Copyright | (c) The University of Glasgow 2001 |
---|---|

License | BSD-style (see the file libraries/base/LICENSE) |

Maintainer | libraries@haskell.org |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell2010 |

This legacy module provides access to the list-specialised operations of Data.List. This module may go away again in future GHC versions and is provided as transitional tool to access some of the list-specialised operations that had to be generalised due to the implementation of the Foldable/Traversable-in-Prelude Proposal (FTP).

If the operations needed are available in GHC.List, it's recommended to avoid importing this module and use GHC.List instead for now.

*Since: 4.8.0.0*

- (++) :: [a] -> [a] -> [a]
- head :: [a] -> a
- last :: [a] -> a
- tail :: [a] -> [a]
- init :: [a] -> [a]
- uncons :: [a] -> Maybe (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]
- 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
- 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 #

Append two lists, i.e.,

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

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

Return all the elements of a list except the last one. The list must be non-empty.

*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.

# List transformations

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

`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, ...]

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

The `intersperse`

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

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

intercalate :: [a] -> [[a]] -> [a] #

`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.

The `transpose`

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

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

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

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

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

The `subsequences`

function returns the list of all subsequences of the argument.

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

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

The `permutations`

function returns the list of all permutations of the argument.

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

# Reducing lists (folds)

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

`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.

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

`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)...)

## Special folds

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

The `product`

function computes the product of a finite list of numbers.

# Building lists

## Scans

## Accumulating maps

## Infinite lists

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

`iterate`

`f x`

returns an infinite list of repeated applications
of `f`

to `x`

:

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

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

`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] #

The `unfoldr`

function is a `dual' to `foldr`

: while `foldr`

reduces a list to a summary value, `unfoldr`

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

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

`(a,b)`

, in which
case, `a`

is a prepended to the list and `b`

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

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

In some cases, `unfoldr`

can undo a `foldr`

operation:

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

if the following holds:

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

A simple use of unfoldr:

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

# Sublists

## Extracting sublists

`take`

`n`

, applied to a list `xs`

, returns the prefix of `xs`

of length `n`

, or `xs`

itself if `n > `

:`length`

xs

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

It is an instance of the more general `genericTake`

,
in which `n`

may be of any integral type.

`drop`

`n xs`

returns the suffix of `xs`

after the first `n`

elements, or `[]`

if `n > `

:`length`

xs

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

It is an instance of the more general `genericDrop`

,
in which `n`

may be of any integral type.

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

`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] #

`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] #

The `dropWhileEnd`

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

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

*Since: 4.5.0.0*

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

`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]) #

`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] #

The `stripPrefix`

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

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

the list after the prefix, if it does.

stripPrefix "foo" "foobar" == Just "bar" stripPrefix "foo" "foo" == Just "" stripPrefix "foo" "barfoo" == Nothing stripPrefix "foo" "barfoobaz" == Nothing

group :: Eq a => [a] -> [[a]] #

The `group`

function takes a list and returns a list of lists such
that the concatenation of the result is equal to the argument. Moreover,
each sublist in the result contains only equal elements. For example,

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

It is a special case of `groupBy`

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

## Predicates

isPrefixOf :: Eq a => [a] -> [a] -> Bool #

The `isPrefixOf`

function takes two lists and returns `True`

iff the first list is a prefix of the second.

isSuffixOf :: Eq a => [a] -> [a] -> Bool #

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.

# Searching lists

## Searching by equality

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

`lookup`

`key assocs`

looks up a key in an association list.

## Searching with a predicate

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

`filter`

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

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

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

The `partition`

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

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

# Indexing lists

These functions treat a list `xs`

as a indexed collection,
with indices ranging from 0 to

.`length`

xs - 1

(!!) :: [a] -> Int -> a infixl 9 #

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] #

The `elemIndices`

function extends `elemIndex`

, by returning the
indices of all elements equal to the query element, in ascending order.

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

The `findIndices`

function extends `findIndex`

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

# Zipping and unzipping lists

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

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

`unzip`

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

# Special lists

## Functions on strings

`lines`

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

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

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

Thus

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

s`s`

.

`words`

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

## "Set" operations

(\\) :: Eq a => [a] -> [a] -> [a] infix 5 #

The `\\`

function is list difference (non-associative).
In the result of `xs`

`\\`

`ys`

, the first occurrence of each element of
`ys`

in turn (if any) has been removed from `xs`

. Thus

(xs ++ ys) \\ xs == ys.

It is a special case of `deleteFirstsBy`

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

union :: Eq a => [a] -> [a] -> [a] #

The `union`

function returns the list union of the two lists.
For example,

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

Duplicates, and elements of the first list, are removed from the
the second list, but if the first list contains duplicates, so will
the result.
It is a special case of `unionBy`

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

intersect :: Eq a => [a] -> [a] -> [a] #

The `intersect`

function takes the list intersection of two lists.
For example,

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

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

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

It is a special case of `intersectBy`

, which allows the programmer to
supply their own equality test. If the element is found in both the first
and the second list, the element from the first list will be used.

## Ordered lists

sortOn :: Ord b => (a -> b) -> [a] -> [a] #

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.

*Since: 4.8.0.0*

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

The `insert`

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

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

# Generalized functions

## The "`By`

" operations

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

'.

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

, for instance

.`sortBy`

(`compare`

`on` `fst`

)

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

context)

The predicate is assumed to define an equivalence.

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

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] #

The `intersectBy`

function is the non-overloaded version of `intersect`

.

### User-supplied comparison (replacing an `Ord`

context)

The function is assumed to define a total ordering.

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

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.

minimumBy :: (a -> a -> Ordering) -> [a] -> a #

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.

## The "`generic`

" operations

The prefix ``generic`

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

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

The `genericLength`

function is an overloaded version of `length`

. In
particular, instead of returning an `Int`

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

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

.

genericTake :: Integral i => i -> [a] -> [a] #

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] #

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]) #

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 #

The `genericIndex`

function is an overloaded version of `!!`

, which
accepts any `Integral`

value as the index.

genericReplicate :: Integral i => i -> a -> [a] #

The `genericReplicate`

function is an overloaded version of `replicate`

,
which accepts any `Integral`

value as the number of repetitions to make.