rio-0.1.22.0: A standard library for Haskell

Safe Haskell | Safe-Inferred
Language | Haskell2010

RIO.List

Contents

- Basic functions
- List transformations
- Reducing lists (folds)
  - Special folds
- Building lists
  - Scans
  - Accumulating maps
  - Infinite lists
  - Unfolding
- Sublists
  - Extracting sublists
  - Predicates
- Searching lists
  - Searching by equality
  - Searching with a predicate
- Indexing lists
- Zipping and unzipping lists
- Special lists
  - Functions on strings
  - "Set" operations
  - Ordered lists
- Generalized functions
  - The "`By`" operations
    - User-supplied equality (replacing an `Eq` context)
    - User-supplied comparison (replacing an `Ord` context)
  - The "`generic`" operations

Description

`List`. Import as:

    import qualified RIO.List as L

This module does not export any partial functions. For those, see RIO.List.Partial

Synopsis

- (++) :: [a] -> [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- null :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- headMaybe :: [a] -> Maybe a
- lastMaybe :: [a] -> Maybe a
- tailMaybe :: [a] -> Maybe [a]
- initMaybe :: [a] -> Maybe [a]
- 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
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- 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
- maximumMaybe :: (Ord a, Foldable t) => t a -> Maybe a
- minimumMaybe :: (Ord a, Foldable t) => t a -> Maybe a
- maximumByMaybe :: Foldable t => (a -> a -> Ordering) -> t a -> Maybe a
- minimumByMaybe :: Foldable t => (a -> a -> Ordering) -> t a -> Maybe a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- mapAccumR :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- iterate :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: HasCallStack => [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]
- stripSuffix :: Eq a => [a] -> [a] -> Maybe [a]
- dropPrefix :: Eq a => [a] -> [a] -> [a]
- dropSuffix :: Eq a => [a] -> [a] -> [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])
- 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]
- linesCR :: 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]
- 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 #

`(++)` appends 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.

#### Performance considerations

Expand

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

#### Examples

Expand

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

    >>> [] ++ [1, 2, 3]
    [1,2,3]

    >>> [3, 2, 1] ++ []
    [3,2,1]

uncons :: [a] -> Maybe (a, [a]) #

\(\mathcal{O}(1)\). Decompose a list into its `head` and `tail`.

- If the list is empty, returns `Nothing`.
- If the list is non-empty, returns ``Just` (x, xs)`, where `x` is the `head` of the list and `xs` its `tail`.

@since base-4.8.0.0

#### Examples

Expand

    >>> uncons []
    Nothing

    >>> uncons [1]
    Just (1,[])

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

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

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

#### Examples

Expand

Basic usage:

    >>> null []
    True

    >>> null [1]
    False

`null` is expected to terminate even for infinite structures. The default implementation terminates provided the structure is bounded on the left (there is a leftmost element).

    >>> null [1..]
    False

@since base-4.8.0.0

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

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

#### Examples

Expand

Basic usage:

    >>> length []
    0

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

@since base-4.8.0.0

headMaybe :: [a] -> Maybe a #

Since: 0.1.3.0

lastMaybe :: [a] -> Maybe a #

Since: 0.1.3.0

tailMaybe :: [a] -> Maybe [a] #

Since: 0.1.3.0

initMaybe :: [a] -> Maybe [a] #

Since: 0.1.3.0

# List transformations

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

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

this means that `map id == id`

#### Examples

Expand

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

    >>> map id [1, 2, 3]
    [1,2,3]

    >>> map (\n -> 3 * n + 1) [1, 2, 3]
    [4,7,10]

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

\(\mathcal{O}(n)\). `reverse` `xs` returns the elements of `xs` in reverse order. `xs` must be finite.

#### Laziness

Expand

`reverse` is lazy in its elements.

    >>> head (reverse [undefined, 1])
    1

    >>> reverse (1 : 2 : undefined)
    *** Exception: Prelude.undefined

#### Examples

Expand

    >>> reverse []
    []

    >>> reverse [42]
    [42]

    >>> reverse [2,5,7]
    [7,5,2]

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

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.

#### Laziness

Expand

`intersperse` has the following properties

    >>> take 1 (intersperse undefined ('a' : undefined))
    "a"

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

#### Examples

Expand

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

    >>> intersperse 1 [3, 4, 5]
    [3,1,4,1,5]

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

`intercalate` `xs xss` is equivalent to `(`concat` (`intersperse` xs xss))`. It inserts the list `xs` in between the lists in `xss` and concatenates the result.

