Copyright | (c) The University of Glasgow 2001 |
---|---|
License | BSD-style (see the file libraries/base/LICENSE) |
Maintainer | libraries@haskell.org |
Stability | stable |
Portability | portable |
Safe Haskell | Safe |
Language | Haskell2010 |
This legacy module provides access to the list-specialised operations of Data.List. This module may go away again in future GHC versions and is provided as transitional tool to access some of the list-specialised operations that had to be generalised due to the implementation of the Foldable/Traversable-in-Prelude Proposal (FTP).
If the operations needed are available in GHC.List, it's recommended to avoid importing this module and use GHC.List instead for now.
Since: base-4.8.0.0
Synopsis
- (++) :: [a] -> [a] -> [a]
- head :: HasCallStack => [a] -> a
- last :: HasCallStack => [a] -> a
- tail :: HasCallStack => [a] -> [a]
- init :: HasCallStack => [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- singleton :: a -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl1 :: HasCallStack => (a -> a -> a) -> [a] -> a
- foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: HasCallStack => (a -> a -> a) -> [a] -> a
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- all :: (a -> Bool) -> [a] -> Bool
- sum :: Num a => [a] -> a
- product :: Num a => [a] -> a
- maximum :: (Ord a, HasCallStack) => [a] -> a
- minimum :: (Ord a, HasCallStack) => [a] -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: HasCallStack => [a] -> [a]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- dropWhileEnd :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
- group :: Eq a => [a] -> [[a]]
- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- isSuffixOf :: Eq a => [a] -> [a] -> Bool
- isInfixOf :: Eq a => [a] -> [a] -> Bool
- elem :: Eq a => a -> [a] -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- find :: (a -> Bool) -> [a] -> Maybe a
- filter :: (a -> Bool) -> [a] -> [a]
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- (!!) :: HasCallStack => [a] -> Int -> a
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- findIndices :: (a -> Bool) -> [a] -> [Int]
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- nub :: Eq a => [a] -> [a]
- delete :: Eq a => a -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- insert :: Ord a => a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- maximumBy :: (a -> a -> Ordering) -> [a] -> a
- minimumBy :: (a -> a -> Ordering) -> [a] -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]
Basic functions
(++) :: [a] -> [a] -> [a] infixr 5 Source #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
WARNING: This function takes linear time in the number of elements of the first list.
head :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
>>>
head [1, 2, 3]
1>>>
head [1..]
1>>>
head []
*** Exception: Prelude.head: empty list
WARNING: This function is partial. You can use case-matching, uncons
or
listToMaybe
instead.
last :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
>>>
last [1, 2, 3]
3>>>
last [1..]
* Hangs forever *>>>
last []
*** Exception: Prelude.last: empty list
WARNING: This function is partial. You can use reverse
with case-matching,
uncons
or listToMaybe
instead.
tail :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
>>>
tail [1, 2, 3]
[2,3]>>>
tail [1]
[]>>>
tail []
*** Exception: Prelude.tail: empty list
WARNING: This function is partial. You can use case-matching or uncons
instead.
init :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(1)\). Test whether a list is empty.
>>>
null []
True>>>
null [1]
False>>>
null [1..]
False
\(\mathcal{O}(n)\). length
returns the length of a finite list as an
Int
. It is an instance of the more general genericLength
, the
result type of which may be any kind of number.
>>>
length []
0>>>
length ['a', 'b', 'c']
3>>>
length [1..]
* Hangs forever *
List transformations
map :: (a -> b) -> [a] -> [b] Source #
\(\mathcal{O}(n)\). map
f xs
is the list obtained by applying f
to
each element of xs
, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>
map (+1) [1, 2, 3]
[2,3,4]
reverse :: [a] -> [a] Source #
reverse
xs
returns the elements of xs
in reverse order.
xs
must be finite.
>>>
reverse []
[]>>>
reverse [42]
[42]>>>
reverse [2,5,7]
[7,5,2]>>>
reverse [1..]
* Hangs forever *
intersperse :: a -> [a] -> [a] Source #
\(\mathcal{O}(n)\). The intersperse
function takes an element and a list
and `intersperses' that element between the elements of the list. For
example,
>>>
intersperse ',' "abcde"
"a,b,c,d,e"
intercalate :: [a] -> [[a]] -> [a] Source #
intercalate
xs xss
is equivalent to (
.
