/
Zipper.hs
804 lines (710 loc) · 29.4 KB
/
Zipper.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
{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ExistentialQuantification #-}
#ifdef TRUSTWORTHY
{-# LANGUAGE Trustworthy #-}
#endif
-----------------------------------------------------------------------------
-- |
-- Module : Control.Lens.Internal.Zipper
-- Copyright : (C) 2012-2013 Edward Kmett
-- License : BSD-style (see the file LICENSE)
-- Maintainer : Edward Kmett <ekmett@gmail.com>
-- Stability : experimental
-- Portability : non-portable
--
-- This module provides internal types and functions used in the implementation
-- of @Control.Lens.Zipper@. You shouldn't need to import it directly, and the
-- exported types can be used to break 'Zipper' invariants.
--
----------------------------------------------------------------------------
module Control.Lens.Internal.Zipper where
import Control.Applicative
import Control.Category ((>>>))
import Control.Monad
import Control.Lens.Getter
import Control.Lens.Indexed
import Control.Lens.Internal.Context
import Control.Lens.Internal.Indexed
import Control.Lens.Lens
import Control.Lens.Setter
import Control.Lens.Traversal
import Control.Lens.Type
import Data.Foldable
import Data.Maybe
import Data.Monoid
import Data.Profunctor.Unsafe
{-# ANN module "HLint: ignore Use foldl" #-}
------------------------------------------------------------------------------
-- Jacket
------------------------------------------------------------------------------
data Jacket i a
= Ap Int -- size
Bool -- left-to-right null check
Bool -- right-to-left null check
(Last i)
(Jacket i a) -- left
(Jacket i a) -- right
| Leaf i a
| Pure
deriving Show
size :: Jacket i a -> Int
size (Ap s _ _ _ _ _) = s
size Leaf{} = 1
size Pure = 0
{-# INLINE size #-}
nullLeft :: Jacket i a -> Bool
nullLeft (Ap _ nl _ _ _ _) = nl
nullLeft (Leaf _ _) = False
nullLeft Pure = True
{-# INLINE nullLeft #-}
nullRight :: Jacket i a -> Bool
nullRight (Ap _ _ nr _ _ _) = nr
nullRight (Leaf _ _) = False
nullRight Pure = True
{-# INLINE nullRight #-}
maximal :: Jacket i a -> Last i
maximal (Ap _ _ _ li _ _) = li
maximal (Leaf i _) = Last (Just i)
maximal Pure = Last Nothing
{-# INLINE maximal #-}
instance Functor (Jacket i) where
fmap f (Ap m nl nr li l r) = Ap m nl nr li (fmap f l) (fmap f r)
fmap f (Leaf i a) = Leaf i (f a)
fmap _ Pure = Pure
{-# INLINE fmap #-}
instance Foldable (Jacket i) where
foldMap f (Ap _ _ _ _ l r) = foldMap f l `mappend` foldMap f r
foldMap f (Leaf _ a) = f a
foldMap _ Pure = mempty
{-# INLINE foldMap #-}
instance Traversable (Jacket i) where
traverse f (Ap m nl nr li l r) = Ap m nl nr li <$> traverse f l <*> traverse f r
traverse f (Leaf i a) = Leaf i <$> f a
traverse _ Pure = pure Pure
{-# INLINE traverse #-}
instance FunctorWithIndex i (Jacket i) where
imap f = go where
go (Ap m nl nr li l r) = Ap m nl nr li (go l) (go r)
go (Leaf i a) = Leaf i (f i a)
go Pure = Pure
{-# INLINE imap #-}
instance FoldableWithIndex i (Jacket i) where
ifoldMap f = go where
go (Ap _ _ _ _ l r) = go l `mappend` go r
go (Leaf i a) = f i a
go Pure = mempty
{-# INLINE ifoldMap #-}
instance TraversableWithIndex i (Jacket i) where
itraverse f = go where
go (Ap m nl nr li l r) = Ap m nl nr li <$> go l <*> go r
go (Leaf i a) = Leaf i <$> f i a
go Pure = pure Pure
{-# INLINE itraverse #-}
-- | This is an illegal 'Monoid'.
