Remove Control.Parallel*, now in package parallel
[packages/random.git] / Control / Applicative.hs
1 -----------------------------------------------------------------------------
2 -- |
3 -- Module : Control.Applicative
4 -- Copyright : Conor McBride and Ross Paterson 2005
5 -- License : BSD-style (see the LICENSE file in the distribution)
6 --
7 -- Maintainer : ross@soi.city.ac.uk
8 -- Stability : experimental
9 -- Portability : portable
10 --
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>.
17 --
18 -- This interface was introduced for parsers by Niklas R&#xF6;jemo, because
19 -- it admits more sharing than the monadic interface. The names here are
20 -- mostly based on recent parsing work by Doaitse Swierstra.
21 --
22 -- This class is also useful with instances of the
23 -- 'Data.Traversable.Traversable' class.
24
25 module Control.Applicative (
26 -- * Applicative functors
27 Applicative(..),
28 -- * Alternatives
29 Alternative(..),
30 -- * Instances
31 Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
32 -- * Utility functions
33 (<$>), (<$), (*>), (<*), (<**>),
34 liftA, liftA2, liftA3,
35 optional, some, many
36 ) where
37
38 #ifdef __HADDOCK__
39 import Prelude
40 #endif
41
42 import Control.Arrow
43 (Arrow(arr, (>>>), (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
44 import Control.Monad (liftM, ap, MonadPlus(..))
45 import Control.Monad.Instances ()
46 import Data.Monoid (Monoid(..))
47
48 infixl 3 <|>
49 infixl 4 <$>, <$
50 infixl 4 <*>, <*, *>, <**>
51
52 -- | A functor with application.
53 --
54 -- Instances should satisfy the following laws:
55 --
56 -- [/identity/]
57 -- @'pure' 'id' '<*>' v = v@
58 --
59 -- [/composition/]
60 -- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
61 --
62 -- [/homomorphism/]
63 -- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
64 --
65 -- [/interchange/]
66 -- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
67 --
68 -- The 'Functor' instance should satisfy
69 --
70 -- @
71 -- 'fmap' f x = 'pure' f '<*>' x
72 -- @
73 --
74 -- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
75
76 class Functor f => Applicative f where
77 -- | Lift a value.
78 pure :: a -> f a
79
80 -- | Sequential application.
81 (<*>) :: f (a -> b) -> f a -> f b
82
83 -- | A monoid on applicative functors.
84 class Applicative f => Alternative f where
85 -- | The identity of '<|>'
86 empty :: f a
87 -- | An associative binary operation
88 (<|>) :: f a -> f a -> f a
89
90 -- instances for Prelude types
91
92 instance Applicative Maybe where
93 pure = return
94 (<*>) = ap
95
96 instance Alternative Maybe where
97 empty = Nothing
98 Nothing <|> p = p
99 Just x <|> _ = Just x
100
101 instance Applicative [] where
102 pure = return
103 (<*>) = ap
104
105 instance Alternative [] where
106 empty = []
107 (<|>) = (++)
108
109 instance Applicative IO where
110 pure = return
111 (<*>) = ap
112
113 instance Applicative ((->) a) where
114 pure = const
115 (<*>) f g x = f x (g x)
116
117 instance Monoid a => Applicative ((,) a) where
118 pure x = (mempty, x)
119 (u, f) <*> (v, x) = (u `mappend` v, f x)
120
121 -- new instances
122
123 newtype Const a b = Const { getConst :: a }
124
125 instance Functor (Const m) where
126 fmap _ (Const v) = Const v
127
128 instance Monoid m => Applicative (Const m) where
129 pure _ = Const mempty
130 Const f <*> Const v = Const (f `mappend` v)
131
132 newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
133
134 instance Monad m => Functor (WrappedMonad m) where
135 fmap f (WrapMonad v) = WrapMonad (liftM f v)
136
137 instance Monad m => Applicative (WrappedMonad m) where
138 pure = WrapMonad . return
139 WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
140
141 instance MonadPlus m => Alternative (WrappedMonad m) where
142 empty = WrapMonad mzero
143 WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
144
145 newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
146
147 instance Arrow a => Functor (WrappedArrow a b) where
148 fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
149
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))
153
154 instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
155 empty = WrapArrow zeroArrow
156 WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
157
158 -- | Lists, but with an 'Applicative' functor based on zipping, so that
159 --
160 -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
161 --
162 newtype ZipList a = ZipList { getZipList :: [a] }
163
164 instance Functor ZipList where
165 fmap f (ZipList xs) = ZipList (map f xs)
166
167 instance Applicative ZipList where
168 pure x = ZipList (repeat x)
169 ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
170
171 -- extra functions
172
173 -- | A synonym for 'fmap'.
174 (<$>) :: Functor f => (a -> b) -> f a -> f b
175 f <$> a = fmap f a
176
177 -- | Replace the value.
178 (<$) :: Functor f => a -> f b -> f a
179 (<$) = (<$>) . const
180
181 -- | Sequence actions, discarding the value of the first argument.
182 (*>) :: Applicative f => f a -> f b -> f b
183 (*>) = liftA2 (const id)
184
185 -- | Sequence actions, discarding the value of the second argument.
186 (<*) :: Applicative f => f a -> f b -> f a
187 (<*) = liftA2 const
188
189 -- | A variant of '<*>' with the arguments reversed.
190 (<**>) :: Applicative f => f a -> f (a -> b) -> f b
191 (<**>) = liftA2 (flip ($))
192
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
197
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 <$> a <*> b
201
202 -- | Lift a ternary function to actions.
203 liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
204 liftA3 f a b c = f <$> a <*> b <*> c
205
206 -- | One or none.
207 optional :: Alternative f => f a -> f (Maybe a)
208 optional v = Just <$> v <|> pure Nothing
209
210 -- | One or more.
211 some :: Alternative f => f a -> f [a]
212 some v = some_v
213 where many_v = some_v <|> pure []
214 some_v = (:) <$> v <*> many_v
215
216 -- | Zero or more.
217 many :: Alternative f => f a -> f [a]
218 many v = many_v
219 where many_v = some_v <|> pure []
220 some_v = (:) <$> v <*> many_v