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.

## Synopsis

- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- singleton :: a -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl1 :: (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]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [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 :: 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]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- insert :: Ord a => a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- maximumBy :: (a -> a -> Ordering) -> [a] -> a
- minimumBy :: (a -> a -> Ordering) -> [a] -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]

# Basic functions

(++) :: [a] -> [a] -> [a] infixr 5 Source #

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

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

`>>>`

1`head [1, 2, 3]`

`>>>`

1`head [1..]`

`>>>`

*** Exception: Prelude.head: empty list`head []`

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

`>>>`

3`last [1, 2, 3]`

`>>>`

* Hangs forever *`last [1..]`

`>>>`

*** Exception: Prelude.last: empty list`last []`

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

`>>>`

[2,3]`tail [1, 2, 3]`

`>>>`

[]`tail [1]`

`>>>`

*** Exception: Prelude.tail: empty list`tail []`

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

`>>>`

[1,2]`init [1, 2, 3]`

`>>>`

[]`init [1]`

`>>>`

*** Exception: Prelude.init: empty list`init []`

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

`>>>`

True`null []`

`>>>`

False`null [1]`

`>>>`

False`null [1..]`

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

`>>>`

0`length []`

`>>>`

3`length ['a', 'b', 'c']`

`>>>`

* Hangs forever *`length [1..]`

# List transformations

map :: (a -> b) -> [a] -> [b] Source #

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

`f xs`

is the list obtained by applying `f`

to
each element of `xs`

, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]

`>>>`

[2,3,4]`map (+1) [1, 2, 3]`

reverse :: [a] -> [a] Source #

`reverse`

`xs`

returns the elements of `xs`

in reverse order.
`xs`

must be finite.

`>>>`

[]`reverse []`

`>>>`

[42]`reverse [42]`

`>>>`

[7,5,2]`reverse [2,5,7]`

`>>>`

* Hangs forever *`reverse [1..]`

intersperse :: a -> [a] -> [a] Source #

\(\mathcal{O}(n)\). The `intersperse`

function takes an element and a list
and `intersperses' that element between the elements of the list. For
example,

`>>>`

"a,b,c,d,e"`intersperse ',' "abcde"`

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.

`>>>`

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

transpose :: [[a]] -> [[a]] Source #

The `transpose`

function transposes the rows and columns of its argument.
For example,

`>>>`

[[1,4],[2,5],[3,6]]`transpose [[1,2,3],[4,5,6]]`

If some of the rows are shorter than the following rows, their elements are skipped:

`>>>`

[[10,20,30],[11,31],[32]]`transpose [[10,11],[20],[],[30,31,32]]`

subsequences :: [a] -> [[a]] Source #

The `subsequences`

function returns the list of all subsequences of the argument.

`>>>`

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

permutations :: [a] -> [[a]] Source #

The `permutations`

function returns the list of all permutations of the argument.

`>>>`

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

# Reducing lists (folds)

foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b Source #

`foldl`

, applied to a binary operator, a starting value (typically
the left-identity of the operator), and a list, reduces the list
using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

The list must be finite.

`>>>`

10`foldl (+) 0 [1..4]`

`>>>`

42`foldl (+) 42 []`

`>>>`

90`foldl (-) 100 [1..4]`

`>>>`

"dcbafoo"`foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']`

`>>>`

* Hangs forever *`foldl (+) 0 [1..]`

foldl1 :: (a -> a -> a) -> [a] -> a Source #

`foldl1`

is a variant of `foldl`

that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike `foldl`

, the accumulated value must be of the same type as the list elements.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

`foldr`

, applied to a binary operator, a starting value (typically
the right-identity of the operator), and a list, reduces the list
using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

foldr1 :: (a -> a -> a) -> [a] -> a Source #

`foldr1`

is a variant of `foldr`

that has no starting value argument,
and thus must be applied to non-empty lists. Note that unlike `foldr`

, the accumulated value must be of the same type as the list elements.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

*** Exception: stack overflow`force $ foldr1 (+) [1..]`

## Special folds

concat :: [[a]] -> [a] Source #

Concatenate a list of lists.

`>>>`

[]`concat []`

`>>>`

[42]`concat [[42]]`

`>>>`

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

and :: [Bool] -> Bool Source #

`and`

returns the conjunction of a Boolean list. For the result to be
`True`

, the list must be finite; `False`

, however, results from a `False`

value at a finite index of a finite or infinite list.

