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 | Trustworthy |
Language | Haskell2010 |
Data.List
Contents
Description
Operations on lists.
- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [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 :: (b -> a -> b) -> b -> [a] -> b
- foldl' :: (b -> a -> b) -> b -> [a] -> b
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldl1' :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (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 => [a] -> a
- minimum :: Ord a => [a] -> a
- 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]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [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])
- (!!) :: [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]
- 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] 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.
Return all the elements of a list except the last one. The list must be non-empty.
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.
List transformations
map :: (a -> b) -> [a] -> [b] Source
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, ...]
reverse
xs
returns the elements of xs
in reverse order.
xs
must be finite.
intersperse :: a -> [a] -> [a] Source
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.
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]]
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"]
permutations :: [a] -> [[a]] Source
The permutations
function returns the list of all permutations of the argument.
permutations "abc" == ["abc","bac","cba","bca","cab","acb"]
Reducing lists (folds)
foldl :: (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.
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)...)
Special folds
product :: Num a => [a] -> a Source
The product
function computes the product of a finite list of numbers.
Building lists
Scans
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), ...]
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.
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.
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: 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
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 contains only equal elements. For example,
group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]
It is a special case of groupBy
, which allows the programmer to supply
their own equality test.
Predicates
isPrefixOf :: Eq a => [a] -> [a] -> Bool Source
The isPrefixOf
function takes two lists and returns True
iff the first list is a prefix of the second.
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.
Both lists must be finite.
Searching lists
Searching by equality
lookup :: Eq a => a -> [(a, b)] -> Maybe b Source
lookup
key assocs
looks up a key in an association list.
Searching with a predicate
filter :: (a -> Bool) -> [a] -> [a] Source
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]
partition :: (a -> Bool) -> [a] -> ([a], [a]) Source
The partition
function takes a predicate 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)
Indexing lists
These functions treat a list xs
as a indexed collection,
with indices ranging from 0 to
.length
xs - 1
(!!) :: [a] -> Int -> a 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.
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.
findIndices :: (a -> Bool) -> [a] -> [Int] Source
The findIndices
function extends findIndex
, by returning the
indices of all elements satisfying the predicate, in ascending order.
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)] Source
zip
takes two lists and returns a list of corresponding pairs.
If one input list is short, excess elements of the longer list are
discarded.
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.
Special lists
Functions on strings
lines :: String -> [String] Source
lines
breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
words :: String -> [String] Source
words
breaks a string up into a list of words, which were delimited
by white space.
"Set" operations
(\\) :: Eq a => [a] -> [a] -> [a] 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.
It is a special case of deleteFirstsBy
, which allows the programmer
to supply their own equality test.
union :: Eq a => [a] -> [a] -> [a] Source
The union
function returns the list union of the two lists.
For example,
"dog" `union` "cow" == "dogcw"
Duplicates, and elements of the first list, are removed from the
the second list, but if the first list contains duplicates, so will
the result.
It is a special case of unionBy
, which allows the programmer to supply
their own equality test.
intersect :: Eq a => [a] -> [a] -> [a] Source
The intersect
function takes the list intersection of two lists.
For example,
[1,2,3,4] `intersect` [2,4,6,8] == [2,4]
If the first list contains duplicates, so will the result.
[1,2,2,3,4] `intersect` [6,4,4,2] == [2,2,4]
It is a special case of intersectBy
, which allows the programmer to
supply their own equality test. If the element is found in both the first
and the second list, the element from the first list will be used.
Ordered lists
insert :: Ord a => a -> [a] -> [a] Source
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.
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.
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] Source
The intersectBy
function is the non-overloaded version of intersect
.
User-supplied comparison (replacing an Ord
context)
The function is assumed to define a total ordering.
maximumBy :: (a -> a -> Ordering) -> [a] -> a Source
The maximumBy
function 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.
minimumBy :: (a -> a -> Ordering) -> [a] -> a Source
The minimumBy
function 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.
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
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
.
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.