#### Laziness

Expand

`intercalate` has the following properties:

    >>> take 5 (intercalate undefined ("Lorem" : undefined))
    "Lorem"

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

#### Examples

Expand

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

    >>> intercalate [0, 1] [[2, 3], [4, 5, 6], []]
    [2,3,0,1,4,5,6,0,1]

    >>> intercalate [1, 2, 3] [[], []]
    [1,2,3]

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

The `transpose` function transposes the rows and columns of its argument.

#### Laziness

Expand

`transpose` is lazy in its elements

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

#### Examples

Expand

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

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

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

For this reason the outer list must be finite; otherwise `transpose` hangs:

    >>> transpose (repeat [])
    * Hangs forever *

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

The `subsequences` function returns the list of all subsequences of the argument.

#### Laziness

Expand

`subsequences` does not look ahead unless it must:

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

#### Examples

Expand

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

This function is productive on infinite inputs:

    >>> take 8 $ subsequences ['a'..]
    ["","a","b","ab","c","ac","bc","abc"]

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

The `permutations` function returns the list of all permutations of the argument.

Note that the order of permutations is not lexicographic. It satisfies the following property:

    map (take n) (take (product [1..n]) (permutations ([1..n] ++ undefined))) == permutations [1..n]

#### Laziness

Expand

The `permutations` function is maximally lazy: for each `n`, the value of ``permutations` xs` starts with those permutations that permute ``take` n xs` and keep ``drop` n xs`.

#### Examples

Expand

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

    >>> permutations [1, 2]
    [[1,2],[2,1]]

    >>> permutations []
    [[]]

This function is productive on infinite inputs:

    >>> take 6 $ map (take 3) $ permutations ['a'..]
    ["abc","bac","cba","bca","cab","acb"]

# Reducing lists (folds)

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

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

In the case of lists, `foldl`, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

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

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

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

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

    foldl f z = foldl f z . toList

#### Examples

Expand

The first example is a strict fold, which in practice is best performed with `foldl'`.

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

Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.

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

A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:

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

WARNING: When it comes to lists, you always want to use either `foldl'` or `foldr` instead.

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

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

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

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

    foldl' f z = foldl' f z . toList

@since base-4.6.0.0

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

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

In the case of lists, `foldr`, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

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

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

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

    foldr f z = foldr f z . toList

#### Examples

Expand

Basic usage:

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

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

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

##### Infinite structures

⚠️ Applying `foldr` to infinite structures usually doesn't terminate.

It may still terminate under one of the following conditions:

- the folding function is short-circuiting
- the folding function is lazy on its second argument

###### Short-circuiting

`(`||`)` short-circuits on `True` values, so the following terminates because there is a `True` value finitely far from the left side:

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

But the following doesn't terminate:

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

###### Laziness in the second argument

Applying `foldr` to infinite structures terminates when the operator is lazy in its second argument (the initial accumulator is never used in this case, and so could be left `undefined`, but `[]` is more clear):

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

## Special folds

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

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

#### Examples

Expand

Basic usage:

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

    >>> concat (Left 42)
    []

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

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

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

#### Examples

Expand

Basic usage:

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

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

and :: Foldable t => t Bool -> Bool #

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

#### Examples

Expand

Basic usage:

    >>> and []
    True

    >>> and [True]
    True

    >>> and [False]
    False

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

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

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

or :: Foldable t => t Bool -> Bool #

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

#### Examples

Expand

Basic usage:

    >>> or []
    False

    >>> or [True]
    True

    >>> or [False]
    False

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

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

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

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

Determines whether any element of the structure satisfies the predicate.

#### Examples

Expand

Basic usage:

    >>> any (> 3) []
    False

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

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

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

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

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

Determines whether all elements of the structure satisfy the predicate.

