-
Notifications
You must be signed in to change notification settings - Fork 273
/
Traversal.hs
1468 lines (1343 loc) · 55.3 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
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE ConstraintKinds #-}
#include "lens-common.h"
-----------------------------------------------------------------------------
-- |
-- Module : Control.Lens.Traversal
-- Copyright : (C) 2012-16 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
-- @
--
-- A 'Traversal' can be used as a 'Fold'.
-- Any 'Traversal' can be used for 'Control.Lens.Getter.Getting' like a 'Fold',
-- because given a 'Data.Monoid.Monoid' @m@, we have an 'Applicative' for
-- @('Const' m)@. Everything you know how to do with a 'Traversable' container,
-- you can with a 'Traversal', and here we provide combinators that generalize
-- the usual 'Traversable' operations.
----------------------------------------------------------------------------
module Control.Lens.Traversal
(
-- * Traversals
Traversal, Traversal'
, Traversal1, Traversal1'
, IndexedTraversal, IndexedTraversal'
, IndexedTraversal1, IndexedTraversal1'
, ATraversal, ATraversal'
, ATraversal1, ATraversal1'
, AnIndexedTraversal, AnIndexedTraversal'
, AnIndexedTraversal1, AnIndexedTraversal1'
, Traversing, Traversing'
, Traversing1, Traversing1'
-- * Traversing and Lensing
, traversal
, traverseOf, forOf, sequenceAOf
, mapMOf, forMOf, sequenceOf
, transposeOf
, mapAccumLOf, mapAccumROf
, scanr1Of, scanl1Of
, failover, ifailover
-- * Monomorphic Traversals
, cloneTraversal
, cloneIndexPreservingTraversal
, cloneIndexedTraversal
, cloneTraversal1
, cloneIndexPreservingTraversal1
, cloneIndexedTraversal1
-- * Parts and Holes
, partsOf, partsOf'
, unsafePartsOf, unsafePartsOf'
, holesOf, holes1Of
, singular, unsafeSingular
-- * Common Traversals
, Traversable(traverse)
, Traversable1(traverse1)
, both, both1
, beside
, taking
, dropping
, failing
, deepOf
-- * Indexed Traversals
-- ** Common
, ignored
, TraverseMin(..)
, TraverseMax(..)
, traversed
, traversed1
, traversed64
, elementOf
, element
, elementsOf
, elements
-- ** Combinators
, ipartsOf
, ipartsOf'
, iunsafePartsOf
, iunsafePartsOf'
, itraverseOf
, iforOf
, imapMOf
, iforMOf
, imapAccumROf
, imapAccumLOf
-- * Reflection
, traverseBy
, traverseByOf
, sequenceBy
, sequenceByOf
-- * Implementation Details
, Bazaar(..), Bazaar'
, Bazaar1(..), Bazaar1'
, loci
, iloci
-- * Fusion
, confusing
) where
import Prelude ()
import Control.Applicative.Backwards
import qualified Control.Category as C
import Control.Comonad
import Control.Lens.Fold
import Control.Lens.Getter (Getting, IndexedGetting, getting)
import Control.Lens.Internal.Bazaar
import Control.Lens.Internal.Context
import Control.Lens.Internal.Fold
import Control.Lens.Internal.Indexed
import Control.Lens.Internal.Prelude
import Control.Lens.Lens
import Control.Lens.Setter (ASetter, AnIndexedSetter, isets, sets)
import Control.Lens.Type
import Control.Monad.Trans.State.Lazy
import Data.Bitraversable
import Data.CallStack
import Data.Functor.Apply
import Data.Functor.Day.Curried
import Data.Functor.Yoneda
import Data.Int
import qualified Data.IntMap as IntMap
import qualified Data.Map as Map
import Data.Map (Map)
import Data.Monoid (Any (..))
import Data.Sequence (Seq, mapWithIndex)
import Data.Vector as Vector (Vector, imap)
import Data.Profunctor.Rep (Representable (..))
import Data.Reflection
import Data.Semigroup.Traversable
import Data.Semigroup.Bitraversable
import Data.Tuple (swap)
import GHC.Magic (inline)
-- $setup
-- >>> :set -XNoOverloadedStrings -XFlexibleContexts
-- >>> import Data.Char (toUpper)
-- >>> import Control.Applicative
-- >>> import Control.Lens
-- >>> import Control.Lens.Internal.Context
-- >>> import Control.DeepSeq (NFData (..), force)
-- >>> import Control.Exception (evaluate,try,ErrorCall(..))
-- >>> import Data.Maybe (fromMaybe)
-- >>> import Data.List.NonEmpty (NonEmpty (..))
