-
Notifications
You must be signed in to change notification settings - Fork 272
/
Traversal.hs
559 lines (511 loc) · 20.3 KB
/
Traversal.hs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE LiberalTypeSynonyms #-}
{-# LANGUAGE TypeOperators #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Lens.Traversal
-- Copyright : (C) 2012 Edward Kmett
-- License : BSD-style (see the file LICENSE)
-- Maintainer : Edward Kmett <ekmett@gmail.com>
-- Stability : provisional
-- Portability : Rank2Types
--
-- A @'Traversal' s t a b@ is a generalization of 'traverse' from
-- 'Traversable'. It allows you to traverse over a structure and change out
-- its contents with monadic or applicative side-effects. Starting from
--
-- @'traverse' :: ('Traversable' t, 'Applicative' f) => (a -> f b) -> t a -> f (t b)@,
--
-- we monomorphize the contents and result to obtain
--
-- > type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
--
-- While a 'Traversal' isn't quite a 'Fold', it _can_ be used for 'Getting'
-- like a 'Fold', because given a 'Monoid' @m@, we have an 'Applicative'
-- for @('Const' m)@. Everything you know how to do with a 'Traversable'
-- container, you can with with a 'Traversal', and here we provide
-- combinators that generalize the usual 'Traversable' operations.
----------------------------------------------------------------------------
module Control.Lens.Traversal
(
-- * Lenses
Traversal
-- ** Lensing Traversals
, element, elementOf
-- * Traversing and Lensing
, traverseOf, forOf, sequenceAOf
, mapMOf, forMOf, sequenceOf
, transposeOf
, mapAccumLOf, mapAccumROf
, scanr1Of, scanl1Of
-- * Parts and Holes
, partsOf, unsafePartsOf
, holesOf
-- * Common Traversals
, Traversable(traverse)
, traverseLeft
, traverseRight
, both
, beside
, taking
, dropping
-- * Cloning Traversals
, cloneTraversal
, ReifiedTraversal(..)
-- * Simple
, SimpleTraversal
, SimpleReifiedTraversal
) where
import Control.Applicative as Applicative
import Control.Applicative.Backwards
import Control.Lens.Evil
import Control.Lens.Fold
import Control.Lens.Internal
import Control.Lens.Unsafe
import Control.Lens.Type
import Control.Monad.State.Class as State
import Control.Monad.Trans.State.Lazy as Lazy
import Data.Maybe
import Data.Traversable
-- $setup
-- >>> import Control.Lens
------------------------------------------------------------------------------
-- Traversals
------------------------------------------------------------------------------
-- | A 'Traversal' can be used directly as a 'Control.Lens.Setter.Setter' or a 'Fold' (but not as a 'Lens') and provides
-- the ability to both read and update multiple fields, subject to some relatively weak 'Traversal' laws.
--
-- These have also been known as multilenses, but they have the signature and spirit of
--
-- @'traverse' :: 'Traversable' f => 'Traversal' (f a) (f b) a b@
--
-- and the more evocative name suggests their application.
--
-- Most of the time the 'Traversal' you will want to use is just 'traverse', but you can also pass any
-- 'Lens' or 'Control.Lens.Iso.Iso' as a 'Traversal', and composition of a 'Traversal' (or 'Lens' or 'Control.Lens.Iso.Iso') with a 'Traversal' (or 'Lens' or 'Control.Lens.Iso.Iso')
-- using (.) forms a valid 'Traversal'.
--
-- The laws for a Traversal @t@ follow from the laws for Traversable as stated in \"The Essence of the Iterator Pattern\".
--
-- @
-- t 'pure' ≡ 'pure'
-- 'fmap' (t f) '.' t g ≡ 'Data.Functor.Compose.getCompose' '.' t ('Data.Functor.Compose.Compose' '.' 'fmap' f '.' g)
-- @
--
-- One consequence of this requirement is that a 'Traversal' needs to leave the same number of elements as a
-- candidate for subsequent 'Traversal' that it started with. Another testament to the strength of these laws
-- is that the caveat expressed in section 5.5 of the \"Essence of the Iterator Pattern\" about exotic
-- 'Traversable' instances that 'traverse' the same entry multiple times was actually already ruled out by the
-- second law in that same paper!