instance Monoid (Jacket i a) where
mempty = Pure
{-# INLINE mempty #-}
mappend l r = Ap (size l + size r) (nullLeft l && nullLeft r) (nullRight r && nullRight l) (maximal l <> maximal r) l r
{-# INLINE mappend #-}
jacketIns :: Bazaar (Indexed i) a b t -> Jacket i a
jacketIns (Bazaar bz) = runAccessor $ bz $ Indexed (\i -> Accessor #. Leaf i)
{-# INLINE jacketIns #-}
------------------------------------------------------------------------------
-- Putting it back in the tree
------------------------------------------------------------------------------
newtype Flow i b a = Flow { runFlow :: Jacket i b -> a }
instance Functor (Flow i b) where
fmap f (Flow g) = Flow (f . g)
{-# INLINE fmap #-}
-- | This is an illegal 'Applicative'.
instance Applicative (Flow i b) where
pure a = Flow (const a)
{-# INLINE pure #-}
Flow mf <*> Flow ma = Flow $ \ s -> case s of
Ap _ _ _ _ l r -> mf l (ma r)
_ -> mf s (ma s)
{-# INLINE (<*>) #-}
jacketOuts :: Bazaar (Indexed i) a b t -> Jacket j b -> t
jacketOuts bz = runFlow $ runBazaar bz $ Indexed $ \ _ _ -> Flow $ \ t -> case t of
Leaf _ a -> a
_ -> error "jacketOuts: wrong shape"
{-# INLINE jacketOuts #-}
-- | This is only a valid 'Lens' if you don't change the shape of the 'Jacket'.
jacket :: AnIndexedTraversal i s t a b -> Lens s t (Jacket i a) (Jacket j b)
jacket l f s = jacketOuts bz <$> f (jacketIns bz) where
bz = l sell s
{-# INLINE jacket #-}
-- $setup
-- >>> import Control.Lens
-- >>> import Data.Char
-- * Paths
-- | A 'Path' into a 'Jacket' that ends at a 'Leaf'.
data Path i a
= ApL Int Bool Bool (Last i) !(Path i a) !(Jacket i a)
| ApR Int Bool Bool (Last i) !(Jacket i a) !(Path i a)
| Start
deriving Show
instance Functor (Path i) where
fmap f (ApL m nl nr li p q) = ApL m nl nr li (fmap f p) (fmap f q)
fmap f (ApR m nl nr li p q) = ApR m nl nr li (fmap f p) (fmap f q)
fmap _ Start = Start
{-# INLINE fmap #-}
-- | Calculate the absolute position of the 'Leaf' targeted by a 'Path'.
--
-- This can be quite expensive for right-biased traversals such as you
-- receive from a list.
offset :: Path i a -> Int
offset Start = 0
offset (ApL _ _ _ _ q _) = offset q
offset (ApR _ _ _ _ l q) = size l + offset q
{-# INLINE offset #-}
-- | Return the total number of children in the 'Jacket' by walking the
-- 'Path' to the root.
pathsize :: Path i a -> Int
pathsize = go 1 where
go n Start = n
go _ (ApL n _ _ _ p _) = go n p
go _ (ApR n _ _ _ _ p) = go n p
{-# INLINE pathsize #-}
-- * Recursion
--
-- For several operations, we unroll the first step of the recursion (or part
-- of it) so GHC can inline better. There are two specific cases that we care
-- about: The "lens case", where the entire tree is just (Leaf (Identity x)), and the
-- "list case", where the traversal tree is right-biased, as in (Ap (Leaf (Identity x))
-- (Ap (Leaf (Identity y)) ...)). It should be safe to delete any of these cases.
-- | Reconstruct a 'Jacket' from a 'Path'.
recompress :: Path i a -> i -> a -> Jacket i a
recompress Start i a = Leaf i a -- Unrolled: The lens case.
recompress (ApL m _ _ li Start r) i a = Ap m False False li (Leaf i a) r -- Unrolled: The list case. In particular, a right-biased tree that we haven't moved rightward in.
recompress p i a = go p (Leaf i a) where
go Start q = q
go (ApL m _ _ li q r) l = go q (Ap m False False li l r)
go (ApR m _ _ li l q) r = go q (Ap m False False li l r)
{-# INLINE recompress #-}
-- | Walk down the tree to the leftmost child.
startl :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r
startl p0 (Leaf i a) _ kp = kp p0 i a -- Unrolled: The lens case.
startl p0 (Ap m nl nr li (Leaf i a) r) _ kp = kp (ApL m nl nr li p0 r) i a -- Unrolled: The list case. (Is this one a good idea?)