-- >>> import Debug.SimpleReflect.Vars
-- >>> import Data.Void
-- >>> import Data.List (sort)
-- >>> import System.Timeout (timeout)
-- >>> import qualified Data.List.NonEmpty as NonEmpty
-- >>> let timingOut :: NFData a => a -> IO a; timingOut = fmap (fromMaybe (error "timeout")) . timeout (5*10^6) . evaluate . force
-- >>> let firstAndThird :: Traversal (a, x, a) (b, x, b) a b; firstAndThird = traversal go where { go :: Applicative f => (a -> f b) -> (a, x, a) -> f (b, x, b); go focus (a, x, a') = liftA3 (,,) (focus a) (pure x) (focus a') }
-- >>> let selectNested :: Traversal (x, [a]) (x, [b]) a b; selectNested = traversal go where { go :: Applicative f => (a -> f b) -> (x, [a]) -> f (x, [b]); go focus (x, as) = liftA2 (,) (pure x) (traverse focus as) }
------------------------------------------------------------------------------
-- Traversals
------------------------------------------------------------------------------
-- | When you see this as an argument to a function, it expects a 'Traversal'.
type ATraversal s t a b = LensLike (Bazaar (->) a b) s t a b
-- | @
-- type 'ATraversal'' = 'Simple' 'ATraversal'
-- @
type ATraversal' s a = ATraversal s s a a
-- | When you see this as an argument to a function, it expects a 'Traversal1'.
type ATraversal1 s t a b = LensLike (Bazaar1 (->) a b) s t a b
-- | @
-- type 'ATraversal1'' = 'Simple' 'ATraversal1'
-- @
type ATraversal1' s a = ATraversal1 s s a a
-- | When you see this as an argument to a function, it expects an 'IndexedTraversal'.
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
-- | When you see this as an argument to a function, it expects an 'IndexedTraversal1'.
type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
-- | @
-- type 'AnIndexedTraversal'' = 'Simple' ('AnIndexedTraversal' i)
-- @
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
-- | @
-- type 'AnIndexedTraversal1'' = 'Simple' ('AnIndexedTraversal1' i)
-- @
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
-- | When you see this as an argument to a function, it expects
--
-- * to be indexed if @p@ is an instance of 'Indexed' i,
--
-- * to be unindexed if @p@ is @(->)@,
--
-- * a 'Traversal' if @f@ is 'Applicative',
--
-- * a 'Getter' if @f@ is only a 'Functor' and 'Data.Functor.Contravariant.Contravariant',
--
-- * a 'Lens' if @f@ is only a 'Functor',
--
-- * a 'Fold' if @f@ is 'Applicative' and 'Data.Functor.Contravariant.Contravariant'.
type Traversing p f s t a b = Over p (BazaarT p f a b) s t a b
type Traversing1 p f s t a b = Over p (BazaarT1 p f a b) s t a b
-- | @
-- type 'Traversing'' f = 'Simple' ('Traversing' f)
-- @
type Traversing' p f s a = Traversing p f s s a a
type Traversing1' p f s a = Traversing1 p f s s a a
--------------------------
-- Traversal Combinators
--------------------------
-- | Build a 'Traversal' by providing a function which specifies the elements you wish to
-- focus.
--
-- The caller provides a function of type:
--
-- @
-- Applicative f => (a -> f b) -> s -> f t
-- @
--
-- Which is a higher order function which accepts a "focusing function" and applies
-- it to all desired focuses within @s@, then constructs a @t@ using the Applicative
-- instance of @f@.
--
-- Only elements which are "focused" using the focusing function will be targeted by the
-- resulting traversal.
--
-- For example, we can explicitly write a traversal which targets the first and third elements
-- of a tuple like this:
--
-- @
-- firstAndThird :: Traversal (a, x, a) (b, x, b) a b
-- firstAndThird = traversal go
-- where
-- go :: Applicative f => (a -> f b) -> (a, x, a) -> f (b, x, b)
-- go focus (a, x, a') = liftA3 (,,) (focus a) (pure x) (focus a')
-- @
--
-- >>> (1,"two",3) & firstAndThird *~ 10
-- (10,"two",30)
--
-- >>> over firstAndThird length ("one",2,"three")
-- (3,2,5)
--
-- We can re-use existing 'Traversal's when writing new ones by passing our focusing function
-- along to them. This example re-uses 'traverse' to focus all elements in a list which is
-- embedded in a tuple. This traversal could also be written simply as @_2 . traverse@.