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
-- | @type SimpleTraversal = 'Simple' 'Traversal'@
type SimpleTraversal s a = Traversal s s a a
--------------------------
-- Traversal Combinators
--------------------------
-- |
-- Map each element of a structure targeted by a Lens or Traversal,
-- evaluate these actions from left to right, and collect the results.
--
-- This function is only provided for consistency, 'id' is strictly more general.
--
-- @'traverseOf' ≡ 'id'@
--
-- This yields the obvious law:
--
-- @'traverse' ≡ 'traverseOf' 'traverse'@
--
-- @
-- 'traverseOf' :: 'Control.Lens.Iso.Iso' s t a b -> (a -> f b) -> s -> f t
-- 'traverseOf' :: 'Lens' s t a b -> (a -> f b) -> s -> f t
-- 'traverseOf' :: 'Traversal' s t a b -> (a -> f b) -> s -> f t
-- @
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
traverseOf = id
{-# INLINE traverseOf #-}
-- | A version of 'traverseOf' with the arguments flipped, such that:
--
-- @'forOf' l ≡ 'flip' ('traverseOf' l)@
--
-- @
-- 'for' ≡ 'forOf' 'traverse'
-- @
--
-- This function is only provided for consistency, 'flip' is strictly more general.
--
-- @
-- 'forOf' ≡ 'flip'
-- @
--
-- @
-- 'forOf' :: 'Control.Lens.Iso.Iso' s t a b -> s -> (a -> f b) -> f t
-- 'forOf' :: 'Lens' s t a b -> s -> (a -> f b) -> f t
-- 'forOf' :: 'Traversal' s t a b -> s -> (a -> f b) -> f t
-- @
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
forOf = flip
{-# INLINE forOf #-}
-- |
-- Evaluate each action in the structure from left to right, and collect
-- the results.
--
-- @
-- 'sequenceA' ≡ 'sequenceAOf' 'traverse' ≡ 'traverse' 'id'
-- 'sequenceAOf' l ≡ 'traverseOf' l id ≡ l id
-- @
--
-- @
-- 'sequenceAOf' :: 'Control.Lens.Iso.Iso' s t (f b) b -> s -> f t
-- 'sequenceAOf' :: 'Lens' s t (f b) b -> s -> f t
-- 'sequenceAOf' :: 'Applicative' f => 'Traversal' s t (f b) b -> s -> f t
-- @
sequenceAOf :: LensLike f s t (f b) b -> s -> f t
sequenceAOf l = l id
{-# INLINE sequenceAOf #-}
-- | Map each element of a structure targeted by a lens to a monadic action,
-- evaluate these actions from left to right, and collect the results.
--
-- @'mapM' ≡ 'mapMOf' 'traverse'@
--
-- @
-- 'mapMOf' :: 'Control.Lens.Iso.Iso' s t a b -> (a -> m b) -> s -> m t
-- 'mapMOf' :: 'Lens' s t a b -> (a -> m b) -> s -> m t
-- 'mapMOf' :: 'Monad' m => 'Traversal' s t a b -> (a -> m b) -> s -> m t
-- @
mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
mapMOf l cmd = unwrapMonad# (l (wrapMonad# cmd))
{-# INLINE mapMOf #-}
-- | 'forMOf' is a flipped version of 'mapMOf', consistent with the definition of 'forM'.
-- @
-- 'forM' ≡ 'forMOf' 'traverse'
-- 'forMOf' l ≡ 'flip' ('mapMOf' l)
-- @
--
-- @
-- 'forMOf' :: 'Control.Lens.Iso.Iso' s t a b -> s -> (a -> m b) -> m t
-- 'forMOf' :: 'Lens' s t a b -> s -> (a -> m b) -> m t
-- 'forMOf' :: 'Monad' m => 'Traversal' s t a b -> s -> (a -> m b) -> m t
-- @
forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
forMOf l a cmd = unwrapMonad (l (wrapMonad# cmd) a)
{-# INLINE forMOf #-}
-- | Sequence the (monadic) effects targeted by a lens in a container from left to right.
