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])
- null :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
- foldl1' :: (a -> a -> a) -> [a] -> a
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- sum :: (Foldable t, Num a) => t a -> a
- product :: (Foldable t, Num a) => t a -> a
- maximum :: forall a. (Foldable t, Ord a) => t a -> a
- minimum :: forall a. (Foldable t, Ord a) => t a -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: [a] -> [a]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- dropWhileEnd :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
- group :: Eq a => [a] -> [[a]]
- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- isSuffixOf :: Eq a => [a] -> [a] -> Bool
- isInfixOf :: Eq a => [a] -> [a] -> Bool
- isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
- elem :: (Foldable t, Eq a) => a -> t a -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- find :: Foldable t => (a -> Bool) -> t a -> Maybe a
- filter :: (a -> Bool) -> [a] -> [a]
- partition :: (a -> Bool) -> [a] -> ([a], [a])
- (!!) :: [a] -> Int -> a
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- findIndices :: (a -> Bool) -> [a] -> [Int]
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- nub :: Eq a => [a] -> [a]
- delete :: Eq a => a -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- insert :: Ord a => a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]

# Basic functions

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

Append two lists, i.e.,

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

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

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

null :: Foldable t => t a -> Bool Source #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

*Since: base-4.8.0.0*

length :: Foldable t => t a -> Int Source #

Returns the size/length of a finite structure as an `Int`

. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.

*Since: base-4.8.0.0*

# 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, ...]

`>>>`

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

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

`reverse`

`xs`

returns the elements of `xs`

in reverse order.
`xs`

must be finite.

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 :: Foldable t => (b -> a -> b) -> b -> t a -> b Source #

Left-associative fold of a structure.

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. This means that `foldl'`

will
diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to
use `foldl'`

instead of `foldl`

. The reason for this is that 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 \(\mathcal{O}(n)\) 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`

foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b Source #

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
list to a single, monolithic result (e.g. `length`

).

For a general `Foldable`

structure this should be semantically identical
to,

foldl' f z =`foldl'`

f z .`toList`

*Since: base-4.6.0.0*

foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b Source #

Right-associative fold of a structure.

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,
`foldr`

can produce a terminating expression from an infinite list.

For a general `Foldable`

structure this should be semantically identical
to,

foldr f z =`foldr`

f z .`toList`

## Special folds

concat :: Foldable t => t [a] -> [a] Source #

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

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #

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

any :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether any element of the structure satisfies the predicate.

all :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether all elements of the structure satisfy the predicate.

sum :: (Foldable t, Num a) => t a -> a Source #

The `sum`

function computes the sum of the numbers of a structure.

*Since: base-4.8.0.0*

product :: (Foldable t, Num a) => t a -> a Source #

The `product`

function computes the product of the numbers of a
structure.

*Since: base-4.8.0.0*

maximum :: forall a. (Foldable t, Ord a) => t a -> a Source #

The largest element of a non-empty structure.

*Since: base-4.8.0.0*

minimum :: forall a. (Foldable t, Ord a) => t a -> a Source #

The least element of a non-empty structure.

*Since: base-4.8.0.0*

# Building lists

## Scans

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

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

## Accumulating maps

mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) Source #

mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) Source #

## Infinite lists

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

`replicate`

`n x`

is a list of length `n`

with `x`

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

,
in which `n`

may be of any integral type.

`cycle`

ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.

## Unfolding

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

The `unfoldr`

function is a `dual' to `foldr`

: while `foldr`

reduces a list to a summary value, `unfoldr`

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

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

`(a,b)`

, in which
case, `a`

is a prepended to the list and `b`

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

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

In some cases, `unfoldr`

can undo a `foldr`

operation:

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

if the following holds:

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

A simple use of unfoldr:

`>>>`

[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

take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []

It is an instance of the more general `genericTake`

,
in which `n`

may be of any integral type.

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

`drop`

`n xs`

returns the suffix of `xs`

after the first `n`

elements, or `[]`

if `n > `

:`length`

xs

drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]

It is an instance of the more general `genericDrop`

,
in which `n`

may be of any integral type.

splitAt :: Int -> [a] -> ([a], [a]) Source #

`splitAt`

`n xs`

returns a tuple where first element is `xs`

prefix of
length `n`

and second element is the remainder of the list:

splitAt 6 "Hello World!" == ("Hello ","World!") splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5]) splitAt 1 [1,2,3] == ([1],[2,3]) splitAt 3 [1,2,3] == ([1,2,3],[]) splitAt 4 [1,2,3] == ([1,2,3],[]) splitAt 0 [1,2,3] == ([],[1,2,3]) splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to `(`

when `take`

n xs, `drop`

n xs)`n`

is not `_|_`

(`splitAt _|_ xs = _|_`

).
`splitAt`

is an instance of the more general `genericSplitAt`

,
in which `n`

may be of any integral type.

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

`takeWhile`

, applied to a predicate `p`

and a list `xs`

, returns the
longest prefix (possibly empty) of `xs`

of elements that satisfy `p`

:

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

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

The `dropWhileEnd`

function drops the largest suffix of a list
in which the given predicate holds for all elements. For example:

`>>>`

"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:

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

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

`break`

, applied to a predicate `p`

and a list `xs`

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

of elements that
*do not satisfy* `p`

and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])

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

\(\mathcal{O}(\min(m,n))\). 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 :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #

Does the element occur in the structure?

*Since: base-4.8.0.0*

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

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

`key assocs`

looks up a key in an association
list.

`>>>`

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 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.

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.

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.

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. 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:

zipWith f [] _|_ = []

`zipWith`

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

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

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

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

`unzip`

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

# Special lists

## Functions on strings

lines :: String -> [String] Source #

`lines`

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

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 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 :: Foldable t => (a -> a -> Ordering) -> t a -> a Source #

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

minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a Source #

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

## The "`generic`

" operations

The prefix ``generic`

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

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

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

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.