--
-- @
-- selectNested :: Traversal (x, [a]) (x, [b]) a b
-- selectNested = traversal go
-- where
-- go :: Applicative f => (a -> f b) -> (x, [a]) -> f (x, [b])
-- go focus (x, as) = liftA2 (,) (pure x) (traverse focus as)
-- @
--
-- >>> selectNested .~ "hello" $ (1,[2,3,4,5])
-- (1,["hello","hello","hello","hello"])
--
-- >>> (1,[2,3,4,5]) & selectNested *~ 3
-- (1,[6,9,12,15])
--
-- Note that the 'traversal' function actually just returns the same function you pass to
-- it. The function it accepts is in fact a valid traversal all on its own! The use of
-- 'traversal' does nothing except verify that the function it is passed matches the signature
-- of a valid traversal. One could remove the @traversal@ combinator from either of the last
-- two examples and use the definition of @go@ directly with no change in behaviour.
--
-- This function exists for consistency with the 'lens', 'prism' and 'iso' constructors
-- as well as to serve as a touchpoint for beginners who wish to construct their own
-- traversals but are uncertain how to do so.
traversal :: ((a -> f b) -> s -> f t) -> LensLike f s t a b
traversal = id
{-# INLINE traversal #-}
-- | 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 each print (1,2,3)
-- 1
-- 2
-- 3
-- ((),(),())
--
-- @
-- 'traverseOf' ≡ 'id'
-- 'itraverseOf' l ≡ 'traverseOf' l '.' 'Indexed'
-- 'itraverseOf' 'itraversed' ≡ 'itraverse'
-- @
--
--
-- This yields the obvious law:
--
-- @
-- 'traverse' ≡ 'traverseOf' 'traverse'
-- @
--
-- @
-- 'traverseOf' :: 'Functor' f => 'Iso' s t a b -> (a -> f b) -> s -> f t
-- 'traverseOf' :: 'Functor' f => 'Lens' s t a b -> (a -> f b) -> s -> f t
-- 'traverseOf' :: 'Apply' f => 'Traversal1' s t a b -> (a -> f b) -> s -> f t
-- 'traverseOf' :: 'Applicative' f => '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 each (1,2,3) print
-- 1
-- 2
-- 3
-- ((),(),())
--
-- This function is only provided for consistency, 'flip' is strictly more general.
--
-- @
-- 'forOf' ≡ 'flip'
-- 'forOf' ≡ 'flip' . 'traverseOf'
-- @
--
-- @
-- 'for' ≡ 'forOf' 'traverse'
-- 'Control.Lens.Indexed.ifor' l s ≡ 'for' l s '.' 'Indexed'
-- @
--
-- @
-- 'forOf' :: 'Functor' f => 'Iso' s t a b -> s -> (a -> f b) -> f t
-- 'forOf' :: 'Functor' f => 'Lens' s t a b -> s -> (a -> f b) -> f t
-- 'forOf' :: 'Applicative' f => '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.
--
-- >>> sequenceAOf both ([1,2],[3,4])
-- [(1,3),(1,4),(2,3),(2,4)]
--
-- @
-- 'sequenceA' ≡ 'sequenceAOf' 'traverse' ≡ 'traverse' 'id'
-- 'sequenceAOf' l ≡ 'traverseOf' l 'id' ≡ l 'id'
-- @
--
-- @
-- 'sequenceAOf' :: 'Functor' f => 'Iso' s t (f b) b -> s -> f t
-- 'sequenceAOf' :: 'Functor' f => '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.
--
-- >>> mapMOf both (\x -> [x, x + 1]) (1,3)
-- [(1,3),(1,4),(2,3),(2,4)]
--
-- @
-- 'mapM' ≡ 'mapMOf' 'traverse'
-- 'imapMOf' l ≡ 'forM' l '.' 'Indexed'
-- @
--
-- @
-- 'mapMOf' :: 'Monad' m => 'Iso' s t a b -> (a -> m b) -> s -> m t
-- 'mapMOf' :: 'Monad' m => '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 = coerce
{-# INLINE mapMOf #-}
-- | 'forMOf' is a flipped version of 'mapMOf', consistent with the definition of 'forM'.
--
-- >>> forMOf both (1,3) $ \x -> [x, x + 1]
-- [(1,3),(1,4),(2,3),(2,4)]
--
-- @
-- 'forM' ≡ 'forMOf' 'traverse'
-- 'forMOf' l ≡ 'flip' ('mapMOf' l)
-- 'iforMOf' l s ≡ 'forM' l s '.' 'Indexed'
-- @
--
-- @
-- 'forMOf' :: 'Monad' m => 'Iso' s t a b -> s -> (a -> m b) -> m t
-- 'forMOf' :: 'Monad' m => '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.
