x <|> _ = Just x
161
162 instance Applicative [] where
163 pure = return
164 (<*>) = ap
165
166 instance Alternative [] where
167 empty = []
168 (<|>) = (++)
169
170 instance Applicative IO where
171 pure = return
172 (<*>) = ap
173
174 #ifndef __NHC__
175 instance Applicative (ST s) where
176 pure = return
177 (<*>) = ap
178
179 instance Applicative (Lazy.ST s) where
180 pure = return
181 (<*>) = ap
182 #endif
183
184 #ifdef __GLASGOW_HASKELL__
185 instance Applicative STM where
186 pure = return
187 (<*>) = ap
188
189 instance Alternative STM where
190 empty = retry
191 (<|>) = orElse
192 #endif
193
194 instance Applicative ((->) a) where
195 pure = const
196 (<*>) f g x = f x (g x)
197
198 instance Monoid a => Applicative ((,) a) where
199 pure x = (mempty, x)
200 (u, f) <*> (v, x) = (u `mappend` v, f x)
201
202 instance Applicative (Either e) where
203 pure = Right
204 Left e <*> _ = Left e
205 Right f <*> r = fmap f r
206
207 -- new instances
208
209 newtype Const a b = Const { getConst :: a }
210
211 instance Functor (Const m) where
212 fmap _ (Const v) = Const v
213
214 instance Monoid m => Applicative (Const m) where
215 pure _ = Const mempty
216 Const f <*> Const v = Const (f `mappend` v)
217
218 newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
219
220 instance Monad m => Functor (WrappedMonad m) where
221 fmap f (WrapMonad v) = WrapMonad (liftM f v)
222
223 instance Monad m => Applicative (WrappedMonad m) where
224 pure = WrapMonad . return
225 WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
226
227 instance MonadPlus m => Alternative (WrappedMonad m) where
228 empty = WrapMonad mzero
229 WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
230
231 newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
232
233 instance Arrow a => Functor (WrappedArrow a b) where
234 fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
235
236 instance Arrow a => Applicative (WrappedArrow a b) where
237 pure x = WrapArrow (arr (const x))
238 WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
239
240 instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
241 empty = WrapArrow zeroArrow
242 WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
243
244 -- | Lists, but with an 'Applicative' functor based on zipping, so that
245 --
246 -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
247 --
248 newtype ZipList a = ZipList { getZipList :: [a] }
249
250 instance Functor ZipList where
251 fmap f (ZipList xs) = ZipList (map f xs)
252
253 instance Applicative ZipList where
254 pure x = ZipList (repeat x)
255 ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
256
257 -- extra functions
258
259 -- | A variant of '<*>' with the arguments reversed.
260 (<**>) :: Applicative f => f a -> f (a -> b) -> f b
261 (<**>) = liftA2 (flip ($))
262
263 -- | Lift a function to actions.
264 -- This function may be used as a value for `fmap` in a `Functor` instance.
265 liftA :: Applicative f => (a -> b) -> f a -> f b
266 liftA f a = pure f <*> a
267
268 -- | Lift a binary function to actions.
269 liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
270 liftA2 f a b = f <$> a <*> b
271
272 -- | Lift a ternary function to actions.
273 liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
274 liftA3 f a b c = f <$> a <*> b <*> c
275
276 -- | One or none.
277 optional :: Alternative f => f a -> f (Maybe a)
278 optional v = Just <$> v <|> pure Nothing