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.

This function takes linear time in the number of elements of the first list. Thus it is better to associate repeated applications of (++) to the right (which is the default behaviour): xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs. For the same reason concat = foldr (++) [] has linear performance, while foldl (++) [] is prone to quadratic slowdown.

\(\mathcal{O}(1)\). 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.

\(\mathcal{O}(n)\). 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. Consider using unsnoc instead.

\(\mathcal{O}(1)\). 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.

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

>>> init [1, 2, 3]
[1,2]
>>> init [1]
[]
>>> init []
*** Exception: Prelude.init: empty list

WARNING: This function is partial. Consider using unsnoc instead.

\(\mathcal{O}(1)\). 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.

>>> uncons []
Nothing
>>> uncons [1]
Just (1,[])
>>> uncons [1, 2, 3]
Just (1,[2,3])

Since: base-4.8.0.0

\(\mathcal{O}(n)\). Decompose a list into init and last.

• If the list is empty, returns Nothing.
• If the list is non-empty, returns Just (xs, x), where xs is the initial part of the list and x is its last element.

>>> unsnoc []
Nothing
>>> unsnoc [1]
Just ([],1)
>>> unsnoc [1, 2, 3]
Just ([1,2],3)

Laziness:

>>> fst <$> unsnoc [undefined]
Just []
>>> head . fst <$> unsnoc (1 : undefined)
Just *** Exception: Prelude.undefined
>>> head . fst <$> unsnoc (1 : 2 : undefined)
Just 1

unsnoc is dual to uncons: for a finite list xs

unsnoc xs = (\(hd, tl) -> (reverse tl, hd)) <$> uncons (reverse xs)

Since: base-4.19.0.0

Construct a list from a single element.

>>> singleton True
[True]

Since: base-4.15.0.0

Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.

Examples

>>> null []
True

>>> null [1]
False

>>> null [1..]
False

Since: base-4.8.0.0

Returns the size/length of a finite structure as an Int. The default implementation just counts elements starting with the leftmost. Instances for structures that can compute the element count faster than via element-by-element counting, should provide a specialised implementation.

Examples

>>> length []
0

>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

Since: base-4.8.0.0

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

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

intersperse has the following laziness properties:

>>> take 1 (intersperse undefined ('a' : undefined))
"a"
>>> take 2 (intersperse ',' ('a' : undefined))
"a*** Exception: Prelude.undefined

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"

intercalate has the following laziness properties:

>>> take 5 (intercalate undefined ("Lorem" : undefined))
"Lorem"
>>> take 6 (intercalate ", " ("Lorem" : undefined))
"Lorem*** Exception: Prelude.undefined

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 *

transpose is lazy:

>>> take 1 (transpose ['a' : undefined, 'b' : undefined])
["ab"]

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"]

subsequences does not look ahead unless it must:

>>> take 1 (subsequences undefined)
[[]]
>>> take 2 (subsequences ('a' : undefined))
["","a"]

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 permutations xs starts with those permutations that permute take n xs and keep 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]

Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.

In the case of lists, foldl, when 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

Note that to produce the outermost application of the operator the entire input list must be traversed. Like all left-associative folds, foldl will diverge if given an infinite list.

If you want an efficient strict left-fold, you probably want to use foldl' instead of foldl. The reason for this is that the latter does not force the inner results (e.g. z `f` x1 in the above example) before applying them to the operator (e.g. to (`f` x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to:

foldl f z = foldl f z . toList

Examples

>>> foldl (+) 42 [1,2,3,4]
52

>>> foldl (\acc c -> c : acc) "abcd" "efgh"
"hgfeabcd"

>>> foldl (\a _ -> a) 0 $ repeat 1
* Hangs forever *

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to Weak Head Normal Form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single strict result (e.g. sum).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

foldl1 f = foldl1 f . toList

Examples

>>> foldl1 (+) [1..4]
10

>>> foldl1 (+) []
*** Exception: Prelude.foldl1: empty list

>>> foldl1 (+) Nothing
*** Exception: foldl1: empty structure

>>> foldl1 (-) [1..4]
-8

>>> foldl1 (&&) [True, False, True, True]
False

>>> foldl1 (||) [False, False, True, True]
True

>>> foldl1 (+) [1..]
* Hangs forever *

A strict version of foldl1.