startl p0 c0 kn kp = go p0 c0 where
go p (Ap m nl nr li l r)
| nullLeft l = go (ApR m nl nr li Pure p) r
| otherwise = go (ApL m nl nr li p r) l
go p (Leaf i a) = kp p i a
go _ Pure = kn
{-# INLINE startl #-}
-- | Walk down the tree to the rightmost child.
startr :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r
startr p0 (Leaf i a) _ kp = kp p0 i a -- Unrolled: The lens case.
startr p0 c0 kn kp = go p0 c0 where
go p (Ap m nl nr li l r)
| nullRight r = go (ApL m nl nr li p Pure) l
| otherwise = go (ApR m nl nr li l p) r
go p (Leaf i a) = kp p i a
go _ Pure = kn
{-# INLINE startr #-}
-- | Move left one 'Leaf'.
movel :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r
movel p0 c0 kn kp = go p0 c0 where
go Start _ = kn
go (ApR m _ _ li l q) r
| nullRight l = go q (Ap m False False li l Pure)
| otherwise = startr (ApL m False False li q r) l kn kp
go (ApL m _ _ li p r) l = go p (Ap m False False li l r)
{-# INLINE movel #-}
-- | Move right one 'Leaf'.
mover :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r
mover p0 c0 kn kp = go p0 c0 where
go Start _ = kn
go (ApL m _ _ li q r) l
| nullLeft r = go q (Ap m False False li Pure r)
| otherwise = startl (ApR m False False li l q) r kn kp
go (ApR m _ _ li l p) r = go p (Ap m False False li l r)
{-# INLINE mover #-}
-----------------------------------------------------------------------------
-- * Zippers
-----------------------------------------------------------------------------
-- | This is used to represent the 'Top' of the 'Zipper'.
--
-- Every 'Zipper' starts with 'Top'.
--
-- /e.g./ @'Top' ':>>' a@ is the type of the trivial 'Zipper'.
data Top
-- | This is the type of a 'Zipper'. It visually resembles a \"breadcrumb trail\" as
-- used in website navigation. Each breadcrumb in the trail represents a level you
-- can move up to.
--
-- This type operator associates to the left, so you can use a type like
--
-- @'Top' ':>>' ('String','Double') ':>>' 'String' ':>>' 'Char'@
--
-- to represent a 'Zipper' from @('String','Double')@ down to 'Char' that has an intermediate
-- crumb for the 'String' containing the 'Char'.
--
-- You can construct a 'Zipper' into *any* data structure with 'zipper'.
--
-- You can repackage up the contents of a 'Zipper' with 'rezip'.
--
-- >>> rezip $ zipper 42
-- 42
--
-- The combinators in this module provide lot of things you can do to the
-- 'Zipper' while you have it open.
--
-- Note that a value of type @h ':>' s ':>' a@ doesn't actually contain a value
-- of type @h ':>' s@ -- as we descend into a level, the previous level is
-- unpacked and stored in 'Coil' form. Only one value of type @_ ':>' _@ exists
-- at any particular time for any particular 'Zipper'.
data Zipper h i a = Ord i => Zipper !(Coil h i a) Int !Int !(Path i a) i a
-- Top :>> Map String Int :> Int :@ String :>> Bool
infixr 9 :@
-- | An empty data type, used to represent the pairing of a position in
-- a 'Zipper' with an index. See ':>'.
data (:@) a i
infixl 8 :>
-- | This type family represents a 'Zipper' with the @p@ variable
-- abstracting over the position and the index, in terms of ':@'. You
-- can visually see it in type signatures as:
--
-- @h ':>' (a ':@' i) = 'Zipper' h i a@
--
type family (:>) h p
type instance h :> (a :@ i) = Zipper h i a
infixl 8 :>>
type h :>> a = Zipper h Int a
-- | This represents the type a 'Zipper' will have when it is fully 'Zipped' back up.
type family Zipped h a
type instance Zipped Top a = a
type instance Zipped (Zipper h i a) s = Zipped h a
-- | A 'Coil' is a linked list of the levels above the current one. The length
-- of a 'Coil' is known at compile time.
--
-- This is part of the internal structure of a 'Zipper'. You shouldn't need to manipulate this directly.
