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.

\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.

\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.

\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.

\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.

\(\mathcal{O}(1)\). Decompose a list into its head and tail. If the list is empty, returns Nothing. If the list is non-empty, returns Just (x, xs), where x is the head of the list and xs its tail.

Since: base-4.8.0.0

\(\mathcal{O}(1)\). Test whether a list is empty.

\(\mathcal{O}(n)\). 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.

\(\mathcal{O}(n)\). 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]

reverse xs returns the elements of xs in reverse order. xs must be finite.

\(\mathcal{O}(n)\). 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 xs xss is equivalent to (concat (intersperse xs xss)). It inserts the list xs in between the lists in xss and concatenates the result.

>>> intercalate ", " ["Lorem", "ipsum", "dolor"]
"Lorem, ipsum, dolor"

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]]

The subsequences function returns the list of all subsequences of the argument.

>>> subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]

The permutations function returns the list of all permutations of the argument.

>>> permutations "abc"
["abc","bac","cba","bca","cab","acb"]

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.

A strict version of foldl.

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.

A strict version of foldl1

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 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.

Concatenate a list of lists.

Map a function over a list and concatenate the results.

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.

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.

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.

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.

The sum function computes the sum of a finite list of numbers.

The product function computes the product of a finite list of numbers.

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.

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.

\(\mathcal{O}(n)\). 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.

\(\mathcal{O}(n)\). A strictly accumulating version of scanl

\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting value argument.

The mapAccumL function behaves like a combination of map and foldl; it applies a function to each element of a list, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new list.

The mapAccumR function behaves like a combination of map and foldr; it applies a function to each element of a list, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new list.

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.

iterate' is the strict version of iterate.

It ensures that the result of each application of force to weak head normal form before proceeding.

repeat x is an infinite list, with x the value of every element.

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.

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]

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 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 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 (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

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] == []

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

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, 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])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

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],[])

break p is equivalent to span (not . p).

\(\mathcal{O}(\min(m,n))\). 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

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.

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 _|_ = [] : _|_

\(\mathcal{O}(n)\). The tails function returns all final segments of the argument, longest first. For example,

>>> tails "abc"
["abc","bc","c",""]

Note that tails has the following strictness property: tails _|_ = _|_ : _|_

\(\mathcal{O}(\min(m,n))\). 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

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.

>>> "ld!" `isSuffixOf` "Hello World!"
True

>>> "World" `isSuffixOf` "Hello World!"
False

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

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.

notElem is the negation of elem.

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list.

>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

The find function takes a predicate and a list and returns the first element in the list matching the predicate, or Nothing if there is no such element.

>>> find (> 4) [1..]
Just 5

>>> find (< 0) [1..10]
Nothing

\(\mathcal{O}(n)\). 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]

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)

>>> partition (`elem` "aeiou") "Hello World!"
("eoo","Hll Wrld!")

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

The elemIndex function returns the index of the first element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.

>>> elemIndex 4 [0..]
Just 4

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]

The findIndex function takes a predicate and a list and returns the index of the first element in the list satisfying the predicate, or Nothing if there is no such element.

>>> findIndex isSpace "Hello World!"
Just 5

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]

\(\mathcal{O}(\min(m,n))\). 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 short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip4 function takes four lists and returns a list of quadruples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip5 function takes five lists and returns a list of five-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip6 function takes six lists and returns a list of six-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zip7 function takes seven lists and returns a list of seven-tuples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zipWith4 function takes a function which combines four elements, as well as four lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zipWith5 function takes a function which combines five elements, as well as five lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zipWith6 function takes a function which combines six elements, as well as six lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

The zipWith7 function takes a function which combines seven elements, as well as seven lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

unzip transforms a list of pairs into a list of first components and a list of second components.

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

The unzip4 function takes a list of quadruples and returns four lists, analogous to unzip.

The unzip5 function takes a list of five-tuples and returns five lists, analogous to unzip.

The unzip6 function takes a list of six-tuples and returns six lists, analogous to unzip.

The unzip7 function takes a list of seven-tuples and returns seven lists, analogous to unzip.

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]

>>> lines "\n"
[""]

>>> lines "one"
["one"]

>>> lines "one\n"
["one"]

>>> lines "one\n\n"
["one",""]

>>> lines "one\ntwo"
["one","two"]

>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

unwords is an inverse operation to words. It joins words with separating spaces.

>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"

\(\mathcal{O}(n^2)\). 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]

\(\mathcal{O}(n)\). delete x removes the first occurrence of x from its list argument. For example,

>>> delete 'a' "banana"
"bnana"

It is a special case of deleteBy, which allows the programmer to supply their own equality test.

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 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.

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.

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]

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.

Elements are arranged from 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,"!")]

Since: base-4.8.0.0

\(\mathcal{O}(n)\). 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]

The nubBy function behaves just like nub, except it uses a user-supplied equality predicate instead of the overloaded == function.

>>> nubBy (\x y -> mod x 3 == mod y 3) [1,2,4,5,6]
[1,2,6]

\(\mathcal{O}(n)\). The deleteBy function behaves like delete, but takes a user-supplied equality predicate.

>>> deleteBy (<=) 4 [1..10]
[1,2,3,5,6,7,8,9,10]

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.

The unionBy function is the non-overloaded version of union.

The intersectBy function is the non-overloaded version of intersect.

The groupBy function is the non-overloaded version of group.

The sortBy function is the non-overloaded version of sort.

>>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

\(\mathcal{O}(n)\). The non-overloaded version of insert.

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.

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"

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.

We can use this to find the shortest entry of a list:

>>> minimumBy (\x y -> compare (length x) (length y)) ["Hello", "World", "!", "Longest", "bar"]
"!"

\(\mathcal{O}(n)\). 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

The genericTake function is an overloaded version of take, which accepts any Integral value as the number of elements to take.

The genericDrop function is an overloaded version of drop, which accepts any Integral value as the number of elements to drop.

The genericSplitAt function is an overloaded version of splitAt, which accepts any Integral value as the position at which to split.

The genericIndex function is an overloaded version of !!, which accepts any Integral value as the index.

The genericReplicate function is an overloaded version of replicate, which accepts any Integral value as the number of repetitions to make.