Right-associative fold of a structure, lazy in the accumulator.

In the case of lists, foldr, when 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)...)

Note that since the head of the resulting expression is produced by an application of the operator to the first element of the list, given an operator lazy in its right argument, foldr can produce a terminating expression from an unbounded list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

Examples

>>> foldr (||) False [False, True, False]
True

>>> foldr (||) False []
False

>>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
"foodcba"

>>> foldr (||) False (True : repeat False)
True

>>> foldr (||) False (repeat False ++ [True])
* Hangs forever *

>>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
[1,4,7,10,13]

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

Examples

>>> foldr1 (+) [1..4]
10

>>> foldr1 (+) []
Exception: Prelude.foldr1: empty list

>>> foldr1 (+) Nothing
*** Exception: foldr1: empty structure

>>> foldr1 (-) [1..4]
-2

>>> foldr1 (&&) [True, False, True, True]
False

>>> foldr1 (||) [False, False, True, True]
True

>>> foldr1 (+) [1..]
* Hangs forever *

The concatenation of all the elements of a container of lists.

Examples

>>> concat (Just [1, 2, 3])
[1,2,3]

>>> concat (Left 42)
[]

>>> concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

Map a function over all the elements of a container and concatenate the resulting lists.

Examples

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]

>>> concatMap (take 3) (Just [1..])
[1,2,3]

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Examples

>>> and []
True

>>> and [True]
True

>>> and [False]
False

>>> and [True, True, False]
False

>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False

>>> and (repeat True)
* Hangs forever *

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Examples

>>> or []
False

>>> or [True]
True

>>> or [False]
False

>>> or [True, True, False]
True

>>> or (True : repeat False) -- Infinite list [True,False,False,False,...
True

>>> or (repeat False)
* Hangs forever *

Determines whether any element of the structure satisfies the predicate.

Examples

>>> 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 *

Determines whether all elements of the structure satisfy the predicate.

Examples

>>> 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 *

The sum function computes the sum of the numbers of a structure.

Examples

>>> sum []
0

>>> sum [42]
42

>>> sum [1..10]
55

>>> sum [4.1, 2.0, 1.7]
7.8

>>> sum [1..]
* Hangs forever *

Since: base-4.8.0.0

The product function computes the product of the numbers of a structure.

Examples

>>> product []
1

>>> product [42]
42

>>> product [1..10]
3628800

>>> product [4.1, 2.0, 1.7]
13.939999999999998

>>> product [1..]
* Hangs forever *

Since: base-4.8.0.0

The largest element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

Examples

>>> maximum [1..10]
10

>>> maximum []
*** Exception: Prelude.maximum: empty list

>>> maximum Nothing
*** Exception: maximum: empty structure

Since: base-4.8.0.0

The least element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

Examples

>>> minimum [1..10]
1

>>> minimum []
*** Exception: Prelude.minimum: empty list

>>> minimum Nothing
*** Exception: minimum: empty structure

Since: base-4.8.0.0

\(\mathcal{O}(n)\). 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"]
>>> take 10 (scanl (+) 0 [1..])
[0,1,3,6,10,15,21,28,36,45]
>>> take 1 (scanl undefined 'a' undefined)
"a"

\(\mathcal{O}(n)\). A strict 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, ...]