--
-- >>> sequenceOf each ([1,2],[3,4],[5,6])
-- [(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]
--
-- @
-- 'sequence' ≡ 'sequenceOf' 'traverse'
-- 'sequenceOf' l ≡ 'mapMOf' l 'id'
-- 'sequenceOf' l ≡ 'unwrapMonad' '.' l 'WrapMonad'
-- @
--
-- @
-- 'sequenceOf' :: 'Monad' m => 'Iso' s t (m b) b -> s -> m t
-- 'sequenceOf' :: 'Monad' m => '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:
--
-- >>> transposeOf traverse [[1,2,3],[4,5,6]]
-- [[1,4],[2,5],[3,6]]
--
-- @
-- 'Data.List.transpose' ≡ 'transposeOf' 'traverse'
-- @
--
-- Since every 'Lens' is a 'Traversal', we can use this as a form of
-- monadic strength as well:
--
-- @
-- 'transposeOf' 'Control.Lens.Tuple._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' :: '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' ('Backwards' ('State' acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- @
mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf = mapAccumLOf . backwards
{-# INLINE mapAccumROf #-}
-- | This generalizes 'Data.Traversable.mapAccumL' to an arbitrary 'Traversal'.
--
-- @
-- 'mapAccumL' ≡ 'mapAccumLOf' 'traverse'
-- @
--
-- 'mapAccumLOf' accumulates 'State' from left to right.
--
-- @
-- 'mapAccumLOf' :: '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' ('State' acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
-- 'mapAccumLOf' l f acc0 s = 'swap' ('runState' (l (\a -> 'state' (\acc -> 'swap' (f acc a))) s) acc0)
-- @
--
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf l f acc0 s = swap (runState (l g s) acc0) where
g a = state $ \acc -> swap (f acc a)
-- This would be much cleaner if the argument order for the function was swapped.
{-# INLINE mapAccumLOf #-}
-- | This permits the use of 'scanr1' over an arbitrary 'Traversal' or 'Lens'.
--
-- @
-- 'scanr1' ≡ 'scanr1Of' 'traverse'
-- @
--
-- @
-- 'scanr1Of' :: '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 (Backwards (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'
-- @
--
-- @
-- 'scanl1Of' :: 'Iso' s t a a -> (a -> a -> a) -> s -> t
-- 'scanl1Of' :: 'Lens' s t a a -> (a -> a -> a) -> s -> t
-- 'scanl1Of' :: 'Traversal' s t a a -> (a -> a -> a) -> s -> t
-- @
scanl1Of :: LensLike (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 #-}
-- | This 'Traversal' allows you to 'traverse' the individual stores in a 'Bazaar'.
loci :: Traversal (Bazaar (->) a c s) (Bazaar (->) b c s) a b
loci f w = getCompose (runBazaar w (Compose #. fmap sell . f))
{-# INLINE loci #-}
-- | This 'IndexedTraversal' allows you to 'traverse' the individual stores in
-- a 'Bazaar' with access to their indices.
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
iloci f w = getCompose (runBazaar w (Compose #. Indexed (\i -> fmap (indexed sell i) . indexed f i)))
{-# INLINE iloci #-}
-------------------------------------------------------------------------------
-- Parts
-------------------------------------------------------------------------------
-- | 'partsOf' turns a 'Traversal' into a 'Lens' that resembles an early version of the 'Data.Data.Lens.uniplate' (or 'Data.Data.Lens.biplate') type.
--
-- /Note:/ You should really try to maintain the invariant of the number of children in the list.
--
-- >>> (a,b,c) & partsOf each .~ [x,y,z]
-- (x,y,z)
--
-- Any extras will be lost. If you do not supply enough, then the remainder will come from the original structure.
--
-- >>> (a,b,c) & partsOf each .~ [w,x,y,z]
-- (w,x,y)
--
-- >>> (a,b,c) & partsOf each .~ [x,y]
-- (x,y,c)
--
-- >>> ('b', 'a', 'd', 'c') & partsOf each %~ sort
-- ('a','b','c','d')
--
-- 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' :: 'Iso'' s a -> 'Lens'' s [a]
-- 'partsOf' :: 'Lens'' s a -> 'Lens'' s [a]
-- 'partsOf' :: 'Traversal'' s a -> 'Lens'' s [a]
-- 'partsOf' :: 'Fold' s a -> 'Getter' s [a]
-- 'partsOf' :: 'Getter' s a -> 'Getter' s [a]
-- @
partsOf :: Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]
partsOf l f s = outs b <$> f (ins b) where b = l sell s
{-# INLINE partsOf #-}
-- | An indexed version of 'partsOf' that receives the entire list of indices as its index.
ipartsOf :: forall i p f s t a. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
ipartsOf l = conjoined
(\f s -> let b = inline l sell s in outs b <$> f (wins b))
(\f s -> let b = inline l sell s; (is, as) = unzip (pins b) in outs b <$> indexed f (is :: [i]) as)
{-# INLINE ipartsOf #-}
-- | A type-restricted version of 'partsOf' that can only be used with a 'Traversal'.