It inserts the list concat
(intersperse
xs xss))xs
in between the lists in xss
and concatenates the
result.
>>>
intercalate ", " ["Lorem", "ipsum", "dolor"]
"Lorem, ipsum, dolor"
transpose :: [[a]] -> [[a]] Source #
The transpose
function transposes the rows and columns of its argument.
For example,
>>>
transpose [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]
If some of the rows are shorter than the following rows, their elements are skipped:
>>>
transpose [[10,11],[20],[],[30,31,32]]
[[10,20,30],[11,31],[32]]
For this reason the outer list must be finite; otherwise transpose
hangs:
>>>
transpose (repeat [])
* Hangs forever *
subsequences :: [a] -> [[a]] Source #
The subsequences
function returns the list of all subsequences of the argument.
>>>
subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]
This function is productive on infinite inputs:
>>>
take 8 $ subsequences ['a'..]
["","a","b","ab","c","ac","bc","abc"]
permutations :: [a] -> [[a]] Source #
The permutations
function returns the list of all permutations of the argument.
>>>
permutations "abc"
["abc","bac","cba","bca","cab","acb"]
The permutations
function is maximally lazy:
for each n
, the value of
starts with those permutations
that permute permutations
xs
and keep take
n xs
.drop
n xs
This function is productive on infinite inputs:
>>>
take 6 $ map (take 3) $ permutations ['a'..]
["abc","bac","cba","bca","cab","acb"]
Note that the order of permutations is not lexicographic. It satisfies the following property:
map (take n) (take (product [1..n]) (permutations ([1..n] ++ undefined))) == permutations [1..n]
Reducing lists (folds)
foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b Source #
foldl
, applied to a binary operator, a starting value (typically
the left-identity of the operator), and a list, reduces the list
using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
The list must be finite.
>>>
foldl (+) 0 [1..4]
10>>>
foldl (+) 42 []
42>>>
foldl (-) 100 [1..4]
90>>>
foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
"dcbafoo">>>
foldl (+) 0 [1..]
* Hangs forever *
foldl1 :: HasCallStack => (a -> a -> a) -> [a] -> a Source #
foldl1
is a variant of foldl
that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike foldl
, the accumulated value must be of the same type as the list elements.
>>>
foldl1 (+) [1..4]
10>>>
foldl1 (+) []
*** Exception: Prelude.foldl1: empty list>>>
foldl1 (-) [1..4]
-8>>>
foldl1 (&&) [True, False, True, True]
False>>>
foldl1 (||) [False, False, True, True]
True>>>
foldl1 (+) [1..]
* Hangs forever *
foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a Source #
A strict version of foldl1
.
foldr :: (a -> b -> b) -> b -> [a] -> b Source #
foldr
, applied to a binary operator, a starting value (typically
the right-identity of the operator), and a list, reduces the list
using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
foldr1 :: HasCallStack => (a -> a -> a) -> [a] -> a Source #
foldr1
is a variant of foldr
that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike foldr
, the accumulated value must be of the same type as the list elements.
>>>
foldr1 (+) [1..4]
10>>>
foldr1 (+) []
*** Exception: Prelude.foldr1: empty list>>>
foldr1 (-) [1..4]
-2>>>
foldr1 (&&) [True, False, True, True]
False>>>
foldr1 (||) [False, False, True, True]
True>>>
force $ foldr1 (+) [1..]
*** Exception: stack overflow
Special folds
concat :: [[a]] -> [a] Source #
Concatenate a list of lists.
>>>
concat []
[]>>>
concat [[42]]
[42]>>>
concat [[1,2,3], [4,5], [6], []]
[1,2,3,4,5,6]
and :: [Bool] -> Bool Source #
and
returns the conjunction of a Boolean list. For the result to be
True
, the list must be finite; False
, however, results from a False
value at a finite index of a finite or infinite list.
>>>
and []
True>>>
and [True]
True>>>
and [False]
False>>>
and [True, True, False]
False>>>
and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True...
False>>>
and (repeat True)
* Hangs forever *
or
returns the disjunction of a Boolean list. For the result to be
False
, the list must be finite; True
, however, results from a True
value at a finite index of a finite or infinite list.
>>>
or []
False>>>
or [True]
True>>>
or [False]
False>>>
or [True, True, False]
True>>>
or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False...
