2 delete, deleteBy, (\\), deleteFirsts, deleteFirstsBy,
3 elemBy, notElemBy, lookupBy, maximumBy, minimumBy,
4 nub, nubBy, partition, sums, products, transpose,
5 zip4, zip5, zip6, zip7,
6 zipWith4, zipWith5, zipWith6, zipWith7,
7 unzip4, unzip5, unzip6, unzip7,
8 genericLength, genericDrop, genericTake, genericSplitAt,
10 elemIndex, elemIndexBy, intersperse, group, groupBy,
12 inits, tails, subsequences, permutations,
13 union, intersect ) where
15 -- delete x removes the first occurrence of x from its list argument.
16 delete :: (Eq a) => a -> [a] -> [a]
17 delete = deleteBy (==)
19 deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
21 deleteBy eq x (y:ys) = if x `eq` y then ys else y : deleteBy eq x ys
23 -- list difference (non-associative). In the result of xs \\ ys,
24 -- the first occurrence of each element of ys in turn (if any)
25 -- has been removed from xs. Thus, (xs ++ ys) \\ xs == ys.
26 (\\) :: (Eq a) => [a] -> [a] -> [a]
27 (\\) = foldl (flip delete)
29 -- Alternate name for \\
30 deleteFirsts :: (Eq a) => [a] -> [a] -> [a]
33 deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
34 deleteFirstsBy eq = foldl (flip (deleteBy eq))
36 -- elem, notElem, lookup, maximumBy and minimumBy are in PreludeList
37 elemBy, notElemBy :: (a -> a -> Bool) -> a -> [a] -> Bool
38 elemBy eq _ [] = False
39 elemBy eq x (y:ys) = x `eq` y || elemBy eq x ys
41 notElemBy eq x xs = not (elemBy eq x xs)
43 lookupBy :: (a -> a -> Bool) -> a -> [(a, b)] -> Maybe b
44 lookupBy eq key [] = Nothing
45 lookupBy eq key ((x,y):xys)
47 | otherwise = lookupBy eq key xys
49 maximumBy :: (a -> a -> a) -> [a] -> a
50 maximumBy max [] = error "List.maximumBy: empty list"
51 maximumBy max xs = foldl1 max xs
53 minimumBy :: (a -> a -> a) -> [a] -> a
54 minimumBy min [] = error "List.minimumBy: empty list"
55 minimumBy min xs = foldl1 min xs
57 -- nub (meaning "essence") remove duplicate elements from its list argument.
58 nub :: (Eq a) => [a] -> [a]
61 nubBy :: (a -> a -> Bool) -> [a] -> [a]
63 nubBy eq (x:xs) = x : nubBy eq (filter (\ y -> not (eq x y)) xs)
65 -- partition takes a predicate and a list and returns a pair of lists:
66 -- those elements of the argument list that do and do not satisfy the
67 -- predicate, respectively; i,e,,
68 -- partition p xs == (filter p xs, filter (not . p) xs).
69 partition :: (a -> Bool) -> [a] -> ([a],[a])
70 partition p xs = foldr select ([],[]) xs
71 where select x (ts,fs) | p x = (x:ts,fs)
72 | otherwise = (ts, x:fs)
74 -- sums and products give a list of running sums or products from
75 -- a list of numbers. e.g., sums [1,2,3] == [0,1,3,6]
76 sums, products :: (Num a) => [a] -> [a]
78 products = scanl (*) 1
80 transpose :: [[a]] -> [[a]]
82 (\xs xss -> zipWith (:) xs (xss ++ repeat []))
85 zip4 :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
88 zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
89 zip5 = zipWith5 (,,,,)
91 zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
93 zip6 = zipWith6 (,,,,,)
95 zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
96 [g] -> [(a,b,c,d,e,f,g)]
97 zip7 = zipWith7 (,,,,,,)
99 zipWith4 :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
100 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
101 = z a b c d : zipWith4 z as bs cs ds
102 zipWith4 _ _ _ _ _ = []
104 zipWith5 :: (a->b->c->d->e->f) ->
105 [a]->[b]->[c]->[d]->[e]->[f]
106 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
107 = z a b c d e : zipWith5 z as bs cs ds es
108 zipWith5 _ _ _ _ _ _ = []
110 zipWith6 :: (a->b->c->d->e->f->g) ->
111 [a]->[b]->[c]->[d]->[e]->[f]->[g]
112 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
113 = z a b c d e f : zipWith6 z as bs cs ds es fs
114 zipWith6 _ _ _ _ _ _ _ = []
116 zipWith7 :: (a->b->c->d->e->f->g->h) ->
117 [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
118 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
119 = z a b c d e f g : zipWith7 z as bs cs ds es fs gs
120 zipWith7 _ _ _ _ _ _ _ _ = []
122 unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
123 unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