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
partsOf' l f s = outs b <$> f (ins b) where b = l sell s
{-# INLINE partsOf' #-}
-- | A type-restricted version of 'ipartsOf' that can only be used with an 'IndexedTraversal'.
ipartsOf' :: forall i p f s t a. (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]
ipartsOf' l = conjoined
(\f s -> let b = inline l sell s in outs b <$> f (wins b))
(\f s -> let b = inline l sell s; (is, as) = unzip (pins b) in outs b <$> indexed f (is :: [i]) as)
{-# INLINE ipartsOf' #-}
-- | 'unsafePartsOf' turns a 'Traversal' into a 'Data.Data.Lens.uniplate' (or 'Data.Data.Lens.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!
--
-- When applied to a 'Fold' the result is merely a 'Getter' (and becomes safe).
--
-- @
-- 'unsafePartsOf' :: '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 => Traversing (->) f s t a b -> LensLike f s t [a] [b]
unsafePartsOf l f s = unsafeOuts b <$> f (ins b) where b = l sell s
{-# INLINE unsafePartsOf #-}
-- | An indexed version of 'unsafePartsOf' that receives the entire list of indices as its index.
iunsafePartsOf :: forall i p f s t a b. (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
iunsafePartsOf l = conjoined
(\f s -> let b = inline l sell s in unsafeOuts b <$> f (wins b))
(\f s -> let b = inline l sell s; (is,as) = unzip (pins b) in unsafeOuts b <$> indexed f (is :: [i]) as)
{-# INLINE iunsafePartsOf #-}
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]
unsafePartsOf' l f s = unsafeOuts b <$> f (ins b) where b = l sell s
{-# INLINE unsafePartsOf' #-}
iunsafePartsOf' :: forall i s t a b. Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
iunsafePartsOf' l = conjoined
(\f s -> let b = inline l sell s in unsafeOuts b <$> f (wins b))
(\f s -> let b = inline l sell s; (is, as) = unzip (pins b) in unsafeOuts b <$> indexed f (is :: [i]) as)
{-# INLINE iunsafePartsOf' #-}
-- | This converts a 'Traversal' that you \"know\" will target one or more elements to a 'Lens'. It can
-- also be used to transform a non-empty 'Fold' into a 'Getter'.
--
-- The resulting 'Lens' or 'Getter' will be partial if the supplied 'Traversal' returns
-- no results.
--
-- >>> [1,2,3] ^. singular _head
-- 1
--
-- >>> Left (ErrorCall "singular: empty traversal") <- try (evaluate ([] ^. singular _head)) :: IO (Either ErrorCall ())
--
-- >>> Left 4 ^. singular _Left
-- 4
--
-- >>> [1..10] ^. singular (ix 7)
-- 8
--
-- >>> [] & singular traverse .~ 0
-- []
--
-- @
-- 'singular' :: 'Traversal' s t a a -> 'Lens' s t a a
-- 'singular' :: 'Fold' s a -> 'Getter' s a
-- 'singular' :: 'IndexedTraversal' i s t a a -> 'IndexedLens' i s t a a
-- 'singular' :: 'IndexedFold' i s a -> 'IndexedGetter' i s a
-- @
singular :: (HasCallStack, Conjoined p, Functor f)
=> Traversing p f s t a a
-> Over p f s t a a
singular l = conjoined
(\afb s -> let b = l sell s in case ins b of
(w:ws) -> unsafeOuts b . (:ws) <$> afb w
[] -> unsafeOuts b . return <$> afb (error "singular: empty traversal"))
(\pafb s -> let b = l sell s in case pins b of
(w:ws) -> unsafeOuts b . (:map extract ws) <$> cosieve pafb w
[] -> unsafeOuts b . return <$> cosieve pafb (error "singular: empty traversal"))
{-# INLINE singular #-}
-- | This converts a 'Traversal' that you \"know\" will target only one element to a 'Lens'. It can also be
-- used to transform a 'Fold' into a 'Getter'.
--
-- The resulting 'Lens' or 'Getter' will be partial if the 'Traversal' targets nothing
-- or more than one element.