True>>>
or (repeat False)
* Hangs forever *
any :: (a -> Bool) -> [a] -> Bool Source #
Applied to a predicate and a list, any
determines if any element
of the list satisfies the predicate. For the result to be
False
, the list must be finite; True
, however, results from a True
value for the predicate applied to an element at a finite index of a finite
or infinite list.
>>>
any (> 3) []
False>>>
any (> 3) [1,2]
False>>>
any (> 3) [1,2,3,4,5]
True>>>
any (> 3) [1..]
True>>>
any (> 3) [0, -1..]
* Hangs forever *
all :: (a -> Bool) -> [a] -> Bool Source #
Applied to a predicate and a list, all
determines if all elements
of the list satisfy the predicate. For the result to be
True
, the list must be finite; False
, however, results from a False
value for the predicate applied to an element at a finite index of a finite
or infinite list.
>>>
all (> 3) []
True>>>
all (> 3) [1,2]
False>>>
all (> 3) [1,2,3,4,5]
False>>>
all (> 3) [1..]
False>>>
all (> 3) [4..]
* Hangs forever *
sum :: Num a => [a] -> a Source #
The sum
function computes the sum of a finite list of numbers.
>>>
sum []
0>>>
sum [42]
42>>>
sum [1..10]
55>>>
sum [4.1, 2.0, 1.7]
7.8>>>
sum [1..]
* Hangs forever *
product :: Num a => [a] -> a Source #
The product
function computes the product of a finite list of numbers.
>>>
product []
1>>>
product [42]
42>>>
product [1..10]
3628800>>>
product [4.1, 2.0, 1.7]
13.939999999999998>>>
product [1..]
* Hangs forever *
maximum :: (Ord a, HasCallStack) => [a] -> a Source #
maximum
returns the maximum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of maximumBy
, which allows the
programmer to supply their own comparison function.
>>>
maximum []
*** Exception: Prelude.maximum: empty list>>>
maximum [42]
42>>>
maximum [55, -12, 7, 0, -89]
55>>>
maximum [1..]
* Hangs forever *
minimum :: (Ord a, HasCallStack) => [a] -> a Source #
minimum
returns the minimum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of minimumBy
, which allows the
programmer to supply their own comparison function.
>>>
minimum []
*** Exception: Prelude.minimum: empty list>>>
minimum [42]
42>>>
minimum [55, -12, 7, 0, -89]
-89>>>
minimum [1..]
* Hangs forever *
Building lists
Scans
scanl :: (b -> a -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanl
is similar to foldl
, but returns a list of
successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs
>>>
scanl (+) 0 [1..4]
[0,1,3,6,10]>>>
scanl (+) 42 []
[42]>>>
scanl (-) 100 [1..4]
[100,99,97,94,90]>>>
scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["foo","afoo","bafoo","cbafoo","dcbafoo"]>>>
scanl (+) 0 [1..]
* Hangs forever *
scanl1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanl1
is a variant of scanl
that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>
scanl1 (+) [1..4]
[1,3,6,10]>>>
scanl1 (+) []
[]>>>
scanl1 (-) [1..4]
[1,-1,-4,-8]>>>
scanl1 (&&) [True, False, True, True]
[True,False,False,False]>>>
scanl1 (||) [False, False, True, True]
[False,False,True,True]>>>
scanl1 (+) [1..]
* Hangs forever *
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanr
is the right-to-left dual of scanl
. Note that the order of parameters on the accumulating function are reversed compared to scanl
.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>
scanr (+) 0 [1..4]
[10,9,7,4,0]>>>
scanr (+) 42 []
[42]>>>
scanr (-) 100 [1..4]
[98,-97,99,-96,100]>>>
scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]>>>
force $ scanr (+) 0 [1..]
*** Exception: stack overflow
scanr1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanr1
is a variant of scanr
that has no starting
value argument.
>>>
scanr1 (+) [1..4]
[10,9,7,4]>>>
scanr1 (+) []
[]>>>
scanr1 (-) [1..4]
[-2,3,-1,4]>>>
scanr1 (&&) [True, False, True, True]
[False,False,True,True]>>>
scanr1 (||) [True, True, False, False]
[True,True,False,False]>>>
force $ scanr1 (+) [1..]
