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 |
Operations on lists.
- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- null :: Foldable t => t a -> Bool
- length :: Foldable t => t 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 :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
- foldl1' :: (a -> a -> a) -> [a] -> a
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- sum :: (Foldable t, Num a) => t a -> a
- product :: (Foldable t, Num a) => t a -> a
- maximum :: forall a. (Foldable t, Ord a) => t a -> a
- minimum :: forall a. (Foldable t, Ord a) => t 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 :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- 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
- isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
- elem :: (Foldable t, Eq a) => a -> t a -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- find :: Foldable t => (a -> Bool) -> t 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]
- 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 :: Foldable t => (a -> a -> Ordering) -> t a -> a
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t 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.
Return all the elements of a list except the last one. The list must be non-empty.
null :: Foldable t => t a -> Bool Source
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
length :: Foldable t => t a -> Int Source
Returns the size/length of a finite structure as an Int
. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.
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]]
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]]
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)
Special folds
concat :: Foldable t => t [a] -> [a] Source
The concatenation of all the elements of a container of lists.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source
Map a function over all the elements of a container and concatenate the resulting lists.
any :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether any element of the structure satisfies the predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether all elements of the structure satisfy the predicate.
sum :: (Foldable t, Num a) => t a -> a Source
The sum
function computes the sum of the numbers of a structure.
product :: (Foldable t, Num a) => t a -> a Source
The product
function computes the product of the numbers of a
structure.
maximum :: forall a. (Foldable t, Ord a) => t a -> a Source
The largest element of a non-empty structure.
minimum :: forall a. (Foldable t, Ord a) => t a -> a Source
The least element of a non-empty structure.
Building lists
Scans
Accumulating maps
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) Source
mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) Source
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. The second list must be
finite.
isSubsequenceOf :: Eq a => [a] -> [a] -> Bool Source
The isSubsequenceOf
function takes two lists and returns True
if the
first list is a subsequence of the second list.
is equivalent to isSubsequenceOf
x y
.elem
x (subsequences
y)
Examples
>>>
isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
True>>>
isSubsequenceOf ['a','d'..'z'] ['a'..'z']
True>>>
isSubsequenceOf [1..10] [10,9..0]
False
Since: 4.8.0.0
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 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.
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
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] 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.
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
sortOn :: Ord b => (a -> b) -> [a] -> [a] Source
Sort a list by comparing the results of a key function applied to each
element. sortOn f
is equivalent to sortBy . comparing f
, but has the
performance advantage of only evaluating f
once for each element in the
input list. This is called the decorate-sort-undecorate paradigm, or
Schwartzian transform.
Since: 4.8.0.0
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 :: Foldable t => (a -> a -> Ordering) -> t a -> a Source
The largest element of a non-empty structure with respect to the given comparison function.
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a Source
The least element of a non-empty structure with respect to the given comparison function.
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.