--
-- @
-- 'sequence' ≡ 'sequenceOf' 'traverse'
-- 'sequenceOf' l ≡ 'mapMOf' l id
-- 'sequenceOf' l ≡ 'unwrapMonad' . l 'WrapMonad'
-- @
--
-- @
-- 'sequenceOf' :: 'Control.Lens.Iso.Iso' s t (m b) b -> s -> m t
-- 'sequenceOf' :: 'Lens' s t (m b) b -> s -> m t
-- 'sequenceOf' :: 'Monad' m => 'Traversal' s t (m b) b -> s -> m t
-- @
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
sequenceOf l = unwrapMonad# (l WrapMonad)
{-# INLINE sequenceOf #-}
-- | This generalizes 'Data.List.transpose' to an arbitrary 'Traversal'.
--
-- Note: 'Data.List.transpose' handles ragged inputs more intelligently, but for non-ragged inputs:
--
-- @'Data.List.transpose' ≡ 'transposeOf' 'traverse'@
--
-- >>> transposeOf traverse [[1,2,3],[4,5,6]]
-- [[1,4],[2,5],[3,6]]
--
-- Since every 'Lens' is a 'Traversal', we can use this as a form of
-- monadic strength as well:
--
-- @'transposeOf' '_2' :: (b, [a]) -> [(b, a)]@
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
transposeOf l = getZipList# (l ZipList)
{-# INLINE transposeOf #-}
-- | This generalizes 'Data.Traversable.mapAccumR' to an arbitrary 'Traversal'.
--
-- @'mapAccumR' ≡ 'mapAccumROf' 'traverse'@
--
-- 'mapAccumROf' accumulates state from right to left.
--
-- @
-- 'mapAccumROf' :: 'Control.Lens.Iso.Iso' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- 'mapAccumROf' :: 'Lens' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- 'mapAccumROf' :: 'Traversal' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- @
mapAccumROf :: LensLike (Lazy.State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf l f s0 a = swap (Lazy.runState (l (\c -> State.state (\s -> swap (f s c))) a) s0)
{-# INLINE mapAccumROf #-}
-- | This generalizes 'Data.Traversable.mapAccumL' to an arbitrary 'Traversal'.
--
-- @'mapAccumL' ≡ 'mapAccumLOf' 'traverse'@
--
-- 'mapAccumLOf' accumulates state from left to right.
--
-- @
-- 'mapAccumLOf' :: 'Control.Lens.Iso.Iso' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- 'mapAccumLOf' :: 'Lens' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- 'mapAccumLOf' :: 'Traversal' s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- @
mapAccumLOf :: LensLike (Backwards (Lazy.State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf = mapAccumROf . backwards
{-# INLINE mapAccumLOf #-}
swap :: (a,b) -> (b,a)
swap (a,b) = (b,a)
{-# INLINE swap #-}
-- | This permits the use of 'scanr1' over an arbitrary 'Traversal' or 'Lens'.
--
-- @'scanr1' ≡ 'scanr1Of' 'traverse'@
--
-- @
-- 'scanr1Of' :: 'Control.Lens.Iso.Iso' s t a a -> (a -> a -> a) -> s -> t
-- 'scanr1Of' :: 'Lens' s t a a -> (a -> a -> a) -> s -> t
-- 'scanr1Of' :: 'Traversal' s t a a -> (a -> a -> a) -> s -> t
-- @
scanr1Of :: LensLike (Lazy.State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
scanr1Of l f = snd . mapAccumROf l step Nothing where
step Nothing a = (Just a, a)
step (Just s) a = (Just r, r) where r = f a s
{-# INLINE scanr1Of #-}
-- | This permits the use of 'scanl1' over an arbitrary 'Traversal' or 'Lens'.