*** Exception: stack overflow
Accumulating maps
Infinite lists
iterate :: (a -> a) -> a -> [a] Source #
iterate
f x
returns an infinite list of repeated applications
of f
to x
:
iterate f x == [x, f x, f (f x), ...]
Note that iterate
is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate'
for a strict
variant of this function.
>>>
take 10 $ iterate not True
[True,False,True,False...>>>
take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63...
repeat
x
is an infinite list, with x
the value of every element.
>>>
repeat 17
[17,17,17,17,17,17,17,17,17...
replicate :: Int -> a -> [a] Source #
replicate
n x
is a list of length n
with x
the value of
every element.
It is an instance of the more general genericReplicate
,
in which n
may be of any integral type.
>>>
replicate 0 True
[]>>>
replicate (-1) True
[]>>>
replicate 4 True
[True,True,True,True]
cycle :: HasCallStack => [a] -> [a] Source #
cycle
ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
>>>
cycle []
*** Exception: Prelude.cycle: empty list>>>
cycle [42]
[42,42,42,42,42,42,42,42,42,42...>>>
cycle [2, 5, 7]
[2,5,7,2,5,7,2,5,7,2,5,7...
Unfolding
unfoldr :: (b -> Maybe (a, b)) -> b -> [a] Source #
The unfoldr
function is a `dual' to foldr
: while foldr
reduces a list to a summary value, unfoldr
builds a list from
a seed value. The function takes the element and returns Nothing
if it is done producing the list or returns Just
(a,b)
, in which
case, a
is a prepended to the list and b
is used as the next
element in a recursive call. For example,
iterate f == unfoldr (\x -> Just (x, f x))
In some cases, unfoldr
can undo a foldr
operation:
unfoldr f' (foldr f z xs) == xs
if the following holds:
f' (f x y) = Just (x,y) f' z = Nothing
A simple use of unfoldr:
>>>
unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
[10,9,8,7,6,5,4,3,2,1]
Sublists
Extracting sublists
take :: Int -> [a] -> [a] Source #
take
n
, applied to a list xs
, returns the prefix of xs
of length n
, or xs
itself if n >=
.length
xs
>>>
take 5 "Hello World!"
"Hello">>>
take 3 [1,2,3,4,5]
[1,2,3]>>>
take 3 [1,2]
[1,2]>>>
take 3 []
[]>>>
take (-1) [1,2]
[]>>>
take 0 [1,2]
[]
It is an instance of the more general genericTake
,
in which n
may be of any integral type.
drop :: Int -> [a] -> [a] Source #
drop
n xs
returns the suffix of xs
after the first n
elements, or []
if n >=
.length
xs
>>>
drop 6 "Hello World!"
"World!">>>
drop 3 [1,2,3,4,5]
[4,5]>>>
drop 3 [1,2]
[]>>>
drop 3 []
[]>>>
drop (-1) [1,2]
[1,2]>>>
drop 0 [1,2]
[1,2]
It is an instance of the more general genericDrop
,
in which n
may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a]) Source #
splitAt
n xs
returns a tuple where first element is xs
prefix of
length n
and second element is the remainder of the list:
>>>
splitAt 6 "Hello World!"
("Hello ","World!")>>>
splitAt 3 [1,2,3,4,5]
([1,2,3],[4,5])>>>
splitAt 1 [1,2,3]
([1],[2,3])>>>
splitAt 3 [1,2,3]
([1,2,3],[])>>>
splitAt 4 [1,2,3]
([1,2,3],[])>>>
splitAt 0 [1,2,3]
([],[1,2,3])>>>
splitAt (-1) [1,2,3]
([],[1,2,3])
It is equivalent to (
when take
n xs, drop
n xs)n
is not _|_
(splitAt _|_ xs = _|_
).
splitAt
is an instance of the more general genericSplitAt
,
in which n
may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a] Source #
takeWhile
, applied to a predicate p
and a list xs
, returns the
longest prefix (possibly empty) of xs
of elements that satisfy p
.