>>> 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]
>>> take 10 (scanl1 (+) [1..])
[1,3,6,10,15,21,28,36,45,55]
>>> take 1 (scanl1 undefined ('a' : undefined))
"a"

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

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

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

Examples

>>> mapAccumL (\a b -> (a + b, a)) 0 [1..10]
(55,[0,1,3,6,10,15,21,28,36,45])

>>> mapAccumL (\a b -> (a <> show b, a)) "0" [1..5]
("012345",["0","01","012","0123","01234"])

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

Examples

>>> mapAccumR (\a b -> (a + b, a)) 0 [1..10]
(55,[54,52,49,45,40,34,27,19,10,0])

>>> mapAccumR (\a b -> (a <> show b, a)) "0" [1..5]
("054321",["05432","0543","054","05","0"])

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,True,False,True,False,True,False]
>>> take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63,66,69]
>>> take 1 $ iterate undefined 42
[42]

iterate' is the strict version of iterate.

It forces the result of each application of the function to weak head normal form (WHNF) before proceeding.

>>> take 1 $ iterate' undefined 42
*** Exception: Prelude.undefined

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 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 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
>>> take 10 (cycle [42])
[42,42,42,42,42,42,42,42,42,42]
>>> take 10 (cycle [2, 5, 7])
[2,5,7,2,5,7,2,5,7,2]
>>> take 1 (cycle (42 : undefined))
[42]

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]

Laziness:

>>> take 1 (unfoldr (\x -> Just (x, undefined)) 'a')
"a"

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]
[]

Laziness:

>>> take 0 undefined
[]
>>> take 1 (1 : undefined)
[1]

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) unless n is _|_: splitAt _|_ xs = _|_, not (_|_, _|_)).

The first component of the tuple is produced lazily:

>>> fst (splitAt 0 undefined)
[]
>>> take 1 (fst (splitAt 10 (1 : undefined)))
[1]

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]
[]

Laziness:

>>> takeWhile (const False) undefined
*** Exception: Prelude.undefined
>>> takeWhile (const False) (undefined : undefined)
[]
>>> take 1 (takeWhile (const True) (1 : undefined))
[1]

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

This function is lazy in spine, but strict in elements, which makes it different from reverse . dropWhile p . reverse, which is strict in spine, but lazy in elements. For instance:

>>> take 1 (dropWhileEnd (< 0) (1 : undefined))
[1]
>>> take 1 (reverse $ dropWhile (< 0) $ reverse (1 : undefined))
*** Exception: Prelude.undefined

but on the other hand

>>> last (dropWhileEnd (< 0) [undefined, 1])
*** Exception: Prelude.undefined
>>> last (reverse $ dropWhile (< 0) $ reverse [undefined, 1])
1

Since: base-4.5.0.0

span, applied to a predicate p and a list xs, returns a tuple where first element is the 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), even if p is _|_.

Laziness:

>>> span undefined []
([],[])
>>> fst (span (const False) undefined)
*** Exception: Prelude.undefined
>>> fst (span (const False) (undefined : undefined))
[]
>>> take 1 (fst (span (const True) (1 : undefined)))
[1]

span produces the first component of the tuple lazily:

>>> take 10 (fst (span (const True) [1..]))
[1,2,3,4,5,6,7,8,9,10]

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) and consequently to (takeWhile (not . p) xs, dropWhile (not . p) xs), even if p is _|_.

Laziness:

>>> break undefined []
([],[])
>>> fst (break (const True) undefined)
*** Exception: Prelude.undefined
>>> fst (break (const True) (undefined : undefined))
[]
>>> take 1 (fst (break (const False) (1 : undefined)))
[1]

break produces the first component of the tuple lazily:

>>> take 10 (fst (break (const False) [1..]))
[1,2,3,4,5,6,7,8,9,10]

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

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 map reverse . scanl (flip (:)) [], but under the hood uses a queue to amortize costs of reverse.

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

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 *

isPrefixOf shortcuts when the first argument is empty:

>>> isPrefixOf [] undefined
True

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 *

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 *

The isSubsequenceOf function takes two lists and returns True if all the elements of the first list occur, in order, in the second. The elements do not have to occur consecutively.

isSubsequenceOf x y is equivalent to elem x (subsequences y).