#ifndef HLINT
data Coil t i a where
Coil :: Coil Top Int a
Snoc :: Ord i => !(Coil h j s) -> AnIndexedTraversal' i s a -> Int -> !Int -> !(Path j s) -> j -> (Jacket i a -> s) -> Coil (Zipper h j s) i a
#endif
-- | This 'Lens' views the current target of the 'Zipper'.
focus :: IndexedLens' i (Zipper h i a) a
focus f (Zipper h t o p i a) = Zipper h t o p i <$> indexed f i a
{-# INLINE focus #-}
-- | Construct a 'Zipper' that can explore anything, and start it at the 'Top'.
zipper :: a -> Top :>> a
zipper = Zipper Coil 0 0 Start 0
{-# INLINE zipper #-}
-- | Return the index of the focus.
focalPoint :: Zipper h i a -> i
focalPoint (Zipper _ _ _ _ i _) = i
{-# INLINE focalPoint #-}
-- | Return the index into the current 'Traversal' within the current level of the 'Zipper'.
--
-- @'jerkTo' ('tooth' l) l = Just'@
--
-- Mnemonically, zippers have a number of 'teeth' within each level. This is which 'tooth' you are currently at.
--
-- This is based on ordinal position regardless of the underlying index type. It may be excessively expensive for a list.
--
-- 'focalPoint' may be much cheaper if you have a 'Traversal' indexed by ordinal position!
tooth :: Zipper h i a -> Int
tooth (Zipper _ t o _ _ _) = t + o
{-# INLINE tooth #-}
-- | Move the 'Zipper' 'upward', closing the current level and focusing on the parent element.
--
-- NB: Attempts to move upward from the 'Top' of the 'Zipper' will fail to typecheck.
--
upward :: Ord j => h :> s:@j :> a:@i -> h :> s:@j
upward (Zipper (Snoc h _ t o p j k) _ _ q i x) = Zipper h t o p j $ k $ recompress q i x
{-# INLINE upward #-}
-- | Jerk the 'Zipper' one 'tooth' to the 'rightward' within the current 'Lens' or 'Traversal'.
--
-- Attempts to move past the start of the current 'Traversal' (or trivially, the current 'Lens')
-- will return 'Nothing'.
--
-- >>> isNothing $ zipper "hello" & rightward
-- True
--
-- >>> zipper "hello" & fromWithin traverse & rightward <&> view focus
-- 'e'
--
-- >>> zipper "hello" & fromWithin traverse & rightward <&> focus .~ 'u' <&> rezip
-- "hullo"
--
-- >>> rezip $ zipper (1,2) & fromWithin both & tug rightward & focus .~ 3
-- (1,3)
rightward :: MonadPlus m => h :> a:@i -> m (h :> a:@i)
rightward (Zipper h t o p i a) = mover p (Leaf i a) mzero $ \q j b -> return $ Zipper h t (o + 1) q j b where
{-# INLINE rightward #-}
-- | Jerk the 'Zipper' 'leftward' one 'tooth' within the current 'Lens' or 'Traversal'.
--
-- Attempts to move past the end of the current 'Traversal' (or trivially, the current 'Lens')
-- will return 'Nothing'.
--
-- >>> isNothing $ zipper "hello" & leftward
-- True
-- >>> isNothing $ zipper "hello" & within traverse >>= leftward
-- True
--
-- >>> zipper "hello" & within traverse <&> tug leftward
-- Just 'h'
--
-- >>> zipper "hello" & fromWithin traverse & tug rightward & tug leftward & view focus
-- 'h'
leftward :: MonadPlus m => h :> a:@i -> m (h :> a:@i)
leftward (Zipper h t o p i a) = movel p (Leaf i a) mzero $ \q j b -> return $ Zipper h t (o - 1) q j b
{-# INLINE leftward #-}
-- | Move to the leftmost position of the current 'Traversal'.
--
-- This is just a convenient alias for @'farthest' 'leftward'@.
--
-- >>> zipper "hello" & fromWithin traverse & rightmost & focus .~ 'a' & rezip
-- "hella"
leftmost :: a :> b:@i -> a :> b:@i
leftmost (Zipper h _ _ p i a) = startl Start (recompress p i a) (error "leftmost: bad Jacket structure") (Zipper h 0 0)
{-# INLINE leftmost #-}
-- | Move to the rightmost position of the current 'Traversal'.