>>>
takeWhile (< 3) [1,2,3,4,1,2,3,4]
[1,2]>>>
takeWhile (< 9) [1,2,3]
[1,2,3]>>>
takeWhile (< 0) [1,2,3]
[]
dropWhileEnd :: (a -> Bool) -> [a] -> [a] Source #
The dropWhileEnd
function drops the largest suffix of a list
in which the given predicate holds for all elements. For example:
>>>
dropWhileEnd isSpace "foo\n"
"foo"
>>>
dropWhileEnd isSpace "foo bar"
"foo bar"
dropWhileEnd isSpace ("foo\n" ++ undefined) == "foo" ++ undefined
Since: base-4.5.0.0
span :: (a -> Bool) -> [a] -> ([a], [a]) Source #
span
, applied to a predicate p
and a list xs
, returns a tuple where
first element is longest prefix (possibly empty) of xs
of elements that
satisfy p
and second element is the remainder of the list:
>>>
span (< 3) [1,2,3,4,1,2,3,4]
([1,2],[3,4,1,2,3,4])>>>
span (< 9) [1,2,3]
([1,2,3],[])>>>
span (< 0) [1,2,3]
([],[1,2,3])
break :: (a -> Bool) -> [a] -> ([a], [a]) Source #
break
, applied to a predicate p
and a list xs
, returns a tuple where
first element is longest prefix (possibly empty) of xs
of elements that
do not satisfy p
and second element is the remainder of the list:
>>>
break (> 3) [1,2,3,4,1,2,3,4]
([1,2,3],[4,1,2,3,4])>>>
break (< 9) [1,2,3]
([],[1,2,3])>>>
break (> 9) [1,2,3]
([1,2,3],[])
stripPrefix :: Eq a => [a] -> [a] -> Maybe [a] Source #
\(\mathcal{O}(\min(m,n))\). The stripPrefix
function drops the given
prefix from a list. It returns Nothing
if the list did not start with the
prefix given, or Just
the list after the prefix, if it does.
>>>
stripPrefix "foo" "foobar"
Just "bar"
>>>
stripPrefix "foo" "foo"
Just ""
>>>
stripPrefix "foo" "barfoo"
Nothing
>>>
stripPrefix "foo" "barfoobaz"
Nothing
group :: Eq a => [a] -> [[a]] Source #
The group
function takes a list and returns a list of lists such
that the concatenation of the result is equal to the argument. Moreover,
each sublist in the result is non-empty and all elements are equal
to the first one. For example,
>>>
group "Mississippi"
["M","i","ss","i","ss","i","pp","i"]
group
is a special case of groupBy
, which allows the programmer to supply
their own equality test.
It's often preferable to use Data.List.NonEmpty.
group
,
which provides type-level guarantees of non-emptiness of inner lists.
inits :: [a] -> [[a]] Source #
The inits
function returns all initial segments of the argument,
shortest first. For example,
>>>
inits "abc"
["","a","ab","abc"]
Note that inits
has the following strictness property:
inits (xs ++ _|_) = inits xs ++ _|_
In particular,
inits _|_ = [] : _|_
inits
is semantically equivalent to
,
but under the hood uses a queue to amortize costs of map
reverse
. scanl
(flip
(:)) []reverse
.
Predicates
isPrefixOf :: Eq a => [a] -> [a] -> Bool Source #
\(\mathcal{O}(\min(m,n))\). The isPrefixOf
function takes two lists and
returns True
iff the first list is a prefix of the second.
>>>
"Hello" `isPrefixOf` "Hello World!"
True>>>
"Hello" `isPrefixOf` "Wello Horld!"
False
For the result to be True
, the first list must be finite;
False
, however, results from any mismatch:
>>>
[0..] `isPrefixOf` [1..]
False>>>
[0..] `isPrefixOf` [0..99]
False>>>
[0..99] `isPrefixOf` [0..]
True>>>
[0..] `isPrefixOf` [0..]
* Hangs forever *
isSuffixOf :: Eq a => [a] -> [a] -> Bool Source #
The isSuffixOf
function takes two lists and returns True
iff
the first list is a suffix of the second.
>>>
"ld!" `isSuffixOf` "Hello World!"
True>>>
"World" `isSuffixOf` "Hello World!"
False
The second list must be finite; however the first list may be infinite:
>>>
[0..] `isSuffixOf` [0..99]
False>>>
[0..99] `isSuffixOf` [0..]
* Hangs forever *
isInfixOf :: Eq a => [a] -> [a] -> Bool Source #
The isInfixOf
function takes two lists and returns True
iff the first list is contained, wholly and intact,
anywhere within the second.
>>>
isInfixOf "Haskell" "I really like Haskell."
True>>>
isInfixOf "Ial" "I really like Haskell."