--
-- @'scanl1' ≡ 'scanl1Of' 'traverse'@
--
-- @
-- 'scanr1Of' :: 'Control.Lens.Iso.Iso' s t a a -> (a -> a -> a) -> s -> t
-- 'scanr1Of' :: 'Lens' s t a a -> (a -> a -> a) -> s -> t
-- 'scanr1Of' :: 'Traversal' s t a a -> (a -> a -> a) -> s -> t
-- @
scanl1Of :: LensLike (Backwards (Lazy.State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
scanl1Of l f = snd . mapAccumLOf l step Nothing where
step Nothing a = (Just a, a)
step (Just s) a = (Just r, r) where r = f s a
{-# INLINE scanl1Of #-}
-------------------------------------------------------------------------------
-- Parts and Holes
-------------------------------------------------------------------------------
-- | 'partsOf' turns a 'Traversal' into a 'Lens' that resembles an early version of the @uniplate@ (or @biplate@) type.
--
-- /Note:/ You should really try to maintain the invariant of the number of children in the list.
--
-- Any extras will be lost. If you do not supply enough, then the remainder will come from the original structure.
--
-- So technically, this is only a lens if you do not change the number of results it returns.
--
-- When applied to a 'Fold' the result is merely a 'Getter'.
--
-- @
-- 'partsOf' :: 'Simple' 'Control.Lens.Iso.Iso' s a -> 'Simple' 'Lens' s [a]
-- 'partsOf' :: 'Simple' 'Lens' s a -> 'Simple' 'Lens' s [a]
-- 'partsOf' :: 'Simple' 'Traversal' s a -> 'Simple' 'Lens' s [a]
-- 'partsOf' :: 'Fold' s a -> 'Getter' s [a]
-- 'partsOf' :: 'Getter' s a -> 'Getter' s [a]
-- @
partsOf :: Functor f => LensLike (EvilBazaar f a a) s t a a -> LensLike f s t [a] [a]
partsOf l f s = evilOuts b <$> f (evilIns b) where b = l evilSell s
{-# INLINE partsOf #-}
-- | 'unsafePartsOf' turns a 'Traversal' into a @uniplate@ (or @biplate@) family.
--
-- If you do not need the types of @s@ and @t@ to be different, it is recommended that
-- you use 'partsOf'
--
-- It is generally safer to traverse with the 'Bazaar' rather than use this
-- combinator. However, it is sometimes convenient.
--
-- This is unsafe because if you don't supply at least as many @b@'s as you were
-- given @a@'s, then the reconstruction of @t@ /will/ result in an error!
--
-- @
-- 'unsafePartsOf' :: 'Control.Lens.Iso.Iso' s t a b -> 'Lens' s t [a] [b]
-- 'unsafePartsOf' :: 'Lens' s t a b -> 'Lens' s t [a] [b]
-- 'unsafePartsOf' :: 'Traversal' s t a b -> 'Lens' s t [a] [b]
-- 'unsafePartsOf' :: 'Fold' s a -> 'Getter' s [a]
-- 'unsafePartsOf' :: 'Getter' s a -> 'Getter' s [a]
-- @
unsafePartsOf :: Functor f => LensLike (EvilBazaar f a b) s t a b -> LensLike f s t [a] [b]
unsafePartsOf l f s = unsafeEvilOuts b <$> f (evilIns b) where b = l evilSell s
{-# INLINE unsafePartsOf #-}
-- | The one-level version of 'contextsOf'. This extracts a list of the immediate children according to a given 'Traversal' as editable contexts.
--
-- Given a context you can use 'pos' to see the values, 'peek' at what the structure would be like with an edited result, or simply 'extract' the original structure.
--
-- @
-- propChildren l x = 'childrenOf' l x '==' 'map' 'pos' ('holesOf' l x)
-- propId l x = 'all' ('==' x) [extract w | w <- 'holesOf' l x]
-- @
--
-- @
-- 'holesOf' :: 'Simple' 'Iso' s a -> s -> ['Context' a a s]
-- 'holesOf' :: 'Simple' 'Lens' s a -> s -> ['Context' a a s]
-- 'holesOf' :: 'Simple' 'Traversal' s a -> s -> ['Context' a a s]
-- @
holesOf :: LensLike (Bazaar a a) s t a a -> s -> [Context a a t]
holesOf l a = f (ins b) (outs b) where
b = l sell a
f [] _ = []
f (x:xs) g = Context (g . (:xs)) x : f xs (g . (x:))
{-# INLINE holesOf #-}
-- | A 'Lens' to 'Control.Lens.Getter.view'/'Control.Lens.Setter.set' the nth element 'elementOf' a 'Traversal', 'Lens' or 'Control.Lens.Iso.Iso'.