>>> isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
True
>>> isSubsequenceOf ['a','d'..'z'] ['a'..'z']
True
>>> isSubsequenceOf [1..10] [10,9..0]
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:

>>> [0,2..10] `isSubsequenceOf` [0..]
True
>>> [0..] `isSubsequenceOf` [0,2..10]
False
>>> [0,2..] `isSubsequenceOf` [0..]
* Hangs forever*

Since: base-4.8.0.0

Does the element occur in the structure?

Note: elem is often used in infix form.

Examples

>>> 3 `elem` []
False

>>> 3 `elem` [1,2]
False

>>> 3 `elem` [1,2,3,4,5]
True

>>> 3 `elem` [1..]
True

>>> 3 `elem` ([4..] ++ [3])
* Hangs forever *

Since: base-4.8.0.0

notElem is the negation of elem.

Examples

>>> 3 `notElem` []
True

>>> 3 `notElem` [1,2]
True

>>> 3 `notElem` [1,2,3,4,5]
False

>>> 3 `notElem` [1..]
False

>>> 3 `notElem` ([4..] ++ [3])
* Hangs forever *

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list. For the result to be Nothing, the list must be finite.

>>> lookup 2 []
Nothing
>>> lookup 2 [(1, "first")]
Nothing
>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Examples

>>> find (> 42) [0, 5..]
Just 45

>>> find (> 12) [1..7]
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 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!")

List index (subscript) operator, starting from 0. Returns Nothing if the index is out of bounds

>>> ['a', 'b', 'c'] !? 0
Just 'a'
>>> ['a', 'b', 'c'] !? 2
Just 'c'
>>> ['a', 'b', 'c'] !? 3
Nothing
>>> ['a', 'b', 'c'] !? (-1)
Nothing

This is the total variant of the partial !! operator.

WARNING: This function takes linear time in the index.

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, and should only be used if you are sure that the indexing will not fail. Otherwise, use !?.

WARNING: This function takes linear time in the index.

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. For the result to be Nothing, the list must be finite.

>>> 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. For the result to be Nothing, the list must be finite.

>>> 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 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.

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.

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, 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:

>>> 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.

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..]

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.

>>> unzip []
([],[])
>>> unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")

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

>>> unzip3 []
([],[],[])
>>> unzip3 [(1, 'a', True), (2, 'b', False)]
([1,2],"ab",[True,False])

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.

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)

words breaks a string up into a list of words, which were delimited by white space (as defined by isSpace). This function trims any white spaces at the beginning and at the end.

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

Appends a \n character to each input string, then concatenates the results. Equivalent to foldMap (s -> s ++ "\n").

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

Note that unlines . lines /= id when the input is not \n-terminated:

>>> unlines . lines $ "foo\nbar"
"foo\nbar\n"

unwords joins words with separating spaces (U+0020 SPACE).

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

unwords is neither left nor right inverse of words:

>>> words (unwords [" "])
[]
>>> unwords (words "foo\nbar")
"foo bar"

\(\mathcal{O}(n^2)\). 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 there exists instance Ord a, it's faster to use nubOrd from the containers package (link to the latest online documentation), which takes only \(\mathcal{O}(n \log d)\) time where d is the number of distinct elements in the list.

Another approach to speed up nub is to use map Data.List.NonEmpty.head . Data.List.NonEmpty.group . sort, which takes \(\mathcal{O}(n \log n)\) time, requires instance Ord a and doesn't preserve the order.

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

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.

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...

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.

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 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

\(\mathcal{O}(n)\). 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. This is the non-overloaded version of (\\).

The second list must be finite, but the first may be infinite.

The unionBy function is the non-overloaded version of union. Both arguments may be infinite.

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.

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.

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.

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

The largest element of a non-empty structure with respect to the given comparison function.

Examples

>>> maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
"Longest"

The least element of a non-empty structure with respect to the given comparison function.

Examples

>>> minimumBy (compare `on` length) ["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

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

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.