`>>>`

True`and []`

`>>>`

True`and [True]`

`>>>`

False`and [False]`

`>>>`

False`and [True, True, False]`

`>>>`

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

`>>>`

* Hangs forever *`and (repeat True)`

`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.

`>>>`

False`or []`

`>>>`

True`or [True]`

`>>>`

False`or [False]`

`>>>`

True`or [True, True, False]`

`>>>`

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

`>>>`

* Hangs forever *`or (repeat False)`

any :: (a -> Bool) -> [a] -> Bool Source #

Applied to a predicate and a list, `any`

determines if any element
of the list satisfies the predicate. For the result to be
`False`

, the list must be finite; `True`

, however, results from a `True`

value for the predicate applied to an element at a finite index of a finite
or infinite list.

`>>>`

False`any (> 3) []`

`>>>`

False`any (> 3) [1,2]`

`>>>`

True`any (> 3) [1,2,3,4,5]`

`>>>`

True`any (> 3) [1..]`

`>>>`

* Hangs forever *`any (> 3) [0, -1..]`

all :: (a -> Bool) -> [a] -> Bool Source #

Applied to a predicate and a list, `all`

determines if all elements
of the list satisfy the predicate. For the result to be
`True`

, the list must be finite; `False`

, however, results from a `False`

value for the predicate applied to an element at a finite index of a finite
or infinite list.

`>>>`

True`all (> 3) []`

`>>>`

False`all (> 3) [1,2]`

`>>>`

False`all (> 3) [1,2,3,4,5]`

`>>>`

False`all (> 3) [1..]`

`>>>`

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

sum :: Num a => [a] -> a Source #

The `sum`

function computes the sum of a finite list of numbers.

`>>>`

0`sum []`

`>>>`

42`sum [42]`

`>>>`

55`sum [1..10]`

`>>>`

7.8`sum [4.1, 2.0, 1.7]`

`>>>`

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

product :: Num a => [a] -> a Source #

The `product`

function computes the product of a finite list of numbers.

`>>>`

1`product []`

`>>>`

42`product [42]`

`>>>`

3628800`product [1..10]`

`>>>`

13.939999999999998`product [4.1, 2.0, 1.7]`

`>>>`

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

maximum :: Ord a => [a] -> a Source #

`maximum`

returns the maximum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of `maximumBy`

, which allows the
programmer to supply their own comparison function.

`>>>`

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

`>>>`

42`maximum [42]`

`>>>`

55`maximum [55, -12, 7, 0, -89]`

`>>>`

* Hangs forever *`maximum [1..]`

minimum :: Ord a => [a] -> a Source #

`minimum`

returns the minimum value from a list,
which must be non-empty, finite, and of an ordered type.
It is a special case of `minimumBy`

, which allows the
programmer to supply their own comparison function.

`>>>`

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

`>>>`

42`minimum [42]`

`>>>`

-89`minimum [55, -12, 7, 0, -89]`

`>>>`

* Hangs forever *`minimum [1..]`

# Building lists

## Scans

scanl :: (b -> a -> b) -> b -> [a] -> [b] Source #

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

is similar to `foldl`

, but returns a list of
successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs

`>>>`

[0,1,3,6,10]`scanl (+) 0 [1..4]`

`>>>`

[42]`scanl (+) 42 []`

`>>>`

[100,99,97,94,90]`scanl (-) 100 [1..4]`

`>>>`

["foo","afoo","bafoo","cbafoo","dcbafoo"]`scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']`

`>>>`

* Hangs forever *`scanl (+) 0 [1..]`

scanl1 :: (a -> a -> a) -> [a] -> [a] Source #

\(\mathcal{O}(n)\). `scanl1`

is a variant of `scanl`

that has no starting
value argument:

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

`>>>`

[1,3,6,10]`scanl1 (+) [1..4]`

`>>>`

[]`scanl1 (+) []`

`>>>`

[1,-1,-4,-8]`scanl1 (-) [1..4]`

`>>>`

[True,False,False,False]`scanl1 (&&) [True, False, True, True]`

`>>>`

[False,False,True,True]`scanl1 (||) [False, False, True, True]`

`>>>`

* Hangs forever *`scanl1 (+) [1..]`

scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #

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

is the right-to-left dual of `scanl`

. Note that the order of parameters on the accumulating function are reversed compared to `scanl`

.
Also note that

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

`>>>`

[10,9,7,4,0]`scanr (+) 0 [1..4]`

`>>>`

[42]`scanr (+) 42 []`

`>>>`

[98,-97,99,-96,100]`scanr (-) 100 [1..4]`

`>>>`

["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]`scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']`

`>>>`

*** Exception: stack overflow`force $ scanr (+) 0 [1..]`

scanr1 :: (a -> a -> a) -> [a] -> [a] Source #

\(\mathcal{O}(n)\). `scanr1`

is a variant of `scanr`

that has no starting
value argument.