--
-- Attempts to access beyond the range of the 'Traversal' will cause an error. This also works transparently
-- with Folds, returning a getter.
--
-- >>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
-- [[1],[5,4]]
--
-- >>> [[1],[3,4]]^.elementOf (folded.folded) 1
-- 3
--
-- >>> [0..]^.elementOf folded 5
-- 5
--
-- >>> take 10 $ (elementOf traverse 3 .~ 16) [0..]
-- [0,1,2,16,4,5,6,7,8,9]
elementOf :: Functor f => LensLike (ElementOf f) s t a a -> Int -> LensLike f s t a a
elementOf l i f s = case getElementOf (l go s) 0 of
Searching _ _ mft -> fromMaybe (error "elOf: index out of range") mft
where
go a = ElementOf $ \j -> Searching (j + 1) a (if i == j then Just (f a) else Nothing)
-- | Access the /nth/ element of a 'Traversable' container.
--
-- Attempts to access beyond the range of the 'Traversal' will cause an error.
--
-- @'element' ≡ 'elementOf' 'traverse'@
element :: Traversable t => Int -> Simple Lens (t a) a
element = elementOf traverse
-- Internal functions used in the implementation of partsOf and holesOf.
ins :: Bazaar a b t -> [a]
ins = toListOf bazaar
{-# INLINE ins #-}
outs :: Bazaar a a t -> [a] -> t
outs = evalState . bazaar (\oldVal -> State.state (unconsWithDefault oldVal))
{-# INLINE outs #-}
evilIns :: EvilBazaar f a b s -> [a]
evilIns = toListOf evilBazaar
{-# INLINE evilIns #-}
evilOuts :: EvilBazaar f a a s -> [a] -> s
evilOuts = evalState . evilBazaar (\oldVal -> State.state (unconsWithDefault oldVal))
{-# INLINE evilOuts #-}
unsafeEvilOuts :: EvilBazaar f a b t -> [b] -> t
unsafeEvilOuts = evalState . evilBazaar (\_ -> State.state (unconsWithDefault fakeVal))
where fakeVal = error "unsafePartsOf: not enough elements were supplied"
{-# INLINE unsafeEvilOuts #-}
unconsWithDefault :: a -> [a] -> (a,[a])
unconsWithDefault d [] = (d,[])
unconsWithDefault _ (x:xs) = (x,xs)
{-# INLINE unconsWithDefault #-}
------------------------------------------------------------------------------
-- Traversals
------------------------------------------------------------------------------
-- | Traverse both parts of a tuple with matching types.
--
-- >>> both *~ 10 $ (1,2)
-- (10,20)
-- >>> over both length ("hello","world")
-- (5,5)
-- >>> ("hello","world")^.both
-- "helloworld"
both :: Traversal (a,a) (b,b) a b
both f ~(a,a') = (,) <$> f a <*> f a'
{-# INLINE both #-}
-- | Apply a different 'Traversal' or 'Control.Lens.Fold.Fold' to each side of a tuple.
--
-- >>> ("hello",["world","!!!"])^..beside id traverse
-- ["hello","world","!!!"]