#### Examples

Expand

Basic usage:

    >>> all (> 3) []
    True

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

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

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

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

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

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

#### Examples

Expand

Basic usage:

    >>> sum []
    0

    >>> sum [42]
    42

    >>> sum [1..10]
    55

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

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

@since base-4.8.0.0

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

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

#### Examples

Expand

Basic usage:

    >>> product []
    1

    >>> product [42]
    42

    >>> product [1..10]
    3628800

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

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

@since base-4.8.0.0

maximumMaybe :: (Ord a, Foldable t) => t a -> Maybe a #

Since: 0.1.3.0

minimumMaybe :: (Ord a, Foldable t) => t a -> Maybe a #

Since: 0.1.3.0

maximumByMaybe :: Foldable t => (a -> a -> Ordering) -> t a -> Maybe a #

Since: 0.1.3.0

minimumByMaybe :: Foldable t => (a -> a -> Ordering) -> t a -> Maybe a #

Since: 0.1.3.0

# Building lists

## Scans

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

#### Examples

Expand

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

    >>> scanl (+) 42 []
    [42]

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

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

    >>> take 10 (scanl (+) 0 [1..])
    [0,1,3,6,10,15,21,28,36,45]

    >>> take 1 (scanl undefined 'a' undefined)
    "a"

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

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

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.

#### Examples

Expand

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

    >>> scanr (+) 42 []
    [42]

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

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

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

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

\(\mathcal{O}(n)\). `scanl1` is a variant of `scanl` that has no starting value argument:

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

#### Examples

Expand

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

    >>> scanl1 (+) []
    []

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

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

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

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

    >>> take 1 (scanl1 undefined ('a' : undefined))
    "a"

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

\(\mathcal{O}(n)\). `scanr1` is a variant of `scanr` that has no starting value argument.

#### Examples

Expand

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

    >>> scanr1 (+) []
    []

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

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

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

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

## Accumulating maps

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

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

#### Examples

Expand

Basic usage:

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

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

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

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

#### Examples

Expand

Basic usage:

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

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

## 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), ...]

#### Laziness

Expand

Note that `iterate` is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See `iterate'` for a strict variant of this function.

    >>> take 1 $ iterate undefined 42
    [42]

#### Examples

Expand

    >>> take 10 $ iterate not True
    [True,False,True,False,True,False,True,False,True,False]

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

`iterate id == `repeat``:

    >>> take 10 $ iterate id 1
    [1,1,1,1,1,1,1,1,1,1]

repeat :: a -> [a] #

`repeat` `x` is an infinite list, with `x` the value of every element.

#### Examples

Expand

    >>> take 10 $ repeat 17
    [17,17,17,17,17,17,17,17,17, 17]

    >>> repeat undefined
    [*** Exception: Prelude.undefined

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.

#### Examples

Expand

    >>> replicate 0 True
    []

    >>> replicate (-1) True
    []

    >>> replicate 4 True
    [True,True,True,True]

cycle :: HasCallStack => [a] -> [a] #

`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.

#### Examples

Expand

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

    >>> take 10 (cycle [42])
    [42,42,42,42,42,42,42,42,42,42]

    >>> take 10 (cycle [2, 5, 7])
    [2,5,7,2,5,7,2,5,7,2]

    >>> take 1 (cycle (42 : undefined))
    [42]

## 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

#### Laziness

Expand

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

#### Examples

Expand

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

    >>> take 10 $ unfoldr (\(x, y) -> Just (x, (y, x + y))) (0, 1)
    [0,1,1,2,3,5,8,13,21,54]

# Sublists

## Extracting sublists

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

`take` `n`, applied to a list `xs`, returns the prefix of `xs` of length `n`, or `xs` itself if `n >= `length` xs`.

It is an instance of the more general `genericTake`, in which `n` may be of any integral type.

#### Laziness

Expand

    >>> take 0 undefined
    []
    >>> take 2 (1 : 2 : undefined)
    [1,2]

#### Examples

Expand

    >>> 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]
    []

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

`drop` `n xs` returns the suffix of `xs` after the first `n` elements, or `[]` if `n >= `length` xs`.

It is an instance of the more general `genericDrop`, in which `n` may be of any integral type.

#### Examples

Expand

    >>> 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]

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` is an instance of the more general `genericSplitAt`, in which `n` may be of any integral type.

#### Laziness

Expand

It is equivalent to `(`take` n xs, `drop` n xs)` unless `n` is `_|_`: `splitAt _|_ xs = _|_`, not `(_|_, _|_)`).

The first component of the tuple is produced lazily:

    >>> fst (splitAt 0 undefined)
    []

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

#### Examples

Expand

    >>> 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])

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`.