--
-- >>> Left (ErrorCall "unsafeSingular: empty traversal") <- try (evaluate ([] & unsafeSingular traverse .~ 0)) :: IO (Either ErrorCall [Integer])
--
-- @
-- 'unsafeSingular' :: 'Traversal' s t a b -> 'Lens' s t a b
-- 'unsafeSingular' :: 'Fold' s a -> 'Getter' s a
-- 'unsafeSingular' :: 'IndexedTraversal' i s t a b -> 'IndexedLens' i s t a b
-- 'unsafeSingular' :: 'IndexedFold' i s a -> 'IndexedGetter' i s a
-- @
unsafeSingular :: (HasCallStack, Conjoined p, Functor f)
=> Traversing p f s t a b
-> Over p f s t a b
unsafeSingular l = conjoined
(\afb s -> let b = inline l sell s in case ins b of
[w] -> unsafeOuts b . return <$> afb w
[] -> error "unsafeSingular: empty traversal"
_ -> error "unsafeSingular: traversing multiple results")
(\pafb s -> let b = inline l sell s in case pins b of
[w] -> unsafeOuts b . return <$> cosieve pafb w
[] -> error "unsafeSingular: empty traversal"
_ -> error "unsafeSingular: traversing multiple results")
{-# INLINE unsafeSingular #-}
------------------------------------------------------------------------------
-- Internal functions used by 'partsOf', etc.
------------------------------------------------------------------------------
ins :: Bizarre (->) w => w a b t -> [a]
ins = toListOf (getting bazaar)
{-# INLINE ins #-}
wins :: (Bizarre p w, Corepresentable p, Comonad (Corep p)) => w a b t -> [a]
wins = getConst #. bazaar (cotabulate $ \ra -> Const [extract ra])
{-# INLINE wins #-}
pins :: (Bizarre p w, Corepresentable p) => w a b t -> [Corep p a]
pins = getConst #. bazaar (cotabulate $ \ra -> Const [ra])
{-# INLINE pins #-}
parr :: (Profunctor p, C.Category p) => (a -> b) -> p a b
parr f = lmap f C.id
{-# INLINE parr #-}
outs :: (Bizarre p w, C.Category p) => w a a t -> [a] -> t
outs = evalState `rmap` bazaar (parr (state . unconsWithDefault))
{-# INLINE outs #-}
unsafeOuts :: (Bizarre p w, Corepresentable p) => w a b t -> [b] -> t
unsafeOuts = evalState `rmap` bazaar (cotabulate (\_ -> state (unconsWithDefault fakeVal)))
where fakeVal = error "unsafePartsOf': not enough elements were supplied"
{-# INLINE unsafeOuts #-}
unconsWithDefault :: a -> [a] -> (a,[a])
unconsWithDefault d [] = (d,[])
unconsWithDefault _ (x:xs) = (x,xs)
{-# INLINE unconsWithDefault #-}
-------------------------------------------------------------------------------
-- Holes
-------------------------------------------------------------------------------
-- | The one-level version of 'Control.Lens.Plated.contextsOf'. This extracts a
-- list of the immediate children according to a given 'Traversal' as editable
-- contexts.
--
-- Given a context you can use 'Control.Comonad.Store.Class.pos' to see the
-- values, 'Control.Comonad.Store.Class.peek' at what the structure would be
-- like with an edited result, or simply 'extract' the original structure.
--
-- @
-- propChildren l x = 'toListOf' l x '==' 'map' 'Control.Comonad.Store.Class.pos' ('holesOf' l x)
-- propId l x = 'all' ('==' x) ['extract' w | w <- 'holesOf' l x]
-- @
--
-- @
-- 'holesOf' :: 'Iso'' s a -> s -> ['Pretext'' (->) a s]
-- 'holesOf' :: 'Lens'' s a -> s -> ['Pretext'' (->) a s]
-- 'holesOf' :: 'Traversal'' s a -> s -> ['Pretext'' (->) a s]
-- 'holesOf' :: 'IndexedLens'' i s a -> s -> ['Pretext'' ('Indexed' i) a s]
-- 'holesOf' :: 'IndexedTraversal'' i s a -> s -> ['Pretext'' ('Indexed' i) a s]
-- @
holesOf :: Conjoined p
=> Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holesOf f xs = flip appEndo [] . fst $
runHoles (runBazaar (f sell xs) (cotabulate holeInOne)) id
{-# INLINE holesOf #-}
holeInOne :: (Corepresentable p, Comonad (Corep p))
=> Corep p a -> Holes t (Endo [Pretext p a a t]) a
holeInOne x = Holes $ \xt ->
( Endo (fmap xt (cosieve sell x) :)
, extract x)
{-# INLINABLE holeInOne #-}
-- | The non-empty version of 'holesOf'.
-- This extract a non-empty list of immediate children according to a given
-- 'Traversal1' as editable contexts.