--
-- This is just a convenient alias for @'farthest' 'rightward'@.
--
-- >>> zipper "hello" & fromWithin traverse & rightmost & focus .~ 'y' & leftmost & focus .~ 'j' & rezip
-- "jelly"
rightmost :: a :> b:@i -> a :> b:@i
rightmost (Zipper h _ _ p i a) = startr Start (recompress p i a) (error "rightmost: bad Jacket structure") (\q -> Zipper h (offset q) 0 q)
{-# INLINE rightmost #-}
-- | This allows you to safely 'tug' 'leftward' or 'tug' 'rightward' on a
-- 'Zipper'. This will attempt the move, and stay where it was if it fails.
--
-- The more general signature allows its use in other circumstances, however.
--
-- @'tug' f x ≡ 'fromMaybe' a (f a)@
--
-- >>> fmap rezip $ zipper "hello" & within traverse <&> tug leftward <&> focus .~ 'j'
-- "jello"
--
-- >>> fmap rezip $ zipper "hello" & within traverse <&> tug rightward <&> focus .~ 'u'
-- "hullo"
tug :: (a -> Maybe a) -> a -> a
tug f a = fromMaybe a (f a)
{-# INLINE tug #-}
-- | This allows you to safely @'tug' 'leftward'@ or @'tug' 'rightward'@
-- multiple times on a 'Zipper', moving multiple steps in a given direction
-- and stopping at the last place you couldn't move from. This lets you safely
-- move a 'Zipper', because it will stop at either end.
--
-- >>> fmap rezip $ zipper "stale" & within traverse <&> tugs rightward 2 <&> focus .~ 'y'
-- "style"
--
-- >>> rezip $ zipper "want" & fromWithin traverse & tugs rightward 2 & focus .~ 'r' & tugs leftward 100 & focus .~ 'c'
-- "cart"
tugs :: (a -> Maybe a) -> Int -> a -> a
tugs f n0
| n0 < 0 = error "tugs: negative tug count"
| otherwise = go n0
where
go 0 a = a
go n a = maybe a (go (n - 1)) (f a)
{-# INLINE tugs #-}
-- | Move in a direction as far as you can go, then stop there.
--
-- This repeatedly applies a function until it returns 'Nothing', and then returns the last answer.
--
-- >>> fmap rezip $ zipper ("hello","world") & downward _1 & within traverse <&> rightmost <&> focus .~ 'a'
-- ("hella","world")
--
-- >>> rezip $ zipper ("hello","there") & fromWithin (both.traverse) & rightmost & focus .~ 'm'
-- ("hello","therm")
farthest :: (a -> Maybe a) -> a -> a
farthest f = go where
go a = maybe a go (f a)
{-# INLINE farthest #-}
-- | This allows for you to repeatedly pull a 'Zipper' in a given direction, failing if it falls off the end.
--
-- >>> isNothing $ zipper "hello" & within traverse >>= jerks rightward 10
-- True
--
-- >>> fmap rezip $ zipper "silly" & within traverse >>= jerks rightward 3 <&> focus .~ 'k'
-- "silky"
jerks :: Monad m => (a -> m a) -> Int -> a -> m a
jerks f n0
| n0 < 0 = fail "jerks: negative jerk count"
| otherwise = go n0
where
go 0 a = return a
go n a = f a >>= go (n - 1)
{-# INLINE jerks #-}
-- | Returns the number of siblings at the current level in the 'Zipper'.
--
-- @'teeth' z '>=' 1@
--
-- /NB:/ If the current 'Traversal' targets an infinite number of elements then this may not terminate.
--
-- This is also a particularly expensive operation to perform on an unbalanced tree.
--
-- >>> zipper ("hello","world") & teeth
-- 1
--
-- >>> zipper ("hello","world") & fromWithin both & teeth
-- 2
--
-- >>> zipper ("hello","world") & downward _1 & teeth
-- 1
--
-- >>> zipper ("hello","world") & downward _1 & fromWithin traverse & teeth
-- 5
--
-- >>> zipper ("hello","world") & fromWithin (_1.traverse) & teeth
-- 5
--
-- >>> zipper ("hello","world") & fromWithin (both.traverse) & teeth
-- 10
teeth :: h :> a:@i -> Int
teeth (Zipper _ _ _ p _ _) = pathsize p
{-# INLINE teeth #-}
-- | Move the 'Zipper' horizontally to the element in the @n@th position in the
-- current level, absolutely indexed, starting with the 'farthest' 'leftward' as @0@.