124 (a:as,b:bs,c:cs,d:ds))
127 unzip5 :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
128 unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
129 (a:as,b:bs,c:cs,d:ds,e:es))
132 unzip6 :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
133 unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
134 (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
137 unzip7 :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
138 unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
139 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
140 ([],[],[],[],[],[],[])
142 genericLength :: (Num i) => [b] -> i
144 genericLength (_:l) = 1 + genericLength l
146 genericDrop :: (Integral i) => i -> [a] -> [a]
147 genericDrop 0 xs = xs
148 genericDrop _ [] = []
149 genericDrop n (_:xs) | n > 0 = genericDrop (n-1) xs
150 genericDrop _ _ = error "List.genericDrop: negative argument"
152 genericTake :: (Integral i) => i -> [a] -> [a]
154 genericTake _ [] = []
155 genericTake n (x:xs) | n > 0 = x : genericTake (n-1) xs
156 genericTake _ _ = error "List.genericTake: negative argument"
158 genericSplitAt :: (Integral i) => i -> [b] -> ([b],[b])
159 genericSplitAt 0 xs = ([],xs)
160 genericSplitAt _ [] = ([],[])
161 genericSplitAt n (x:xs) | n > 0 = (x:xs',xs'') where
162 (xs',xs'') = genericSplitAt (n-1) xs
163 genericSplitAt _ _ = error "List.genericSplitAt: negative argument"
165 genericReplicate :: (Integral i) => i -> a -> [a]
166 genericReplicate n x = genericTake n (repeat x)
168 -- l !! (elemIndex l x) == x if x `elem` l
169 elemIndex :: Eq a => [a] -> a -> Int
170 elemIndex = elemIndexBy (==)
172 elemIndexBy :: (a -> a -> Bool) -> [a] -> a -> Int
173 elemIndexBy eq [] x = error "List.elemIndexBy: empty list"
174 elemIndexBy eq (x:xs) x' = if x `eq` x' then 0 else 1 + elemIndexBy eq xs x'
176 -- group splits its list argument into a list of lists of equal, adjacent
178 -- group "Mississippi" == ["M","i","ss","i","ss","i","pp","i"]
179 group :: (Eq a) => [a] -> [[a]]
182 groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
184 groupBy eq (x:xs) = (x:ys) : groupBy eq zs
185 where (ys,zs) = span (eq x) xs
188 mapAccumL :: (a -> b -> (a, c)) -> a -> [b] -> (a, [c])
189 mapAccumL f s [] = (s, [])
190 mapAccumL f s (x:xs) = (s'',y:ys)
191 where (s', y ) = f s x
192 (s'',ys) = mapAccumL f s' xs
194 mapAccumR :: (a -> b -> (a, c)) -> a -> [b] -> (a, [c])
195 mapAccumR f s [] = (s, [])
196 mapAccumR f s (x:xs) = (s'', y:ys)
197 where (s'',y ) = f s' x
198 (s', ys) = mapAccumR f s xs
200 -- intersperse sep inserts sep between the elements of its list argument.
201 -- e.g. intersperse ',' "abcde" == "a,b,c,d,e"
202 intersperse :: a -> [a] -> [a]
203 intersperse sep [] = []
204 intersperse sep [x] = [x]
205 intersperse sep (x:xs) = x : sep : intersperse sep xs
207 -- inits xs returns the list of initial segments of xs, shortest first.
208 -- e.g., inits "abc" == ["","a","ab","abc"]
209 inits :: [a] -> [[a]]
211 inits (x:xs) = [[]] ++ map (x:) (inits xs)
213 -- tails xs returns the list of all final segments of xs, longest first.
214 -- e.g., tails "abc" == ["abc", "bc", "c",""]
215 tails :: [a] -> [[a]]
217 tails xxs@(_:xs) = xxs : tails xs
219 -- subsequences xs returns the list of all subsequences of xs.
220 -- e.g., subsequences "abc" == ["","c","b","bc","a","ac","ab","abc"]
221 subsequences :: [a] -> [[a]]
222 subsequences [] = [[]]
223 subsequences (x:xs) = subsequences xs ++ map (x:) (subsequences xs)
225 -- permutations xs returns the list of all permutations of xs.
226 -- e.g., permutations "abc" == ["abc","bac","bca","acb","cab","cba"]
227 permutations :: [a] -> [[a]]
228 permutations [] = [[]]
229 permutations (x:xs) = [zs | ys <- permutations xs, zs <- interleave x ys ]
230 where interleave :: a -> [a] -> [[a]]
231 interleave x [] = [[x]]
232 interleave x (y:ys) = [x:y:ys] ++ map (y:) (interleave x ys)
234 union :: (Eq a) => [a] -> [a] -> [a]
235 union xs ys = xs ++ (ys \\ xs)
237 intersect :: (Eq a) => [a] -> [a] -> [a]
238 intersect xs ys = [x | x <- xs, x `elem` ys]