beside :: Applicative f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (s,s') (t,t') a b
beside l r f ~(s,s') = (,) <$> l f s <*> r f s'
{-# INLINE beside #-}
-- | A traversal for tweaking the left-hand value of an 'Either':
--
-- >>> over traverseLeft (+1) (Left 2)
-- Left 3
-- >>> over traverseLeft (+1) (Right 2)
-- Right 2
-- >>> Right 42 ^.traverseLeft :: String
-- ""
-- >>> Left "hello" ^.traverseLeft
-- "hello"
--
-- @traverseLeft :: 'Applicative' f => (a -> f b) -> 'Either' a c -> f ('Either' b c)@
traverseLeft :: Traversal (Either a c) (Either b c) a b
traverseLeft f (Left a) = Left <$> f a
traverseLeft _ (Right c) = pure $ Right c
{-# INLINE traverseLeft #-}
-- | traverse the right-hand value of an 'Either':
--
-- @'traverseRight' ≡ 'Data.Traversable.traverse'@
--
-- Unfortunately the instance for
-- @'Data.Traversable.Traversable' ('Either' c)@ is still missing from base,
-- so this can't just be 'Data.Traversable.traverse'
--
-- >>> over traverseRight (+1) (Left 2)
-- Left 2
-- >>> over traverseRight (+1) (Right 2)
-- Right 3
-- >>> Right "hello" ^.traverseRight
-- "hello"
-- >>> Left "hello" ^.traverseRight :: [Double]
-- []
--
-- @traverseRight :: 'Applicative' f => (a -> f b) -> 'Either' c a -> f ('Either' c a)@
traverseRight :: Traversal (Either c a) (Either c b) a b
traverseRight _ (Left c) = pure $ Left c
traverseRight f (Right a) = Right <$> f a
{-# INLINE traverseRight #-}
-- | Visit the first /n/ targets of a 'Traversal', 'Fold', 'Getter' or 'Lens'.
--
-- >>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
-- ["hello","world"]
--
-- >>> [1..]^.. taking 3 traverse
-- [1,2,3]
--
-- >>> over (taking 5 traverse) succ "hello world"
-- "ifmmp world"
taking :: Applicative f => Int -> SimpleLensLike (EvilBazaar f a a) s a -> SimpleLensLike f s a
taking n l f s = evilOuts bz <$> traverse f (take n $ evilIns bz)
where
bz = l (\i -> EvilBazaar ($ i)) s
{-# INLINE taking #-}
-- | Visit all but the first /n/ targets of a 'Traversal', 'Fold', 'Getter' or 'Lens'.
--
-- >>> ("hello","world") ^? dropping 1 both
-- Just "world"
--
-- Dropping works on infinite traversals as well.
--
-- >>> [1..]^? dropping 1 folded
-- Just 2
dropping :: Applicative f => Int -> SimpleLensLike (Indexing f) s a -> SimpleLensLike f s a
dropping n l f s = case runIndexing (l (\a -> Indexing $ \i -> (if i >= n then f a else pure a, i + 1)) s) 0 of
(r, _) -> r
{-# INLINE dropping #-}
------------------------------------------------------------------------------
-- Cloning Traversals
------------------------------------------------------------------------------
-- | A 'Traversal' is completely characterized by its behavior on a 'Bazaar'.
--
-- Cloning a 'Traversal' is one way to make sure you aren't given
-- something weaker, such as a 'Control.Lens.Traversal.Fold' and can be
-- used as a way to pass around traversals that have to be monomorphic in @f@.
--
-- Note: This only accepts a proper 'Traversal' (or 'Lens'). To clone a 'Lens'
-- as such, use 'cloneLens'
--
-- Note: It is usually better to 'ReifyTraversal' and use 'reflectTraversal'
-- than to 'cloneTraversal'. The former can execute at full speed, while the
-- latter needs to round trip through the 'Bazaar'.
--
-- >>> let foo l a = (view (cloneTraversal l) a, set (cloneTraversal l) 10 a)
-- >>> foo both ("hello","world")
-- ("helloworld",(10,10))
--
-- @'cloneTraversal' :: 'LensLike' ('Bazaar' a b) s t a b -> 'Traversal' s t a b@
cloneTraversal :: Applicative f => ((a -> Bazaar a b b) -> s -> Bazaar a b t) -> (a -> f b) -> s -> f t
cloneTraversal l f = bazaar f . l sell
{-# INLINE cloneTraversal #-}
-- | A form of 'Traversal' that can be stored monomorphically in a container.
data ReifiedTraversal s t a b = ReifyTraversal { reflectTraversal :: Traversal s t a b }
-- | @type SimpleReifiedTraversal = 'Simple' 'ReifiedTraversal'@
type SimpleReifiedTraversal s a = ReifiedTraversal s s a a