--
-- This returns 'Nothing' if the target element doesn't exist.
--
-- @'jerkTo' n ≡ 'jerks' 'rightward' n '.' 'farthest' 'leftward'@
--
-- >>> isNothing $ zipper "not working." & jerkTo 20
-- True
-- >>> isNothing $ zipper "not working." & fromWithin traverse & jerkTo 20
-- True
--
-- >>> fmap rezip $ zipper "not working" & within traverse >>= jerkTo 2 <&> focus .~ 'w'
-- Just "now working"
jerkTo :: MonadPlus m => Int -> (h :> a:@i) -> m (h :> a:@i)
jerkTo n z = case compare k n of
LT -> jerks rightward (n - k) z
EQ -> return z
GT -> jerks leftward (k - n) z
where k = tooth z
{-# INLINE jerkTo #-}
-- | Move the 'Zipper' horizontally to the element in the @n@th position of the
-- current level, absolutely indexed, starting with the 'farthest' 'leftward' as @0@.
--
-- If the element at that position doesn't exist, then this will clamp to the range @0 '<=' n '<' 'teeth'@.
--
-- @'tugTo' n ≡ 'tugs' 'rightward' n '.' 'farthest' 'leftward'@
--
-- >>> rezip $ zipper "not working." & fromWithin traverse & tugTo 100 & focus .~ '!' & tugTo 1 & focus .~ 'u'
-- "nut working!"
tugTo :: Int -> h :> a:@i -> h :> a:@i
tugTo n z = case compare k n of
LT -> tugs rightward (n - k) z
EQ -> z
GT -> tugs leftward (k - n) z
where k = tooth z
{-# INLINE tugTo #-}
-- | Move towards a particular index in the current 'Traversal'.
moveToward :: i -> h :> a:@i -> h :> a:@i
moveToward i z@(Zipper h _ _ p0 j s0)
| i == j = z
| otherwise = go Start (recompress p0 j s0)
where
go _ Pure = z
go p (Ap m nl nr li l r)
| Last (Just k) <- maximal l, k >= i = go (ApL m nl nr li p r) l
| otherwise = go (ApR m nl nr li l p) r
go p (Leaf k a) = Zipper h (offset p) 0 p k a
{-# INLINE moveToward #-}
-- | Move horizontally to a particular index @i@ in the current
-- 'Traversal'. In the case of simple zippers, the index is 'Int' and
-- we can move between traversals fairly easily:
--
-- >>> zipper (42, 32) & fromWithin both & moveTo 0 <&> view focus
-- 42
--
-- >>> zipper (42, 32) & fromWithin both & moveTo 1 <&> view focus
-- 32
--
moveTo :: MonadPlus m => i -> h :> a:@i -> m (h :> a:@i)
moveTo i z = case moveToward i z of
z'@(Zipper _ _ _ _ j _)
| i == j -> return z'
| otherwise -> mzero
{-# INLINE moveTo #-}
lensed :: ALens' s a -> IndexedLens' Int s a
lensed l f = cloneLens l (indexed f (0 :: Int))
{-# INLINE lensed #-}
-- | Step down into a 'Lens'. This is a constrained form of 'fromWithin' for when you know
-- there is precisely one target that can never fail.
--
-- @
-- 'downward' :: 'Lens'' s a -> (h :> s) -> h :> s :> a
-- 'downward' :: 'Iso'' s a -> (h :> s) -> h :> s :> a
-- @
downward :: forall j h s a. ALens' s a -> h :> s:@j -> h :> s:@j :>> a
downward l (Zipper h t o p j s) = Zipper (Snoc h l' t o p j go) 0 0 Start 0 (s^.l')
where l' :: IndexedLens' Int s a
l' = lensed l
go (Leaf _ b) = set l' b s
go _ = error "downward: rezipping"
{-# INLINE downward #-}
idownward :: forall i j h s a. Ord i => AnIndexedLens' i s a -> h :> s:@j -> h :> s:@j :> a:@i
idownward l (Zipper h t o p j s) = Zipper (Snoc h l' t o p j go) 0 0 Start i a
where l' :: IndexedLens' i s a
l' = cloneIndexedLens l
(i, a) = iview l' s
go (Leaf _ b) = set l' b s
go _ = error "idownward: rezipping"
{-# INLINE idownward #-}
-- | Step down into the 'leftmost' entry of a 'Traversal'.
