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
|
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE AllowAmbiguousTypes #-}
module Xanthous.Util
( EqEqProp(..)
, EqProp(..)
, foldlMapM
, foldlMapM'
, between
, appendVia
-- * Foldable
-- ** Uniqueness
-- *** Predicates on uniqueness
, isUniqueOf
, isUnique
-- *** Removing all duplicate elements in n * log n time
, uniqueOf
, unique
-- *** Removing sequentially duplicate elements in linear time
, uniqOf
, uniq
-- ** Bag sequence algorithms
, takeWhileInclusive
) where
import Xanthous.Prelude hiding (foldr)
import Test.QuickCheck.Checkers
import Data.Foldable (foldr)
import Data.Monoid
newtype EqEqProp a = EqEqProp a
deriving newtype Eq
instance Eq a => EqProp (EqEqProp a) where
(=-=) = eq
foldlMapM :: forall g b a m. (Foldable g, Monoid b, Applicative m) => (a -> m b) -> g a -> m b
foldlMapM f = foldr f' (pure mempty)
where
f' :: a -> m b -> m b
f' x = liftA2 mappend (f x)
-- Strict in the monoidal accumulator. For monads strict
-- in the left argument of bind, this will run in constant
-- space.
foldlMapM' :: forall g b a m. (Foldable g, Monoid b, Monad m) => (a -> m b) -> g a -> m b
foldlMapM' f xs = foldr f' pure xs mempty
where
f' :: a -> (b -> m b) -> b -> m b
f' x k bl = do
br <- f x
let !b = mappend bl br
k b
between
:: Ord a
=> a -- ^ lower bound
-> a -- ^ upper bound
-> a -- ^ scrutinee
-> Bool
between lower upper x = x >= lower && x <= upper
-- |
-- >>> appendVia Sum 1 2
-- 3
appendVia :: (Rewrapping s t, Semigroup s) => (Unwrapped s -> s) -> Unwrapped s -> Unwrapped s -> Unwrapped s
appendVia wrap x y = op wrap $ wrap x <> wrap y
--------------------------------------------------------------------------------
-- | Returns True if the targets of the given 'Fold' are unique per the 'Ord' instance for @a@
--
-- >>> isUniqueOf (folded . _1) ([(1, 2), (2, 2), (3, 2)] :: [(Int, Int)])
-- True
--
-- >>> isUniqueOf (folded . _2) ([(1, 2), (2, 2), (3, 2)] :: [(Int, Int)])
-- False
--
-- @
-- 'isUniqueOf' :: Ord a => 'Getter' s a -> s -> 'Bool'
-- 'isUniqueOf' :: Ord a => 'Fold' s a -> s -> 'Bool'
-- 'isUniqueOf' :: Ord a => 'Lens'' s a -> s -> 'Bool'
-- 'isUniqueOf' :: Ord a => 'Iso'' s a -> s -> 'Bool'
-- 'isUniqueOf' :: Ord a => 'Traversal'' s a -> s -> 'Bool'
-- 'isUniqueOf' :: Ord a => 'Prism'' s a -> s -> 'Bool'
-- @
isUniqueOf :: Ord a => Getting (Endo (Set a, Bool)) s a -> s -> Bool
isUniqueOf aFold = orOf _2 . foldrOf aFold rejectUnique (mempty, True)
where
rejectUnique x (seen, acc)
| seen ^. contains x = (seen, False)
| otherwise = (seen & contains x .~ True, acc)
-- | Returns true if the given 'Foldable' container contains only unique
-- elements, as determined by the 'Ord' instance for @a@
--
-- >>> isUnique ([3, 1, 2] :: [Int])
-- True
--
-- >>> isUnique ([1, 1, 2, 2, 3, 1] :: [Int])
-- False
isUnique :: (Foldable f, Ord a) => f a -> Bool
isUnique = isUniqueOf folded
-- | O(n * log n). Returns a monoidal, 'Cons'able container (a list, a Set,
-- etc.) consisting of the unique (per the 'Ord' instance for @a@) targets of
-- the given 'Fold'
--