False
For the result to be True
, the first list must be finite;
for the result to be False
, the second list must be finite:
>>>
[20..50] `isInfixOf` [0..]
True>>>
[0..] `isInfixOf` [20..50]
False>>>
[0..] `isInfixOf` [0..]
* Hangs forever *
Searching lists
Searching by equality
elem :: Eq a => a -> [a] -> Bool infix 4 Source #
elem
is the list membership predicate, usually written in infix form,
e.g., x `elem` xs
. For the result to be
False
, the list must be finite; True
, however, results from an element
equal to x
found at a finite index of a finite or infinite list.
>>>
3 `elem` []
False>>>
3 `elem` [1,2]
False>>>
3 `elem` [1,2,3,4,5]
True>>>
3 `elem` [1..]
True>>>
3 `elem` [4..]
* Hangs forever *
Searching with a predicate
filter :: (a -> Bool) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). filter
, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
>>>
filter odd [1, 2, 3]
[1,3]
partition :: (a -> Bool) -> [a] -> ([a], [a]) Source #
The partition
function takes a predicate and a list, and returns
the pair of lists of elements which do and do not satisfy the
predicate, respectively; i.e.,
partition p xs == (filter p xs, filter (not . p) xs)
>>>
partition (`elem` "aeiou") "Hello World!"
("eoo","Hll Wrld!")
Indexing lists
These functions treat a list xs
as a indexed collection,
with indices ranging from 0 to
.length
xs - 1
(!!) :: HasCallStack => [a] -> Int -> a infixl 9 Source #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex
,
which takes an index of any integral type.
>>>
['a', 'b', 'c'] !! 0
'a'>>>
['a', 'b', 'c'] !! 2
'c'>>>
['a', 'b', 'c'] !! 3
*** Exception: Prelude.!!: index too large>>>
['a', 'b', 'c'] !! (-1)
*** Exception: Prelude.!!: negative index
WARNING: This function is partial. You can use atMay instead.
elemIndices :: Eq a => a -> [a] -> [Int] Source #
The elemIndices
function extends elemIndex
, by returning the
indices of all elements equal to the query element, in ascending order.
>>>
elemIndices 'o' "Hello World"
[4,7]
findIndices :: (a -> Bool) -> [a] -> [Int] Source #
The findIndices
function extends findIndex
, by returning the
indices of all elements satisfying the predicate, in ascending order.
>>>
findIndices (`elem` "aeiou") "Hello World!"
[1,4,7]
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)] Source #
\(\mathcal{O}(\min(m,n))\). zip
takes two lists and returns a list of
corresponding pairs.
>>>
zip [1, 2] ['a', 'b']
[(1,'a'),(2,'b')]
If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>
zip [1] ['a', 'b']
[(1,'a')]>>>
zip [1, 2] ['a']
[(1,'a')]>>>
zip [] [1..]
[]>>>
zip [1..] []
[]
zip
is right-lazy:
>>>
zip [] undefined
[]>>>
zip undefined []
*** Exception: Prelude.undefined ...
zip
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #
\(\mathcal{O}(\min(m,n))\). zipWith
generalises zip
by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example,
is applied to two lists to produce the list of
corresponding sums:zipWith
(+)
>>>
zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]
zipWith
is right-lazy:
>>>
let f = undefined
>>>
zipWith f [] undefined
[]
zipWith
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #
The zipWith3
function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith
.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] Source #
zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h] Source #
unzip :: [(a, b)] -> ([a], [b]) Source #
unzip
transforms a list of pairs into a list of first components
and a list of second components.
>>>
unzip []
([],[])>>>
unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")
Special lists
Functions on strings
lines :: String -> [String] Source #
Splits the argument into a list of lines stripped of their terminating
\n
characters. The \n
terminator is optional in a final non-empty
line of the argument string.
For example:
>>>
lines "" -- empty input contains no lines
[]>>>
lines "\n" -- single empty line
[""]>>>
lines "one" -- single unterminated line
["one"]>>>
lines "one\n" -- single non-empty line
["one"]>>>
lines "one\n\n" -- second line is empty
["one",""]>>>
lines "one\ntwo" -- second line is unterminated
["one","two"]>>>
lines "one\ntwo\n" -- two non-empty lines
["one","two"]
When the argument string is empty, or ends in a \n
character, it can be
recovered by passing the result of lines
to the unlines
function.