#### Laziness

Expand

    >>> takeWhile (const False) undefined
    *** Exception: Prelude.undefined

    >>> takeWhile (const False) (undefined : undefined)
    []

    >>> take 1 (takeWhile (const True) (1 : undefined))
    [1]

#### Examples

Expand

    >>> 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]
    []

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

`dropWhile` `p xs` returns the suffix remaining after `takeWhile` `p xs`.

#### Examples

Expand

    >>> dropWhile (< 3) [1,2,3,4,5,1,2,3]
    [3,4,5,1,2,3]

    >>> dropWhile (< 9) [1,2,3]
    []

    >>> dropWhile (< 0) [1,2,3]
    [1,2,3]

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

The `dropWhileEnd` function drops the largest suffix of a list in which the given predicate holds for all elements.

#### Laziness

Expand

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

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

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

but on the other hand

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

    >>> last (reverse $ dropWhile (< 0) $ reverse [undefined, 1])
    1

#### Examples

Expand

    >>> dropWhileEnd isSpace "foo\n"
    "foo"

    >>> dropWhileEnd isSpace "foo bar"
    "foo bar"
    >>> dropWhileEnd (> 10) [1..20]
    [1,2,3,4,5,6,7,8,9,10]

@since base-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 the longest prefix (possibly empty) of `xs` of elements that satisfy `p` and second element is the remainder of the list:

`span` `p xs` is equivalent to `(`takeWhile` p xs, `dropWhile` p xs)`, even if `p` is `_|_`.

#### Laziness

Expand

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

`span` produces the first component of the tuple lazily:

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

#### Examples

Expand

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

#### Laziness

Expand

    >>> break undefined []
    ([],[])

    >>> fst (break (const True) undefined)
    *** Exception: Prelude.undefined

    >>> fst (break (const True) (undefined : undefined))
    []

    >>> take 1 (fst (break (const False) (1 : undefined)))
    [1]

`break` produces the first component of the tuple lazily:

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

#### Examples

Expand

    >>> 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] #

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

##### Examples

Expand

    >>> stripPrefix "foo" "foobar"
    Just "bar"

    >>> stripPrefix "foo" "foo"
    Just ""

    >>> stripPrefix "foo" "barfoo"
    Nothing

    >>> stripPrefix "foo" "barfoobaz"
    Nothing

stripSuffix #

Arguments

:: Eq a |
=> [a] | suffix
-> [a] |
-> Maybe [a] |

Remove the suffix from the given list, if present

Since: 0.0.0

dropPrefix #

Arguments

:: Eq a |
=> [a] | prefix
-> [a] |
-> [a] |

Drop prefix if present, otherwise return original list.

Since: 0.0.0.0

dropSuffix #

Arguments

:: Eq a |
=> [a] | suffix
-> [a] |
-> [a] |

Drop prefix if present, otherwise return original list.

Since: 0.0.0.0

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 is non-empty, all elements are equal to the first one, and consecutive equal elements of the input end up in the same element of the output list.

`group` is a special case of `groupBy`, which allows the programmer to supply their own equality test.

It's often preferable to use `Data.List.NonEmpty.``group`, which provides type-level guarantees of non-emptiness of inner lists. A common idiom to squash repeating elements `map` `head` `.` `group` is better served by `map` `Data.List.NonEmpty.``head` `.` `Data.List.NonEmpty.``group` because it avoids partial functions.

#### Examples

Expand

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

    >>> group [1, 1, 1, 2, 2, 3, 4, 5, 5]
    [[1,1,1],[2,2],[3],[4],[5,5]]

inits :: [a] -> [[a]] #

The `inits` function returns all initial segments of the argument, shortest first.

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

#### Laziness

Expand

Note that `inits` has the following strictness property: `inits (xs ++ _|_) = inits xs ++ _|_`

In particular, `inits _|_ = [] : _|_`

#### Examples

Expand

    >>> inits "abc"
    ["","a","ab","abc"]

    >>> inits []
    [[]]

inits is productive on infinite lists:

    >>> take 5 $ inits [1..]
    [[],[1],[1,2],[1,2,3],[1,2,3,4]]

tails :: [a] -> [[a]] #

\(\mathcal{O}(n)\). The `tails` function returns all final segments of the argument, longest first.