`>>>`

[10,9,7,4]`scanr1 (+) [1..4]`

`>>>`

[]`scanr1 (+) []`

`>>>`

[-2,3,-1,4]`scanr1 (-) [1..4]`

`>>>`

[False,False,True,True]`scanr1 (&&) [True, False, True, True]`

`>>>`

[True,True,False,False]`scanr1 (||) [True, True, False, False]`

`>>>`

*** Exception: stack overflow`force $ scanr1 (+) [1..]`

## Accumulating maps

## Infinite lists

iterate :: (a -> a) -> a -> [a] Source #

`iterate`

`f x`

returns an infinite list of repeated applications
of `f`

to `x`

:

iterate f x == [x, f x, f (f x), ...]

Note that `iterate`

is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See `iterate'`

for a strict
variant of this function.

`>>>`

[True,False,True,False...`take 10 $ iterate not True`

`>>>`

[42,45,48,51,54,57,60,63...`take 10 $ iterate (+3) 42`

`repeat`

`x`

is an infinite list, with `x`

the value of every element.

`>>>`

[17,17,17,17,17,17,17,17,17...`take 20 $ repeat 17`

replicate :: Int -> a -> [a] Source #

`replicate`

`n x`

is a list of length `n`

with `x`

the value of
every element.
It is an instance of the more general `genericReplicate`

,
in which `n`

may be of any integral type.

`>>>`

[]`replicate 0 True`

`>>>`

[]`replicate (-1) True`

`>>>`

[True,True,True,True]`replicate 4 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.

`>>>`

*** Exception: Prelude.cycle: empty list`cycle []`

`>>>`

[42,42,42,42,42,42,42,42,42,42...`take 20 $ cycle [42]`

`>>>`

[2,5,7,2,5,7,2,5,7,2,5,7...`take 20 $ cycle [2, 5, 7]`

## Unfolding

unfoldr :: (b -> Maybe (a, b)) -> b -> [a] Source #

The `unfoldr`

function is a `dual' to `foldr`

: while `foldr`

reduces a list to a summary value, `unfoldr`

builds a list from
a seed value. The function takes the element and returns `Nothing`

if it is done producing the list or returns `Just`

`(a,b)`

, in which
case, `a`

is a prepended to the list and `b`

is used as the next
element in a recursive call. For example,

iterate f == unfoldr (\x -> Just (x, f x))

In some cases, `unfoldr`

can undo a `foldr`

operation:

unfoldr f' (foldr f z xs) == xs

if the following holds:

f' (f x y) = Just (x,y) f' z = Nothing

A simple use of unfoldr:

`>>>`

[10,9,8,7,6,5,4,3,2,1]`unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10`

# 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

`>>>`

"Hello"`take 5 "Hello World!"`

`>>>`

[1,2,3]`take 3 [1,2,3,4,5]`

`>>>`

[1,2]`take 3 [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

`>>>`

"World!"`drop 6 "Hello World!"`

`>>>`

[4,5]`drop 3 [1,2,3,4,5]`

`>>>`

[]`drop 3 [1,2]`

`>>>`

[]`drop 3 []`

`>>>`

[1,2]`drop (-1) [1,2]`

`>>>`

[1,2]`drop 0 [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:

`>>>`

("Hello ","World!")`splitAt 6 "Hello World!"`

`>>>`

([1,2,3],[4,5])`splitAt 3 [1,2,3,4,5]`

`>>>`

([1],[2,3])`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]`

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`

.