Otherwise, unlines
appends the missing terminating \n
. This makes
unlines . lines
idempotent:
(unlines . lines) . (unlines . lines) = (unlines . lines)
"Set" operations
nub :: Eq a => [a] -> [a] Source #
\(\mathcal{O}(n^2)\). The nub
function removes duplicate elements from a
list. In particular, it keeps only the first occurrence of each element. (The
name nub
means `essence'.) It is a special case of nubBy
, which allows
the programmer to supply their own equality test.
>>>
nub [1,2,3,4,3,2,1,2,4,3,5]
[1,2,3,4,5]
If the order of outputs does not matter and there exists instance Ord a
,
it's faster to use
map
Data.List.NonEmpty.
head
. Data.List.NonEmpty.
group
. sort
,
which takes only \(\mathcal{O}(n \log n)\) time.
(\\) :: Eq a => [a] -> [a] -> [a] infix 5 Source #
The \\
function is list difference (non-associative).
In the result of xs
\\
ys
, the first occurrence of each element of
ys
in turn (if any) has been removed from xs
. Thus
(xs ++ ys) \\ xs == ys
.
>>>
"Hello World!" \\ "ell W"
"Hoorld!"
It is a special case of deleteFirstsBy
, which allows the programmer
to supply their own equality test.
The second list must be finite, but the first may be infinite.
>>>
take 5 ([0..] \\ [2..4])
[0,1,5,6,7]>>>
take 5 ([0..] \\ [2..])
* Hangs forever *
union :: Eq a => [a] -> [a] -> [a] Source #
The union
function returns the list union of the two lists.
It is a special case of unionBy
, which allows the programmer to supply
their own equality test.
For example,
>>>
"dog" `union` "cow"
"dogcw"
If equal elements are present in both lists, an element from the first list will be used. If the second list contains equal elements, only the first one will be retained:
>>>
import Data.Semigroup
>>>
union [Arg () "dog"] [Arg () "cow"]
[Arg () "dog"]>>>
union [] [Arg () "dog", Arg () "cow"]
[Arg () "dog"]
However if the first list contains duplicates, so will the result:
>>>
"coot" `union` "duck"
"cootduk">>>
"duck" `union` "coot"
"duckot"
union
is productive even if both arguments are infinite.
intersect :: Eq a => [a] -> [a] -> [a] Source #
The intersect
function takes the list intersection of two lists.
It is a special case of intersectBy
, which allows the programmer to
supply their own equality test.
For example,
>>>
[1,2,3,4] `intersect` [2,4,6,8]
[2,4]
If equal elements are present in both lists, an element from the first list will be used, and all duplicates from the second list quashed:
>>>
import Data.Semigroup
>>>
intersect [Arg () "dog"] [Arg () "cow", Arg () "cat"]
[Arg () "dog"]
However if the first list contains duplicates, so will the result.
>>>
"coot" `intersect` "heron"
"oo">>>
"heron" `intersect` "coot"
"o"
If the second list is infinite, intersect
either hangs
or returns its first argument in full. Otherwise if the first list
is infinite, intersect
might be productive:
>>>
intersect [100..] [0..]
[100,101,102,103...>>>
intersect [0] [1..]
* Hangs forever *>>>
intersect [1..] [0]
* Hangs forever *>>>
intersect (cycle [1..3]) [2]
[2,2,2,2...
Ordered lists
sort :: Ord a => [a] -> [a] Source #
The sort
function implements a stable sorting algorithm.
It is a special case of sortBy
, which allows the programmer to supply
their own comparison function.
Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.
>>>
sort [1,6,4,3,2,5]
[1,2,3,4,5,6]
The argument must be finite.
sortOn :: Ord b => (a -> b) -> [a] -> [a] Source #
Sort a list by comparing the results of a key function applied to each
element.
is equivalent to sortOn
f
, but has the
performance advantage of only evaluating sortBy
(comparing
f)f
once for each element in the
input list. This is called the decorate-sort-undecorate paradigm, or
Schwartzian transform.
Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.
>>>
sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]
The argument must be finite.
Since: base-4.8.0.0
insert :: Ord a => a -> [a] -> [a] Source #
\(\mathcal{O}(n)\). The insert
function takes an element and a list and
inserts the element into the list at the first position where it is less than
or equal to the next element. In particular, if the list is sorted before the
call, the result will also be sorted. It is a special case of insertBy
,
which allows the programmer to supply their own comparison function.
