96ea010d8b359e962501ad37123823b324f7add8
[packages/base.git] / Data / Traversable.hs
1 {-# LANGUAGE Trustworthy #-}
2 {-# LANGUAGE CPP #-}
3
4 -----------------------------------------------------------------------------
5 -- |
6 -- Module : Data.Traversable
7 -- Copyright : Conor McBride and Ross Paterson 2005
8 -- License : BSD-style (see the LICENSE file in the distribution)
9 --
10 -- Maintainer : libraries@haskell.org
11 -- Stability : experimental
12 -- Portability : portable
13 --
14 -- Class of data structures that can be traversed from left to right,
15 -- performing an action on each element.
16 --
17 -- See also
18 --
19 -- * /Applicative Programming with Effects/,
20 -- by Conor McBride and Ross Paterson, online at
21 -- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
22 --
23 -- * /The Essence of the Iterator Pattern/,
24 -- by Jeremy Gibbons and Bruno Oliveira,
25 -- in /Mathematically-Structured Functional Programming/, 2006, and online at
26 -- <http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/#iterator>.
27 --
28 -- Note that the functions 'mapM' and 'sequence' generalize "Prelude"
29 -- functions of the same names from lists to any 'Traversable' functor.
30 -- To avoid ambiguity, either import the "Prelude" hiding these names
31 -- or qualify uses of these function names with an alias for this module.
32
33 module Data.Traversable (
34 Traversable(..),
35 for,
36 forM,
37 mapAccumL,
38 mapAccumR,
39 fmapDefault,
40 foldMapDefault,
41 ) where
42
43 import Prelude hiding (mapM, sequence, foldr)
44 import qualified Prelude (mapM, foldr)
45 import Control.Applicative
46 import Data.Foldable (Foldable())
47 import Data.Monoid (Monoid)
48
49 #if defined(__GLASGOW_HASKELL__)
50 import GHC.Arr
51 #elif defined(__HUGS__)
52 import Hugs.Array
53 #elif defined(__NHC__)
54 import Array
55 #endif
56
57 -- | Functors representing data structures that can be traversed from
58 -- left to right.
59 --
60 -- Minimal complete definition: 'traverse' or 'sequenceA'.
61 --
62 -- Instances are similar to 'Functor', e.g. given a data type
63 --
64 -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
65 --
66 -- a suitable instance would be
67 --
68 -- > instance Traversable Tree where
69 -- > traverse f Empty = pure Empty
70 -- > traverse f (Leaf x) = Leaf <$> f x
71 -- > traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
72 --
73 -- This is suitable even for abstract types, as the laws for '<*>'
74 -- imply a form of associativity.
75 --
76 -- The superclass instances should satisfy the following:
77 --
78 -- * In the 'Functor' instance, 'fmap' should be equivalent to traversal
79 -- with the identity applicative functor ('fmapDefault').
80 --
81 -- * In the 'Foldable' instance, 'Data.Foldable.foldMap' should be
82 -- equivalent to traversal with a constant applicative functor
83 -- ('foldMapDefault').
84 --
85 class (Functor t, Foldable t) => Traversable t where
86 -- | Map each element of a structure to an action, evaluate
87 -- these actions from left to right, and collect the results.
88 traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
89 traverse f = sequenceA . fmap f
90
91 -- | Evaluate each action in the structure from left to right,
92 -- and collect the results.
93 sequenceA :: Applicative f => t (f a) -> f (t a)
94 sequenceA = traverse id
95
96 -- | Map each element of a structure to a monadic action, evaluate
97 -- these actions from left to right, and collect the results.
98 mapM :: Monad m => (a -> m b) -> t a -> m (t b)
99 mapM f = unwrapMonad . traverse (WrapMonad . f)
100
101 -- | Evaluate each monadic action in the structure from left to right,
102 -- and collect the results.
103 sequence :: Monad m => t (m a) -> m (t a)
104 sequence = mapM id
105
106 -- instances for Prelude types
107
108 instance Traversable Maybe where
109 traverse _ Nothing = pure Nothing
110 traverse f (Just x) = Just <$> f x
111
112 instance Traversable [] where
113 {-# INLINE traverse #-} -- so that traverse can fuse
114 traverse f = Prelude.foldr cons_f (pure [])
115 where cons_f x ys = (:) <$> f x <*> ys
116
117 mapM = Prelude.mapM
118
119 instance Ix i => Traversable (Array i) where
120 traverse f arr = listArray (bounds arr) `fmap` traverse f (elems arr)
121
122 -- general functions
123
124 -- | 'for' is 'traverse' with its arguments flipped.
125 for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
126 {-# INLINE for #-}
127 for = flip traverse
128
129 -- | 'forM' is 'mapM' with its arguments flipped.
130 forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
131 {-# INLINE forM #-}
132 forM = flip mapM
133
134 -- left-to-right state transformer
135 newtype StateL s a = StateL { runStateL :: s -> (s, a) }
136
137 instance Functor (StateL s) where
138 fmap f (StateL k) = StateL $ \ s -> let (s', v) = k s in (s', f v)
139
140 instance Applicative (StateL s) where
141 pure x = StateL (\ s -> (s, x))
142 StateL kf <*> StateL kv = StateL $ \ s ->
143 let (s', f) = kf s
144 (s'', v) = kv s'
145 in (s'', f v)
146
147 -- |The 'mapAccumL' function behaves like a combination of 'fmap'
148 -- and 'foldl'; it applies a function to each element of a structure,
149 -- passing an accumulating parameter from left to right, and returning
150 -- a final value of this accumulator together with the new structure.
151 mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
152 mapAccumL f s t = runStateL (traverse (StateL . flip f) t) s
153
154 -- right-to-left state transformer
155 newtype StateR s a = StateR { runStateR :: s -> (s, a) }
156
157 instance Functor (StateR s) where
158 fmap f (StateR k) = StateR $ \ s -> let (s', v) = k s in (s', f v)
159
160 instance Applicative (StateR s) where
161 pure x = StateR (\ s -> (s, x))
162 StateR kf <*> StateR kv = StateR $ \ s ->
163 let (s', v) = kv s
164 (s'', f) = kf s'
165 in (s'', f v)
166
167 -- |The 'mapAccumR' function behaves like a combination of 'fmap'
168 -- and 'foldr'; it applies a function to each element of a structure,
169 -- passing an accumulating parameter from right to left, and returning
170 -- a final value of this accumulator together with the new structure.
171 mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
172 mapAccumR f s t = runStateR (traverse (StateR . flip f) t) s
173
174 -- | This function may be used as a value for `fmap` in a `Functor`
175 -- instance, provided that 'traverse' is defined. (Using
176 -- `fmapDefault` with a `Traversable` instance defined only by
177 -- 'sequenceA' will result in infinite recursion.)
178 fmapDefault :: Traversable t => (a -> b) -> t a -> t b
179 {-# INLINE fmapDefault #-}
180 fmapDefault f = getId . traverse (Id . f)
181
182 -- | This function may be used as a value for `Data.Foldable.foldMap`
183 -- in a `Foldable` instance.
184 foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
185 foldMapDefault f = getConst . traverse (Const . f)
186
187 -- local instances
188
189 newtype Id a = Id { getId :: a }
190
191 instance Functor Id where
192 fmap f (Id x) = Id (f x)
193
194 instance Applicative Id where
195 pure = Id
196 Id f <*> Id x = Id (f x)