--
-- @
-- 'within' :: 'Traversal'' s a -> (h :> s) -> 'Maybe' (h :> s :> a)
-- 'within' :: 'Prism'' s a -> (h :> s) -> 'Maybe' (h :> s :> a)
-- 'within' :: 'Lens'' s a -> (h :> s) -> 'Maybe' (h :> s :> a)
-- 'within' :: 'Iso'' s a -> (h :> s) -> 'Maybe' (h :> s :> a)
-- @
-- @'within' :: 'MonadPlus' m => 'ATraversal'' s a -> (h :> s:@j) -> m (h :> s:@j :>> a)@
within :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
within = iwithin . indexing
{-# INLINE within #-}
iwithin :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> s:@j) -> m (h :> s:@j :> a:@i)
iwithin l (Zipper h t o p j s) = case jacket l (Context id) s of
Context k xs -> startl Start xs mzero $ \q i a -> return $ Zipper (Snoc h l t o p j k) 0 0 q i a
{-# INLINE iwithin #-}
-- | Step down into every entry of a 'Traversal' simultaneously.
--
-- >>> zipper ("hello","world") & withins both >>= leftward >>= withins traverse >>= rightward <&> focus %~ toUpper <&> rezip :: [(String,String)]
-- [("hEllo","world"),("heLlo","world"),("helLo","world"),("hellO","world")]
--
-- @
-- 'withins' :: 'Traversal'' s a -> (h :> s) -> [h :> s :> a]
-- 'withins' :: 'Lens'' s a -> (h :> s) -> [h :> s :> a]
-- 'withins' :: 'Iso'' s a -> (h :> s) -> [h :> s :> a]
-- @
withins :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
withins = iwithins . indexing
{-# INLINE withins #-}
iwithins :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> s:@j) -> m (h :> s:@j :> a:@i)
iwithins z (Zipper h t o p j s) = case jacket z (Context id) s of
Context k xs -> let up = Snoc h z t o p j k
go q (Ap m nl nr li l r) = go (ApL m nl nr li q r) l `mplus` go (ApR m nl nr li l q) r
go q (Leaf i a) = return $ Zipper up (offset q) 0 q i a
go _ Pure = mzero
in go Start xs
{-# INLINE iwithins #-}
-- | Unsafely step down into a 'Traversal' that is /assumed/ to be non-empty.
--
-- If this invariant is not met then this will usually result in an error!
--
-- @
-- 'fromWithin' :: 'Traversal'' s a -> (h ':>' s) -> h ':>' s ':>' a
-- 'fromWithin' :: 'Lens'' s a -> (h ':>' s) -> h ':>' s ':>' a
-- 'fromWithin' :: 'Iso'' s a -> (h ':>' s) -> h ':>' s ':>' a
-- @
--
-- You can reason about this function as if the definition was:
--
-- @'fromWithin' l ≡ 'fromJust' '.' 'within' l@
fromWithin :: LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> s:@j) -> h :> s:@j :>> a
fromWithin = ifromWithin . indexing
{-# INLINE fromWithin #-}
ifromWithin :: Ord i => AnIndexedTraversal' i s a -> (h :> s:@j) -> h :> s:@j :> a:@i
ifromWithin l (Zipper h t o p j s) = case jacket l (Context id) s of
Context k xs -> let up = Snoc h l t o p j k in
startl Start xs (Zipper up 0 0 Start (error "fromWithin an empty Traversal")
(error "fromWithin an empty Traversal"))
(Zipper up 0 0)
{-# INLINE ifromWithin #-}
-- | This enables us to pull the 'Zipper' back up to the 'Top'.
class Zipping h a where
recoil :: Coil h i a -> Jacket i a -> Zipped h a
instance Zipping Top a where
recoil Coil (Leaf _ a) = a
recoil Coil _ = error "recoil: expected Leaf"
{-# INLINE recoil #-}
instance Zipping h s => Zipping (Zipper h i s) a where
recoil (Snoc h _ _ _ p i k) as = recoil h $ recompress p i (k as)
{-# INLINE recoil #-}
-- | Close something back up that you opened as a 'Zipper'.