>>>
insert 4 [1,2,3,5,6,7]
[1,2,3,4,5,6,7]
Generalized functions
The "By
" operations
By convention, overloaded functions have a non-overloaded
counterpart whose name is suffixed with `By
'.
It is often convenient to use these functions together with
on
, for instance
.sortBy
(compare
`on` fst
)
User-supplied equality (replacing an Eq
context)
The predicate is assumed to define an equivalence.
deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] Source #
The deleteFirstsBy
function takes a predicate and two lists and
returns the first list with the first occurrence of each element of
the second list removed. This is the non-overloaded version of (\\)
.
The second list must be finite, but the first may be infinite.
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] Source #
The intersectBy
function is the non-overloaded version of intersect
.
It is productive for infinite arguments only if the first one
is a subset of the second.
groupBy :: (a -> a -> Bool) -> [a] -> [[a]] Source #
The groupBy
function is the non-overloaded version of group
.
When a supplied relation is not transitive, it is important to remember that equality is checked against the first element in the group, not against the nearest neighbour:
>>>
groupBy (\a b -> b - a < 5) [0..19]
[[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14],[15,16,17,18,19]]
It's often preferable to use Data.List.NonEmpty.
groupBy
,
which provides type-level guarantees of non-emptiness of inner lists.
User-supplied comparison (replacing an Ord
context)
The function is assumed to define a total ordering.
sortBy :: (a -> a -> Ordering) -> [a] -> [a] Source #
The sortBy
function is the non-overloaded version of sort
.
The argument must be finite.
>>>
sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]
The supplied comparison relation is supposed to be reflexive and antisymmetric,
otherwise, e. g., for _ _ -> GT
, the ordered list simply does not exist.
The relation is also expected to be transitive: if it is not then sortBy
might fail to find an ordered permutation, even if it exists.
insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a] Source #
\(\mathcal{O}(n)\). The non-overloaded version of insert
.
maximumBy :: (a -> a -> Ordering) -> [a] -> a Source #
The maximumBy
function is the non-overloaded version of maximum
,
which takes a comparison function and a list
and returns the greatest element of the list by the comparison function.
The list must be finite and non-empty.
We can use this to find the longest entry of a list:
>>>
maximumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]
"Longest"
minimumBy :: (a -> a -> Ordering) -> [a] -> a Source #
The minimumBy
function is the non-overloaded version of minimum
,
which takes a comparison function and a list
and returns the least element of the list by the comparison function.
The list must be finite and non-empty.
We can use this to find the shortest entry of a list:
>>>
minimumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]
"!"
The "generic
" operations
The prefix `generic
' indicates an overloaded function that
is a generalized version of a Prelude function.
genericLength :: Num i => [a] -> i Source #
\(\mathcal{O}(n)\). The genericLength
function is an overloaded version
of length
. In particular, instead of returning an Int
, it returns any
type which is an instance of Num
. It is, however, less efficient than
length
.
>>>
genericLength [1, 2, 3] :: Int
3>>>
genericLength [1, 2, 3] :: Float
3.0
Users should take care to pick a return type that is wide enough to contain
the full length of the list. If the width is insufficient, the overflow
behaviour will depend on the (+)
implementation in the selected Num
instance. The following example overflows because the actual list length
of 200 lies outside of the Int8
range of -128..127
.
>>>
genericLength [1..200] :: Int8
-56
genericTake :: Integral i => i -> [a] -> [a] Source #
The genericTake
function is an overloaded version of take
, which
accepts any Integral
value as the number of elements to take.
genericDrop :: Integral i => i -> [a] -> [a] Source #
The genericDrop
function is an overloaded version of drop
, which
accepts any Integral
value as the number of elements to drop.
genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) Source #
The genericSplitAt
function is an overloaded version of splitAt
, which
accepts any Integral
value as the position at which to split.
genericIndex :: Integral i => [a] -> i -> a Source #
The genericIndex
function is an overloaded version of !!
, which
accepts any Integral
value as the index.
genericReplicate :: Integral i => i -> a -> [a] Source #
The genericReplicate
function is an overloaded version of replicate
,
which accepts any Integral
value as the number of repetitions to make.