`>>>`

[1,2]`takeWhile (< 3) [1,2,3,4,1,2,3,4]`

`>>>`

[1,2,3]`takeWhile (< 9) [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:

`>>>`

"foo"`dropWhileEnd isSpace "foo\n"`

`>>>`

"foo bar"`dropWhileEnd isSpace "foo bar"`

dropWhileEnd isSpace ("foo\n" ++ undefined) == "foo" ++ undefined

*Since: base-4.5.0.0*

span :: (a -> Bool) -> [a] -> ([a], [a]) Source #

`span`

, applied to a predicate `p`

and a list `xs`

, returns a tuple where
first element is longest prefix (possibly empty) of `xs`

of elements that
satisfy `p`

and second element is the remainder of the list:

`>>>`

([1,2],[3,4,1,2,3,4])`span (< 3) [1,2,3,4,1,2,3,4]`

`>>>`

([1,2,3],[])`span (< 9) [1,2,3]`

`>>>`

([],[1,2,3])`span (< 0) [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:

`>>>`

([1,2,3],[4,1,2,3,4])`break (> 3) [1,2,3,4,1,2,3,4]`

`>>>`

([],[1,2,3])`break (< 9) [1,2,3]`

`>>>`

([1,2,3],[])`break (> 9) [1,2,3]`

stripPrefix :: Eq a => [a] -> [a] -> Maybe [a] Source #

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

function drops the given
prefix from a list. It returns `Nothing`

if the list did not start with the
prefix given, or `Just`

the list after the prefix, if it does.

`>>>`

Just "bar"`stripPrefix "foo" "foobar"`

`>>>`

Just ""`stripPrefix "foo" "foo"`

`>>>`

Nothing`stripPrefix "foo" "barfoo"`

`>>>`

Nothing`stripPrefix "foo" "barfoobaz"`

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,

`>>>`

["M","i","ss","i","ss","i","pp","i"]`group "Mississippi"`

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 #

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

function takes two lists and
returns `True`

iff the first list is a prefix of the second.

`>>>`

True`"Hello" `isPrefixOf` "Hello World!"`

`>>>`

False`"Hello" `isPrefixOf` "Wello Horld!"`

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.

`>>>`

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

`>>>`

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

isSubsequenceOf :: Eq a => [a] -> [a] -> Bool Source #

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.

is equivalent to `isSubsequenceOf`

x y

.`elem`

x (`subsequences`

y)

#### Examples

`>>>`

True`isSubsequenceOf "GHC" "The Glorious Haskell Compiler"`

`>>>`

True`isSubsequenceOf ['a','d'..'z'] ['a'..'z']`

`>>>`

False`isSubsequenceOf [1..10] [10,9..0]`

*Since: base-4.8.0.0*

# Searching lists

## Searching by equality

elem :: Eq a => a -> [a] -> Bool infix 4 Source #

`elem`

is the list membership predicate, usually written in infix form,
e.g., `x `elem` xs`

. For the result to be
`False`

, the list must be finite; `True`

, however, results from an element
equal to `x`

found at a finite index of a finite or infinite list.

`>>>`

False`3 `elem` []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

* Hangs forever *`3 `elem` [4..]`

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #

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

`key assocs`

looks up a key in an association
list.

`>>>`

Nothing`lookup 2 []`

`>>>`

Nothing`lookup 2 [(1, "first")]`

`>>>`

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

## Searching with a predicate

filter :: (a -> Bool) -> [a] -> [a] Source #

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

, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

`>>>`

[1,3]`filter odd [1, 2, 3]`

partition :: (a -> Bool) -> [a] -> ([a], [a]) Source #

The `partition`

function takes a predicate and a list, and returns
the pair of lists of elements which do and do not satisfy the
predicate, respectively; i.e.,

partition p xs == (filter p xs, filter (not . p) xs)

`>>>`

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

# 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.

`>>>`

'a'`['a', 'b', 'c'] !! 0`

`>>>`

'c'`['a', 'b', 'c'] !! 2`

`>>>`

*** Exception: Prelude.!!: index too large`['a', 'b', 'c'] !! 3`

`>>>`

*** Exception: Prelude.!!: negative index`['a', 'b', 'c'] !! (-1)`

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.

`>>>`

[4,7]`elemIndices 'o' "Hello World"`

findIndices :: (a -> Bool) -> [a] -> [Int] Source #

The `findIndices`

function extends `findIndex`

, by returning the
indices of all elements satisfying the predicate, in ascending order.

`>>>`

[1,4,7]`findIndices (`elem` "aeiou") "Hello World!"`

# Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)] Source #

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

takes two lists and returns a list of
corresponding pairs.