--
-- >>> let head1 f s = runPretext (NonEmpty.head $ holes1Of traversed1 s) f
-- >>> ('a' :| "bc") ^. head1
-- 'a'
--
-- >>> ('a' :| "bc") & head1 %~ toUpper
-- 'A' :| "bc"
--
-- @
-- 'holes1Of' :: 'Iso'' s a -> s -> 'NonEmpty' ('Pretext'' (->) a s)
-- 'holes1Of' :: 'Lens'' s a -> s -> 'NonEmpty' ('Pretext'' (->) a s)
-- 'holes1Of' :: 'Traversal1'' s a -> s -> 'NonEmpty' ('Pretext'' (->) a s)
-- 'holes1Of' :: 'IndexedLens'' i s a -> s -> 'NonEmpty' ('Pretext'' ('Indexed' i) a s)
-- 'holes1Of' :: 'IndexedTraversal1'' i s a -> s -> 'NonEmpty' ('Pretext'' ('Indexed' i) a s)
-- @
holes1Of :: Conjoined p
=> Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t)
holes1Of f xs = flip getNonEmptyDList [] . fst $
runHoles (runBazaar1 (f sell xs) (cotabulate holeInOne1)) id
{-# INLINE holes1Of #-}
holeInOne1 :: forall p a t. (Corepresentable p, C.Category p)
=> Corep p a -> Holes t (NonEmptyDList (Pretext p a a t)) a
holeInOne1 x = Holes $ \xt ->
( NonEmptyDList (fmap xt (cosieve sell x) :|)
, cosieve (C.id :: p a a) x)
-- We are very careful to share as much structure as possible among
-- the results (in the common case where the traversal allows for such).
-- Note in particular the recursive knot in the implementation of <*>
-- for Holes. This sharing magic was inspired by Noah "Rampion" Easterly's
-- implementation of a related holes function: see
-- https://stackoverflow.com/a/49001904/1477667. The Holes type is
-- inspired by Roman Cheplyaka's answer to that same question.
newtype Holes t m x = Holes { runHoles :: (x -> t) -> (m, x) }
instance Functor (Holes t m) where
fmap f xs = Holes $ \xt ->
let
(qf, qv) = runHoles xs (xt . f)
in (qf, f qv)
instance Semigroup m => Apply (Holes t m) where
fs <.> xs = Holes $ \xt ->
let
(pf, pv) = runHoles fs (xt . ($ qv))
(qf, qv) = runHoles xs (xt . pv)
in (pf <> qf, pv qv)
instance Monoid m => Applicative (Holes t m) where
pure x = Holes $ \_ -> (mempty, x)
fs <*> xs = Holes $ \xt ->
let
(pf, pv) = runHoles fs (xt . ($ qv))
(qf, qv) = runHoles xs (xt . pv)
in (pf `mappend` qf, pv qv)
#if MIN_VERSION_base(4,10,0)
liftA2 f xs ys = Holes $ \xt ->
let
(pf, pv) = runHoles xs (xt . flip f qv)
(qf, qv) = runHoles ys (xt . f pv)
in (pf `mappend` qf, f pv qv)
#endif
------------------------------------------------------------------------------
-- Traversals
------------------------------------------------------------------------------
-- | Traverse both parts of a 'Bitraversable' container with matching types.
--
-- Usually that type will be a pair. Use 'Control.Lens.Each.each' to traverse
-- the elements of arbitrary homogeneous tuples.
--
-- >>> (1,2) & both *~ 10
-- (10,20)
--
-- >>> over both length ("hello","world")
-- (5,5)
--
-- >>> ("hello","world")^.both
-- "helloworld"
--
-- @
-- 'both' :: 'Traversal' (a, a) (b, b) a b
-- 'both' :: 'Traversal' ('Either' a a) ('Either' b b) a b
-- @
both :: Bitraversable r => Traversal (r a a) (r b b) a b
both f = bitraverse f f
{-# INLINE both #-}
-- | Traverse both parts of a 'Bitraversable1' container with matching types.
--
-- Usually that type will be a pair.
--
-- @
-- 'both1' :: 'Traversal1' (a, a) (b, b) a b
-- 'both1' :: 'Traversal1' ('Either' a a) ('Either' b b) a b
-- @
both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
both1 f = bitraverse1 f f
{-# INLINE both1 #-}
-- | Apply a different 'Traversal' or 'Fold' to each side of a 'Bitraversable' container.
