Safe Haskell | Trustworthy |
---|---|

Language | Haskell2010 |

This module reexports functinons to work with list, `NonEmpty`

and String types.

## Synopsis

- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
- transpose :: [[a]] -> [[a]]
- tails :: [a] -> [[a]]
- subsequences :: [a] -> [[a]]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- permutations :: [a] -> [[a]]
- isPrefixOf :: Eq a => [a] -> [a] -> Bool
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- inits :: [a] -> [[a]]
- genericTake :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericReplicate :: Integral i => i -> a -> [a]
- genericLength :: Num i => [a] -> i
- genericDrop :: Integral i => i -> [a] -> [a]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- take :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- reverse :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- iterate :: (a -> a) -> a -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- cycle :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- data NonEmpty a = a :| [a]
- tail :: NonEmpty a -> [a]
- nonEmpty :: [a] -> Maybe (NonEmpty a)
- last :: NonEmpty a -> a
- init :: NonEmpty a -> [a]
- head :: NonEmpty a -> a
- groupWith :: (Foldable f, Eq b) => (a -> b) -> f a -> [NonEmpty a]
- groupBy :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a]
- groupAllWith :: Ord b => (a -> b) -> [a] -> [NonEmpty a]
- group :: (Foldable f, Eq a) => f a -> [NonEmpty a]
- sortWith :: Ord b => (a -> b) -> [a] -> [a]

# Documentation

(++) :: [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.

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

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

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

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

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:

`>>>`

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

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]] #

The `subsequences`

function returns the list of all subsequences of the argument.

`>>>`

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

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 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*

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

The `permutations`

function returns the list of all permutations of the argument.

`>>>`

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

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

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

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

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

`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"]`

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.

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.

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.

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

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

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.

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

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

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

`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')]`

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`

.

`>>>`

[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]`

`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.

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:

`>>>`

("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.

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

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

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

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

`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..]`

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.

`>>>`

[]`replicate 0 True`

`>>>`

[]`replicate (-1) True`

`>>>`

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

`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`

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), ...]

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`

`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.

`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]`

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:

`>>>`

([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]`

Non-empty (and non-strict) list type.

*Since: base-4.9.0.0*

a :| [a] infixr 5 |

#### Instances

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

`groupAllWith`

operates like `groupWith`

, but sorts the list
first so that each equivalence class has, at most, one list in the
output

group :: (Foldable f, Eq a) => f a -> [NonEmpty a] #

The `group`

function takes a stream and returns a list of
streams such that flattening the resulting list is equal to the
argument. Moreover, each stream in the resulting list
contains only equal elements. For example, in list notation:

'group' $ 'cycle' "Mississippi" = "M" : "i" : "ss" : "i" : "ss" : "i" : "pp" : "i" : "M" : "i" : ...