add an INLINE to the list version of traverse, to enable fusion
[ghc.git] / libraries / base / Data / Traversable.hs
1 -----------------------------------------------------------------------------
2 -- |
3 -- Module : Data.Traversable
4 -- Copyright : Conor McBride and Ross Paterson 2005
5 -- License : BSD-style (see the LICENSE file in the distribution)
6 --
7 -- Maintainer : libraries@haskell.org
8 -- Stability : experimental
9 -- Portability : portable
10 --
11 -- Class of data structures that can be traversed from left to right,
12 -- performing an action on each element.
13 --
14 -- See also
15 --
16 -- * /Applicative Programming with Effects/,
17 -- by Conor McBride and Ross Paterson, online at
18 -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
19 --
20 -- * /The Essence of the Iterator Pattern/,
21 -- by Jeremy Gibbons and Bruno Oliveira,
22 -- in /Mathematically-Structured Functional Programming/, 2006, and online at
23 -- <http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/#iterator>.
24 --
25 -- Note that the functions 'mapM' and 'sequence' generalize "Prelude"
26 -- functions of the same names from lists to any 'Traversable' functor.
27 -- To avoid ambiguity, either import the "Prelude" hiding these names
28 -- or qualify uses of these function names with an alias for this module.
29
30 module Data.Traversable (
31 Traversable(..),
32 for,
33 forM,
34 mapAccumL,
35 mapAccumR,
36 fmapDefault,
37 foldMapDefault,
38 ) where
39
40 import Prelude hiding (mapM, sequence, foldr)
41 import qualified Prelude (mapM, foldr)
42 import Control.Applicative
43 import Data.Foldable (Foldable())
44 import Data.Monoid (Monoid)
45
46 #if defined(__GLASGOW_HASKELL__)
47 import GHC.Arr
48 #elif defined(__HUGS__)
49 import Hugs.Array
50 #elif defined(__NHC__)
51 import Array
52 #endif
53
54 -- | Functors representing data structures that can be traversed from
55 -- left to right.
56 --
57 -- Minimal complete definition: 'traverse' or 'sequenceA'.
58 --
59 -- Instances are similar to 'Functor', e.g. given a data type
60 --
61 -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
62 --
63 -- a suitable instance would be
64 --
65 -- > instance Traversable Tree where
66 -- > traverse f Empty = pure Empty
67 -- > traverse f (Leaf x) = Leaf <$> f x
68 -- > traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
69 --
70 -- This is suitable even for abstract types, as the laws for '<*>'
71 -- imply a form of associativity.
72 --
73 -- The superclass instances should satisfy the following:
74 --
75 -- * In the 'Functor' instance, 'fmap' should be equivalent to traversal
76 -- with the identity applicative functor ('fmapDefault').
77 --
78 -- * In the 'Foldable' instance, 'Data.Foldable.foldMap' should be
79 -- equivalent to traversal with a constant applicative functor
80 -- ('foldMapDefault').
81 --
82 class (Functor t, Foldable t) => Traversable t where
83 -- | Map each element of a structure to an action, evaluate
84 -- these actions from left to right, and collect the results.
85 traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
86 traverse f = sequenceA . fmap f
87
88 -- | Evaluate each action in the structure from left to right,
89 -- and collect the results.
90 sequenceA :: Applicative f => t (f a) -> f (t a)
91 sequenceA = traverse id
92
93 -- | Map each element of a structure to a monadic action, evaluate
94 -- these actions from left to right, and collect the results.
95 mapM :: Monad m => (a -> m b) -> t a -> m (t b)
96 mapM f = unwrapMonad . traverse (WrapMonad . f)
97
98 -- | Evaluate each monadic action in the structure from left to right,
99 -- and collect the results.
100 sequence :: Monad m => t (m a) -> m (t a)
101 sequence = mapM id
102
103 -- instances for Prelude types
104
105 instance Traversable Maybe where
106 traverse _ Nothing = pure Nothing
107 traverse f (Just x) = Just <$> f x
108
109 instance Traversable [] where
110 {-# INLINE traverse #-} -- so that traverse can fuse
111 traverse f = Prelude.foldr cons_f (pure [])
112 where cons_f x ys = (:) <$> f x <*> ys
113
114 mapM = Prelude.mapM
115
116 instance Ix i => Traversable (Array i) where
117 traverse f arr = listArray (bounds arr) `fmap` traverse f (elems arr)
118
119 -- general functions
120
121 -- | 'for' is 'traverse' with its arguments flipped.
122 for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
123 {-# INLINE for #-}
124 for = flip traverse
125
126 -- | 'forM' is 'mapM' with its arguments flipped.
127 forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
128 {-# INLINE forM #-}
129 forM = flip mapM
130
131 -- left-to-right state transformer
132 newtype StateL s a = StateL { runStateL :: s -> (s, a) }
133
134 instance Functor (StateL s) where
135 fmap f (StateL k) = StateL $ \ s ->
136 let (s', v) = k s in (s', f v)
137
138 instance Applicative (StateL s) where
139 pure x = StateL (\ s -> (s, x))
140 StateL kf <*> StateL kv = StateL $ \ s ->
141 let (s', f) = kf s
142 (s'', v) = kv s'
143 in (s'', f v)
144
145 -- |The 'mapAccumL' function behaves like a combination of 'fmap'
146 -- and 'foldl'; it applies a function to each element of a structure,
147 -- passing an accumulating parameter from left to right, and returning
148 -- a final value of this accumulator together with the new structure.
149 mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
150 mapAccumL f s t = runStateL (traverse (StateL . flip f) t) s
151
152 -- right-to-left state transformer
153 newtype StateR s a = StateR { runStateR :: s -> (s, a) }
154
155 instance Functor (StateR s) where
156 fmap f (StateR k) = StateR $ \ s ->
157 let (s', v) = k s in (s', f v)
158
159 instance Applicative (StateR s) where
160 pure x = StateR (\ s -> (s, x))
161 StateR kf <*> StateR kv = StateR $ \ s ->
162 let (s', v) = kv s
163 (s'', f) = kf s'
164 in (s'', f v)
165
166 -- |The 'mapAccumR' function behaves like a combination of 'fmap'
167 -- and 'foldr'; it applies a function to each element of a structure,
168 -- passing an accumulating parameter from right to left, and returning
169 -- a final value of this accumulator together with the new structure.
170 mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
171 mapAccumR f s t = runStateR (traverse (StateR . flip f) t) s
172
173 -- | This function may be used as a value for `fmap` in a `Functor` instance.
174 fmapDefault :: Traversable t => (a -> b) -> t a -> t b
175 fmapDefault f = getId . traverse (Id . f)
176
177 -- | This function may be used as a value for `Data.Foldable.foldMap`
178 -- in a `Foldable` instance.
179 foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
180 foldMapDefault f = getConst . traverse (Const . f)
181
182 -- local instances
183
184 newtype Id a = Id { getId :: a }
185
186 instance Functor Id where
187 fmap f (Id x) = Id (f x)
188
189 instance Applicative Id where
190 pure = Id
191 Id f <*> Id x = Id (f x)