--
-- @
-- 'beside' :: 'Traversal' s t a b -> 'Traversal' s' t' a b -> 'Traversal' (r s s') (r t t') a b
-- 'beside' :: 'IndexedTraversal' i s t a b -> 'IndexedTraversal' i s' t' a b -> 'IndexedTraversal' i (r s s') (r t t') a b
-- 'beside' :: 'IndexPreservingTraversal' s t a b -> 'IndexPreservingTraversal' s' t' a b -> 'IndexPreservingTraversal' (r s s') (r t t') a b
-- @
--
-- @
-- 'beside' :: 'Traversal' s t a b -> 'Traversal' s' t' a b -> 'Traversal' (s,s') (t,t') a b
-- 'beside' :: 'Lens' s t a b -> 'Lens' s' t' a b -> 'Traversal' (s,s') (t,t') a b
-- 'beside' :: 'Fold' s a -> 'Fold' s' a -> 'Fold' (s,s') a
-- 'beside' :: 'Getter' s a -> 'Getter' s' a -> 'Fold' (s,s') a
-- @
--
-- @
-- 'beside' :: 'IndexedTraversal' i s t a b -> 'IndexedTraversal' i s' t' a b -> 'IndexedTraversal' i (s,s') (t,t') a b
-- 'beside' :: 'IndexedLens' i s t a b -> 'IndexedLens' i s' t' a b -> 'IndexedTraversal' i (s,s') (t,t') a b
-- 'beside' :: 'IndexedFold' i s a -> 'IndexedFold' i s' a -> 'IndexedFold' i (s,s') a
-- 'beside' :: 'IndexedGetter' i s a -> 'IndexedGetter' i s' a -> 'IndexedFold' i (s,s') a
-- @
--
-- @
-- 'beside' :: 'IndexPreservingTraversal' s t a b -> 'IndexPreservingTraversal' s' t' a b -> 'IndexPreservingTraversal' (s,s') (t,t') a b
-- 'beside' :: 'IndexPreservingLens' s t a b -> 'IndexPreservingLens' s' t' a b -> 'IndexPreservingTraversal' (s,s') (t,t') a b
-- 'beside' :: 'IndexPreservingFold' s a -> 'IndexPreservingFold' s' a -> 'IndexPreservingFold' (s,s') a
-- 'beside' :: 'IndexPreservingGetter' s a -> 'IndexPreservingGetter' s' a -> 'IndexPreservingFold' (s,s') a
-- @
--
-- >>> ("hello",["world","!!!"])^..beside id traverse
-- ["hello","world","!!!"]
beside :: (Representable q, Applicative (Rep q), Applicative f, Bitraversable r)
=> Optical p q f s t a b
-> Optical p q f s' t' a b
-> Optical p q f (r s s') (r t t') a b
beside l r f = tabulate $ getCompose #. bitraverse (Compose #. sieve (l f)) (Compose #. sieve (r f))
{-# INLINE beside #-}
-- | Visit the first /n/ targets of a 'Traversal', 'Fold', 'Getter' or 'Lens'.
--
-- >>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
-- ["hello","world"]
--
-- >>> timingOut $ [1..] ^.. taking 3 traverse
-- [1,2,3]
--
-- >>> over (taking 5 traverse) succ "hello world"
-- "ifmmp world"
--
-- @
-- 'taking' :: 'Int' -> 'Traversal'' s a -> 'Traversal'' s a
-- 'taking' :: 'Int' -> 'Lens'' s a -> 'Traversal'' s a
-- 'taking' :: 'Int' -> 'Iso'' s a -> 'Traversal'' s a
-- 'taking' :: 'Int' -> 'Prism'' s a -> 'Traversal'' s a
-- 'taking' :: 'Int' -> 'Getter' s a -> 'Fold' s a
-- 'taking' :: 'Int' -> 'Fold' s a -> 'Fold' s a
-- 'taking' :: 'Int' -> 'IndexedTraversal'' i s a -> 'IndexedTraversal'' i s a
-- 'taking' :: 'Int' -> 'IndexedLens'' i s a -> 'IndexedTraversal'' i s a
-- 'taking' :: 'Int' -> 'IndexedGetter' i s a -> 'IndexedFold' i s a
-- 'taking' :: 'Int' -> 'IndexedFold' i s a -> 'IndexedFold' i s a
-- @
taking :: (Conjoined p, Applicative f)
=> Int
-> Traversing p f s t a a
-> Over p f s t a a
taking n l = conjoined
(\ afb s -> let b = inline l sell s in outs b <$> traverse afb (take n $ ins b))
(\ pafb s -> let b = inline l sell s in outs b <$> traverse (cosieve pafb) (take n $ pins b))
{-# 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' :: 'Int' -> 'Traversal'' s a -> 'Traversal'' s a
-- 'dropping' :: 'Int' -> 'Lens'' s a -> 'Traversal'' s a
-- 'dropping' :: 'Int' -> 'Iso'' s a -> 'Traversal'' s a
-- 'dropping' :: 'Int' -> 'Prism'' s a -> 'Traversal'' s a
-- 'dropping' :: 'Int' -> 'Getter' s a -> 'Fold' s a