#### Laziness

Expand

Note that `tails` has the following strictness property: `tails _|_ = _|_ : _|_`

    >>> tails undefined
    [*** Exception: Prelude.undefined

    >>> drop 1 (tails [undefined, 1, 2])
    [[1, 2], [2], []]

#### Examples

Expand

    >>> tails "abc"
    ["abc","bc","c",""]

    >>> tails [1, 2, 3]
    [[1,2,3],[2,3],[3],[]]

    >>> tails []
    [[]]

## Predicates

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.

#### Examples

Expand

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

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

For the result to be `True`, the first list must be finite; `False`, however, results from any mismatch:

    >>> [0..] `isPrefixOf` [1..]
    False

    >>> [0..] `isPrefixOf` [0..99]
    False

    >>> [0..99] `isPrefixOf` [0..]
    True

    >>> [0..] `isPrefixOf` [0..]
    * Hangs forever *

`isPrefixOf` shortcuts when the first argument is empty:

    >>> isPrefixOf [] undefined
    True

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.

#### Examples

Expand

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

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

The second list must be finite; however the first list may be infinite:

    >>> [0..] `isSuffixOf` [0..99]
    False

    >>> [0..99] `isSuffixOf` [0..]
    * Hangs forever *

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

The `isInfixOf` function takes two lists and returns `True` iff the first list is contained, wholly and intact, anywhere within the second.

#### Examples

Expand

    >>> isInfixOf "Haskell" "I really like Haskell."
    True

    >>> isInfixOf "Ial" "I really like Haskell."
    False

For the result to be `True`, the first list must be finite; for the result to be `False`, the second list must be finite:

    >>> [20..50] `isInfixOf` [0..]
    True

    >>> [0..] `isInfixOf` [20..50]
    False

    >>> [0..] `isInfixOf` [0..]
    * Hangs forever *

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

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

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

Note: `isSubsequenceOf` is often used in infix form.

@since base-4.8.0.0

#### Examples

Expand

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

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

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

For the result to be `True`, the first list must be finite; for the result to be `False`, the second list must be finite:

    >>> [0,2..10] `isSubsequenceOf` [0..]
    True

    >>> [0..] `isSubsequenceOf` [0,2..10]
    False

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

# Searching lists

## Searching by equality

elem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

Note: `elem` is often used in infix form.

#### Examples

Expand

Basic usage:

    >>> 3 `elem` []
    False

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

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

For infinite structures, the default implementation of `elem` terminates if the sought-after value exists at a finite distance from the left side of the structure:

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

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

@since base-4.8.0.0

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #

`notElem` is the negation of `elem`.

#### Examples

Expand

Basic usage:

    >>> 3 `notElem` []
    True

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

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

For infinite structures, `notElem` terminates if the value exists at a finite distance from the left side of the structure:

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

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

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

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

#### Examples

Expand

    >>> lookup 2 []
    Nothing

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

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

## Searching with a predicate

find :: Foldable t => (a -> Bool) -> t a -> Maybe a #

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

#### Examples

Expand

Basic usage:

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

    >>> find (> 12) [1..7]
    Nothing

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]

#### Examples

Expand

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

    >>> filter (\l -> length l > 3) ["Hello", ", ", "World", "!"]
    ["Hello","World"]

    >>> filter (/= 3) [1, 2, 3, 4, 3, 2, 1]
    [1,2,4,2,1]

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

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)

#### Examples

Expand

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

    >>> partition even [1..10]
    ([2,4,6,8,10],[1,3,5,7,9])

    >>> partition (< 5) [1..10]
    ([1,2,3,4],[5,6,7,8,9,10])

# Indexing lists

These functions treat a list `xs` as a indexed collection, with indices ranging from 0 to ``length` xs - 1`.

elemIndex :: Eq a => a -> [a] -> Maybe Int #

The `elemIndex` function returns the index of the first element in the given list which is equal (by `==`) to the query element, or `Nothing` if there is no such element. For the result to be `Nothing`, the list must be finite.

#### Examples

Expand

    >>> elemIndex 4 [0..]
    Just 4

    >>> elemIndex 'o' "haskell"
    Nothing

    >>> elemIndex 0 [1..]
    * hangs forever *

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.

#### Examples

Expand

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

    >>> elemIndices 1 [1, 2, 3, 1, 2, 3]
    [0,3]

findIndex :: (a -> Bool) -> [a] -> Maybe Int #

The `findIndex` function takes a predicate and a list and returns the index of the first element in the list satisfying the predicate, or `Nothing` if there is no such element. For the result to be `Nothing`, the list must be finite.