rezip :: Zipping h a => (h :> a:@i) -> Zipped h a
rezip (Zipper h _ _ p i a) = recoil h (recompress p i a)
{-# INLINE rezip #-}
-- | Extract the current 'focus' from a 'Zipper' as a 'Pretext', with access to the current index.
focusedContext :: (Indexable i p, Zipping h a) => (h :> a:@i) -> Pretext p a a (Zipped h a)
focusedContext (Zipper h t o p i a) = Pretext (\f -> rezip . Zipper h t o p i <$> indexed f i a)
{-# INLINE focusedContext #-}
-----------------------------------------------------------------------------
-- * Tapes
-----------------------------------------------------------------------------
-- | A 'Tape' is a recorded path through the 'Traversal' chain of a 'Zipper'.
data Tape h i a where
Tape :: Track h i a -> i -> Tape h i a
-- | Save the current path as as a 'Tape' we can play back later.
saveTape :: Zipper h i a -> Tape h i a
saveTape (Zipper h _ _ _ i _) = Tape (peel h) i
{-# INLINE saveTape #-}
-- | Restore ourselves to a previously recorded position precisely.
--
-- If the position does not exist, then fail.
restoreTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)
restoreTape (Tape h n) = restoreTrack h >=> moveTo n
{-# INLINE restoreTape #-}
-- | Restore ourselves to a location near our previously recorded position.
--
-- When moving left to right through a 'Traversal', if this will clamp at each
-- level to the range @0 '<=' k '<' 'teeth'@, so the only failures will occur
-- when one of the sequence of downward traversals find no targets.
restoreNearTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)
restoreNearTape (Tape h n) a = liftM (moveToward n) (restoreNearTrack h a)
{-# INLINE restoreNearTape #-}
-- | Restore ourselves to a previously recorded position.
--
-- This *assumes* that nothing has been done in the meantime to affect the existence of anything on the entire path.
--
-- Motions 'leftward' or 'rightward' are clamped, but all traversals included on the 'Tape' are assumed to be non-empty.
--
-- Violate these assumptions at your own risk!
unsafelyRestoreTape :: Tape h i a -> Zipped h a -> Zipper h i a
unsafelyRestoreTape (Tape h n) = unsafelyRestoreTrack h >>> moveToward n
{-# INLINE unsafelyRestoreTape #-}
-----------------------------------------------------------------------------
-- * Tracks
-----------------------------------------------------------------------------
-- | This is used to peel off the path information from a 'Coil' for use when saving the current path for later replay.
peel :: Coil h i a -> Track h i a
peel Coil = Track
peel (Snoc h l _ _ _ i _) = Fork (peel h) i l
{-# INLINE peel #-}
-- | The 'Track' forms the bulk of a 'Tape'.
data Track t i a where
Track :: Track Top Int a
Fork :: Ord i => Track h j s -> j -> AnIndexedTraversal' i s a -> Track (Zipper h j s) i a
-- | Restore ourselves to a previously recorded position precisely.
--
-- If the position does not exist, then fail.
restoreTrack :: MonadPlus m => Track h i a -> Zipped h a -> m (Zipper h i a)
restoreTrack Track = return . zipper
restoreTrack (Fork h n l) = restoreTrack h >=> moveTo n >=> iwithin l
-- | Restore ourselves to a location near our previously recorded position.
--
-- When moving 'leftward' to 'rightward' through a 'Traversal', if this will clamp at each level to the range @0 '<=' k '<' 'teeth'@,
-- so the only failures will occur when one of the sequence of downward traversals find no targets.
restoreNearTrack :: MonadPlus m => Track h i a -> Zipped h a -> m (Zipper h i a)
restoreNearTrack Track = return . zipper
restoreNearTrack (Fork h n l) = restoreNearTrack h >=> moveToward n >>> iwithin l
-- | Restore ourselves to a previously recorded position.
--
-- This *assumes* that nothing has been done in the meantime to affect the existence of anything on the entire 'Path'.
--
-- Motions 'leftward' or 'rightward' are clamped, but all traversals included on the 'Tape' are assumed to be non-empty.
--
-- Violate these assumptions at your own risk!
unsafelyRestoreTrack :: Track h i a -> Zipped h a -> Zipper h i a
unsafelyRestoreTrack Track = zipper
unsafelyRestoreTrack (Fork h n l) = unsafelyRestoreTrack h >>> moveToward n >>> ifromWithin l