-- >>> uniqueOf (folded . _2) ([(1, 2), (2, 2), (3, 2), (4, 3)] :: [(Int, Int)]) :: [Int]
-- [2,3]
--
-- @
-- 'uniqueOf' :: Ord a => 'Getter' s a -> s -> [a]
-- 'uniqueOf' :: Ord a => 'Fold' s a -> s -> [a]
-- 'uniqueOf' :: Ord a => 'Lens'' s a -> s -> [a]
-- 'uniqueOf' :: Ord a => 'Iso'' s a -> s -> [a]
-- 'uniqueOf' :: Ord a => 'Traversal'' s a -> s -> [a]
-- 'uniqueOf' :: Ord a => 'Prism'' s a -> s -> [a]
-- @
uniqueOf
:: (Monoid c, Ord w, Cons c c w w) => Getting (Endo (Set w, c)) a w -> a -> c
uniqueOf aFold = snd . foldrOf aFold rejectUnique (mempty, mempty)
where
rejectUnique x (seen, acc)
| seen ^. contains x = (seen, acc)
| otherwise = (seen & contains x .~ True, cons x acc)
-- | Returns a monoidal, 'Cons'able container (a list, a Set, etc.) consisting
-- of the unique (per the 'Ord' instance for @a@) contents of the given
-- 'Foldable' container
--
-- >>> unique [1, 1, 2, 2, 3, 1] :: [Int]
-- [2,3,1]
-- >>> unique [1, 1, 2, 2, 3, 1] :: Set Int
-- fromList [3,2,1]
unique :: (Foldable f, Cons c c a a, Ord a, Monoid c) => f a -> c
unique = uniqueOf folded
--------------------------------------------------------------------------------
-- | O(n). Returns a monoidal, 'Cons'able container (a list, a Vector, etc.)
-- consisting of the targets of the given 'Fold' with sequential duplicate
-- elements removed
--
-- This function (sorry for the confusing name) differs from 'uniqueOf' in that
-- it only compares /sequentially/ duplicate elements (and thus operates in
-- linear time).
-- cf 'Data.Vector.uniq' and POSIX @uniq@ for the name
--
-- >>> uniqOf (folded . _2) ([(1, 2), (2, 2), (3, 1), (4, 2)] :: [(Int, Int)]) :: [Int]
-- [2,1,2]
--
-- @
-- 'uniqOf' :: Eq a => 'Getter' s a -> s -> [a]
-- 'uniqOf' :: Eq a => 'Fold' s a -> s -> [a]
-- 'uniqOf' :: Eq a => 'Lens'' s a -> s -> [a]
-- 'uniqOf' :: Eq a => 'Iso'' s a -> s -> [a]
-- 'uniqOf' :: Eq a => 'Traversal'' s a -> s -> [a]
-- 'uniqOf' :: Eq a => 'Prism'' s a -> s -> [a]
-- @
uniqOf :: (Monoid c, Cons c c w w, Eq w) => Getting (Endo (Maybe w, c)) a w -> a -> c
uniqOf aFold = snd . foldrOf aFold rejectSeen (Nothing, mempty)
where
rejectSeen x (Nothing, acc) = (Just x, x <| acc)
rejectSeen x tup@(Just a, acc)
| x == a = tup
| otherwise = (Just x, x <| acc)
-- | O(n). Returns a monoidal, 'Cons'able container (a list, a Vector, etc.)
-- consisting of the targets of the given 'Foldable' container with sequential
-- duplicate elements removed
--
-- This function (sorry for the confusing name) differs from 'unique' in that
-- it only compares /sequentially/ unique elements (and thus operates in linear
-- time).
-- cf 'Data.Vector.uniq' and POSIX @uniq@ for the name
--
-- >>> uniq [1, 1, 1, 2, 2, 2, 3, 3, 1] :: [Int]
-- [1,2,3,1]
--
-- >>> uniq [1, 1, 1, 2, 2, 2, 3, 3, 1] :: Vector Int
-- [1,2,3,1]
--
uniq :: (Foldable f, Eq a, Cons c c a a, Monoid c) => f a -> c
uniq = uniqOf folded
-- | Like 'takeWhile', but inclusive
takeWhileInclusive :: (a -> Bool) -> [a] -> [a]
takeWhileInclusive _ [] = []
takeWhileInclusive p (x:xs) = x : if p x then takeWhileInclusive p xs else []
|