#### Examples

Expand

    >>> findIndex isSpace "Hello World!"
    Just 5

    >>> findIndex odd [0, 2, 4, 6]
    Nothing

    >>> findIndex even [1..]
    Just 1

    >>> findIndex odd [0, 2 ..]
    * hangs forever *

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

The `findIndices` function extends `findIndex`, by returning the indices of all elements satisfying the predicate, in ascending order.

#### Examples

Expand

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

    >>> findIndices (\l -> length l > 3) ["a", "bcde", "fgh", "ijklmnop"]
    [1,3]

# Zipping and unzipping lists

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

\(\mathcal{O}(\min(m,n))\). `zip` takes two lists and returns a list of corresponding pairs.

`zip` is right-lazy:

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

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

#### Examples

Expand

    >>> zip [1, 2, 3] ['a', 'b', 'c']
    [(1,'a'),(2,'b'),(3,'c')]

If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:

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

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

    >>> zip [] [1..]
    []

    >>> zip [1..] []
    []

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] #

`zip3` takes three lists and returns a list of triples, analogous to `zip`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)] #

The `zip4` function takes four lists and returns a list of quadruples, analogous to `zip`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)] #

The `zip5` function takes five lists and returns a list of five-tuples, analogous to `zip`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)] #

The `zip6` function takes six lists and returns a list of six-tuples, analogous to `zip`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)] #

The `zip7` function takes seven lists and returns a list of seven-tuples, analogous to `zip`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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..]

`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.

#### Examples

Expand

``zipWith` `(+)`` can be applied to two lists to produce the list of corresponding sums:

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

    >>> zipWith (++) ["hello ", "foo"] ["world!", "bar"]
    ["hello world!","foobar"]

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

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

#### Examples

Expand

    >>> zipWith3 (\x y z -> [x, y, z]) "123" "abc" "xyz"
    ["1ax","2by","3cz"]

    >>> zipWith3 (\x y z -> (x * y) + z) [1, 2, 3] [4, 5, 6] [7, 8, 9]
    [11,18,27]

zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e] #

The `zipWith4` function takes a function which combines four elements, as well as four lists and returns a list of their point-wise combination, analogous to `zipWith`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] #

The `zipWith5` function takes a function which combines five elements, as well as five lists and returns a list of their point-wise combination, analogous to `zipWith`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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

The `zipWith6` function takes a function which combines six elements, as well as six lists and returns a list of their point-wise combination, analogous to `zipWith`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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

The `zipWith7` function takes a function which combines seven elements, as well as seven lists and returns a list of their point-wise combination, analogous to `zipWith`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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

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

#### Examples

Expand

    >>> unzip []
    ([],[])

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

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) #

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

#### Examples

Expand

    >>> unzip3 []
    ([],[],[])

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

unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d]) #

The `unzip4` function takes a list of quadruples and returns four lists, analogous to `unzip`.

unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e]) #

The `unzip5` function takes a list of five-tuples and returns five lists, analogous to `unzip`.

unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f]) #

The `unzip6` function takes a list of six-tuples and returns six lists, analogous to `unzip`.

unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g]) #

The `unzip7` function takes a list of seven-tuples and returns seven lists, analogous to `unzip`.

# Special lists

## Functions on strings

lines :: String -> [String] #

Splits the argument into a list of lines stripped of their terminating `\n` characters. The `\n` terminator is optional in a final non-empty line of the argument string.

When the argument string is empty, or ends in a `\n` character, it can be recovered by passing the result of `lines` to the `unlines` function. Otherwise, `unlines` appends the missing terminating `\n`. This makes `unlines . lines` idempotent:

    (unlines . lines) . (unlines . lines) = (unlines . lines)

#### Examples

Expand

    >>> lines ""           -- empty input contains no lines
    []

    >>> lines "\n"         -- single empty line
    [""]

    >>> lines "one"        -- single unterminated line
    ["one"]

    >>> lines "one\n"      -- single non-empty line
    ["one"]

    >>> lines "one\n\n"    -- second line is empty
    ["one",""]

    >>> lines "one\ntwo"   -- second line is unterminated
    ["one","two"]

    >>> lines "one\ntwo\n" -- two non-empty lines
    ["one","two"]

linesCR :: String -> [String] #

`linesCR` breaks a `String` up into a list of `String`s at newline `Char`s. It is very similar to `lines`, but it also removes any trailing `'r'` `Char`s. The resulting `String` values do not contain newlines or trailing `'r'` characters.