`>>>`

[(1,'a'),(2,'b')]`zip [1, 2] ['a', '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:

`>>>`

[(1,'a')]`zip [1] ['a', 'b']`

`>>>`

[(1,'a')]`zip [1, 2] ['a']`

`>>>`

[]`zip [] [1..]`

`>>>`

[]`zip [1..] []`

`zip`

is right-lazy:

`>>>`

[]`zip [] undefined`

`>>>`

*** Exception: Prelude.undefined ...`zip undefined []`

`zip`

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

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

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

generalises `zip`

by zipping with the
function given as the first argument, instead of a tupling function.

zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]

For example,

is applied to two lists to produce the list of
corresponding sums:`zipWith`

(+)

`>>>`

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

`zipWith`

is right-lazy:

`>>>`

`let f = undefined`

`>>>`

[]`zipWith f [] undefined`

`zipWith`

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

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #

The `zipWith3`

function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to `zipWith`

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

zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]

zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] Source #

zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h] Source #

unzip :: [(a, b)] -> ([a], [b]) Source #

`unzip`

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

`>>>`

([],[])`unzip []`

`>>>`

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

# 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.

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"`

`>>>`

["one"]`lines "one"`

`>>>`

["one"]`lines "one\n"`

`>>>`

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

`>>>`

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

`>>>`

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

Thus

contains at least as many elements as newlines in `lines`

s`s`

.

words :: String -> [String] Source #

`words`

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

`>>>`

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

## "Set" operations

nub :: Eq a => [a] -> [a] Source #

\(\mathcal{O}(n^2)\). The `nub`

function removes duplicate elements from a
list. In particular, it keeps only the first occurrence of each element. (The
name `nub`

means `essence'.) It is a special case of `nubBy`

, which allows
the programmer to supply their own equality test.

`>>>`

[1,2,3,4,5]`nub [1,2,3,4,3,2,1,2,4,3,5]`

(\\) :: 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.

`>>>`

"Hoorld!"`"Hello World!" \\ "ell W"`

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,

`>>>`

"dogcw"`"dog" `union` "cow"`

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,

`>>>`

[2,4]`[1,2,3,4] `intersect` [2,4,6,8]`

If the first list contains duplicates, so will the result.

`>>>`

[2,2,4]`[1,2,2,3,4] `intersect` [6,4,4,2]`

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.

Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.

`>>>`

[(1,"Hello"),(2,"world"),(4,"!")]`sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]`

*Since: base-4.8.0.0*

insert :: Ord a => a -> [a] -> [a] Source #

\(\mathcal{O}(n)\). The `insert`

function takes an element and a list and
inserts the element into the list at the first position where it is less than
or equal to the next element. In particular, if the list is sorted before the
call, the result will also be sorted. It is a special case of `insertBy`

,
which allows the programmer to supply their own comparison function.

`>>>`

[1,2,3,4,5,6,7]`insert 4 [1,2,3,5,6,7]`

# Generalized functions

## The "`By`

" operations

By convention, overloaded functions have a non-overloaded
counterpart whose name is suffixed with ``By`

'.

It is often convenient to use these functions together with
`on`

, for instance

.`sortBy`

(`compare`

``on``

`fst`

)

### User-supplied equality (replacing an `Eq`

context)

The predicate is assumed to define an equivalence.

deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a] Source #

The `deleteFirstsBy`

function takes a predicate and two lists and
returns the first list with the first occurrence of each element of
the second list removed.

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.

insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a] Source #

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

.

maximumBy :: (a -> a -> Ordering) -> [a] -> a Source #

The `maximumBy`

function 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:

`>>>`

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

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.

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

`>>>`

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

## The "`generic`

" operations

The prefix ``generic`

' indicates an overloaded function that
is a generalized version of a Prelude function.

genericLength :: Num i => [a] -> i Source #

\(\mathcal{O}(n)\). The `genericLength`

function is an overloaded version
of `length`

. In particular, instead of returning an `Int`

, it returns any
type which is an instance of `Num`

. It is, however, less efficient than
`length`

.

`>>>`

3`genericLength [1, 2, 3] :: Int`

`>>>`

3.0`genericLength [1, 2, 3] :: Float`

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`

.

`>>>`

-56`genericLength [1..200] :: Int8`

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.