Since: 0.1.0.0

words :: String -> [String] #

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

#### Examples

Expand

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

    >>> words " foo bar "
    ["foo","bar"]

unlines :: [String] -> String #

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

#### Examples

Expand

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

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

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

unwords :: [String] -> String #

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

`unwords` is neither left nor right inverse of `words`:

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

#### Examples

Expand

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

    >>> unwords ["foo", "bar", "", "baz"]
    "foo bar  baz"

## "Set" operations

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

\(\mathcal{O}(n^2)\). 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.

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

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

#### Examples

Expand

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

    >>> nub "hello, world!"
    "helo, wrd!"

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

\(\mathcal{O}(n)\). `delete` `x` removes the first occurrence of `x` from its list argument.

It is a special case of `deleteBy`, which allows the programmer to supply their own equality test.

#### Examples

Expand

    >>> delete 'a' "banana"
    "bnana"

    >>> delete "not" ["haskell", "is", "not", "awesome"]
    ["haskell","is","awesome"]

(\\) :: 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.

#### Examples

Expand

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

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

    >>> take 5 ([0..] \\ [2..4])
    [0,1,5,6,7]

    >>> take 5 ([0..] \\ [2..])
    * Hangs forever *

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

The `union` function returns the list union of the two lists. It is a special case of `unionBy`, which allows the programmer to supply their own equality test.

#### Examples

Expand

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

If equal elements are present in both lists, an element from the first list will be used. If the second list contains equal elements, only the first one will be retained:

    >>> import Data.Semigroup(Arg(..))
    >>> union [Arg () "dog"] [Arg () "cow"]
    [Arg () "dog"]
    >>> union [] [Arg () "dog", Arg () "cow"]
    [Arg () "dog"]

However if the first list contains duplicates, so will the result:

    >>> "coot" `union` "duck"
    "cootduk"
    >>> "duck" `union` "coot"
    "duckot"

`union` is productive even if both arguments are infinite.

    >>> [0, 2 ..] `union` [1, 3 ..]
    [0,2,4,6,8,10,12..

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

The `intersect` function takes the list intersection of two lists. It is a special case of `intersectBy`, which allows the programmer to supply their own equality test.

##### Examples

Expand

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

If equal elements are present in both lists, an element from the first list will be used, and all duplicates from the second list quashed:

    >>> import Data.Semigroup
    >>> intersect [Arg () "dog"] [Arg () "cow", Arg () "cat"]
    [Arg () "dog"]

However if the first list contains duplicates, so will the result.

    >>> "coot" `intersect` "heron"
    "oo"
    >>> "heron" `intersect` "coot"
    "o"

If the second list is infinite, `intersect` either hangs or returns its first argument in full. Otherwise if the first list is infinite, `intersect` might be productive:

    >>> intersect [100..] [0..]
    [100,101,102,103...
    >>> intersect [0] [1..]
    * Hangs forever *
    >>> intersect [1..] [0]
    * Hangs forever *
    >>> intersect (cycle [1..3]) [2]
    [2,2,2,2...

## Ordered lists

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

The `sort` function implements a stable sorting algorithm. It is a special case of `sortBy`, which allows the programmer to supply their own comparison function.

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

The argument must be finite.

#### Examples

Expand

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

    >>> sort "haskell"
    "aehklls"

    >>> import Data.Semigroup(Arg(..))
    >>> sort [Arg ":)" 0, Arg ":D" 0, Arg ":)" 1, Arg ":3" 0, Arg ":D" 1]
    [Arg ":)" 0,Arg ":)" 1,Arg ":3" 0,Arg ":D" 0,Arg ":D" 1]

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.

The argument must be finite.

#### Examples

Expand

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

    >>> sortOn length ["jim", "creed", "pam", "michael", "dwight", "kevin"]
    ["jim","pam","creed","kevin","dwight","michael"]

#### Performance notes

Expand

This function minimises the projections performed, by materialising the projections in an intermediate list.

For trivial projections, you should prefer using `sortBy` with `comparing`, for example:

    >>> sortBy (comparing fst) [(3, 1), (2, 2), (1, 3)]
    [(1,3),(2,2),(3,1)]

Or, for the exact same API as `sortOn`, you can use `sortBy . comparing`:

    >>> (sortBy . comparing) fst [(3, 1), (2, 2), (1, 3)]
    [(1,3),(2,2),(3,1)]

@since base-4.8.0.0

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

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

#### Examples

Expand

    >>> insert (-1) [1, 2, 3]
    [-1,1,2,3]

    >>> insert 'd' "abcefg"
    "abcdefg"

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

# 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.

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

The `nubBy` function behaves just like `nub`, except it uses a user-supplied equality predicate instead of the overloaded `(==)` function.

#### Examples

Expand

    >>> nubBy (\x y -> mod x 3 == mod y 3) [1,2,4,5,6]
    [1,2,6]

    >>> nubBy (/=) [2, 7, 1, 8, 2, 8, 1, 8, 2, 8]
    [2,2,2]

    >>> nubBy (>) [1, 2, 3, 2, 1, 5, 4, 5, 3, 2]
    [1,2,3,5,5]

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

\(\mathcal{O}(n)\). The `deleteBy` function behaves like `delete`, but takes a user-supplied equality predicate.

#### Examples

Expand

    >>> deleteBy (<=) 4 [1..10]
    [1,2,3,5,6,7,8,9,10]

    >>> deleteBy (/=) 5 [5, 5, 4, 3, 5, 2]
    [5,5,3,5,2]

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. This is the non-overloaded version of `(\\)`.

    (\\) == deleteFirstsBy (==)

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

#### Examples

Expand

    >>> deleteFirstsBy (>) [1..10] [3, 4, 5]
    [4,5,6,7,8,9,10]

    >>> deleteFirstsBy (/=) [1..10] [1, 3, 5]
    [4,5,6,7,8,9,10]

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

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

#### Examples

Expand

    >>> unionBy (>) [3, 4, 5] [1, 2, 3, 4, 5, 6]
    [3,4,5,4,5,6]

    >>> import Data.Semigroup (Arg(..))
    >>> unionBy (/=) [Arg () "Saul"] [Arg () "Kim"]
    [Arg () "Saul", Arg () "Kim"]

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

The `intersectBy` function is the non-overloaded version of `intersect`. It is productive for infinite arguments only if the first one is a subset of the second.

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

The `groupBy` function is the non-overloaded version of `group`.

When a supplied relation is not transitive, it is important to remember that equality is checked against the first element in the group, not against the nearest neighbour:

    >>> groupBy (\a b -> b - a < 5) [0..19]
    [[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14],[15,16,17,18,19]]

It's often preferable to use `Data.List.NonEmpty.``groupBy`, which provides type-level guarantees of non-emptiness of inner lists.

#### Examples

Expand

    >>> groupBy (/=) [1, 1, 1, 2, 3, 1, 4, 4, 5]
    [[1],[1],[1,2,3],[1,4,4,5]]

    >>> groupBy (>) [1, 3, 5, 1, 4, 2, 6, 5, 4]
    [[1],[3],[5,1,4,2],[6,5,4]]

    >>> groupBy (const not) [True, False, True, False, False, False, True]
    [[True,False],[True,False,False,False],[True]]

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

The function is assumed to define a total ordering.

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

The `sortBy` function is the non-overloaded version of `sort`. The argument must be finite.

The supplied comparison relation is supposed to be reflexive and antisymmetric, otherwise, e. g., for `_ _ -> GT`, the ordered list simply does not exist. The relation is also expected to be transitive: if it is not then `sortBy` might fail to find an ordered permutation, even if it exists.

#### Examples

Expand

    >>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
    [(1,"Hello"),(2,"world"),(4,"!")]

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

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

#### Examples

Expand

    >>> insertBy (\x y -> compare (length x) (length y)) [1, 2] [[1], [1, 2, 3], [1, 2, 3, 4]]
    [[1],[1,2],[1,2,3],[1,2,3,4]]

## The "`generic`" operations

The prefix ``generic`' indicates an overloaded function that is a generalized version of a Prelude function.

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`.

#### Examples

Expand

    >>> genericLength [1, 2, 3] :: Int
    3
    >>> genericLength [1, 2, 3] :: Float
    3.0

Users should take care to pick a return type that is wide enough to contain the full length of the list. If the width is insufficient, the overflow behaviour will depend on the `(+)` implementation in the selected `Num` instance. The following example overflows because the actual list length of 200 lies outside of the `Int8` range of `-128..127`.

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

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.