base-4.18.1.0: Basic libraries

Copyright | (c) The University of Glasgow 2001
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | stable
Portability | portable
Safe Haskell | Safe
Language | Haskell2010

GHC.OldList

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

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: base-4.8.0.0

Synopsis

- (++) :: [a] -> [a] -> [a]
- head :: HasCallStack => [a] -> a
- last :: HasCallStack => [a] -> a
- tail :: HasCallStack => [a] -> [a]
- init :: HasCallStack => [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- singleton :: a -> [a]
- null :: [a] -> Bool
- length :: [a] -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl' :: forall a b. (b -> a -> b) -> b -> [a] -> b
- foldl1 :: HasCallStack => (a -> a -> a) -> [a] -> a
- foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: HasCallStack => (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, HasCallStack) => [a] -> a
- minimum :: (Ord a, HasCallStack) => [a] -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: 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]
- 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])
- (!!) :: HasCallStack => [a] -> Int -> a
- elemIndex :: Eq a => a -> [a] -> Maybe Int
- elemIndices :: Eq a => a -> [a] -> [Int]
- findIndex :: (a -> Bool) -> [a] -> Maybe Int
- findIndices :: (a -> Bool) -> [a] -> [Int]
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
- zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]
- zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]
- zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]
- zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]
- zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]
- zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
- unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])
- unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])
- unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- nub :: Eq a => [a] -> [a]
- delete :: Eq a => a -> [a] -> [a]
- (\\) :: Eq a => [a] -> [a] -> [a]
- union :: Eq a => [a] -> [a] -> [a]
- intersect :: Eq a => [a] -> [a] -> [a]
- sort :: Ord a => [a] -> [a]
- sortOn :: Ord b => (a -> b) -> [a] -> [a]
- insert :: Ord a => a -> [a] -> [a]
- nubBy :: (a -> a -> Bool) -> [a] -> [a]
- deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
- deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
- insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
- maximumBy :: (a -> a -> Ordering) -> [a] -> a
- minimumBy :: (a -> a -> Ordering) -> [a] -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]

# Basic functions

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

Append two lists, i.e.,

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

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

WARNING: This function takes linear time in the number of elements of the first list.

head :: HasCallStack => [a] -> a Source #

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

    >>> head [1, 2, 3]
    1
    >>> head [1..]
    1
    >>> head []
    *** Exception: Prelude.head: empty list

WARNING: This function is partial. You can use case-matching, `uncons` or `listToMaybe` instead.

last :: HasCallStack => [a] -> a Source #

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

    >>> last [1, 2, 3]
    3
    >>> last [1..]
    * Hangs forever *
    >>> last []
    *** Exception: Prelude.last: empty list

WARNING: This function is partial. You can use `reverse` with case-matching, `uncons` or `listToMaybe` instead.

tail :: HasCallStack => [a] -> [a] Source #

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

    >>> tail [1, 2, 3]
    [2,3]
    >>> tail [1]
    []
    >>> tail []
    *** Exception: Prelude.tail: empty list

WARNING: This function is partial. You can use case-matching or `uncons` instead.

init :: HasCallStack => [a] -> [a] Source #

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

    >>> init [1, 2, 3]
    [1,2]
    >>> init [1]
    []
    >>> init []
    *** Exception: Prelude.init: empty list

WARNING: This function is partial. You can use `reverse` with case-matching or `uncons` instead.

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

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

    >>> uncons []
    Nothing
    >>> uncons [1]
    Just (1,[])
    >>> uncons [1, 2, 3]
    Just (1,[2,3])

Since: base-4.8.0.0

singleton :: a -> [a] Source #

Produce singleton list.

    >>> singleton True
    [True]

Since: base-4.15.0.0

null :: [a] -> Bool Source #

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

    >>> null []
    True
    >>> null [1]
    False
    >>> null [1..]
    False

length :: [a] -> Int Source #

\(\mathcal{O}(n)\). `length` returns the length of a finite list as an `Int`. It is an instance of the more general `genericLength`, the result type of which may be any kind of number.

    >>> length []
    0
    >>> length ['a', 'b', 'c']
    3
    >>> length [1..]
    * Hangs forever *

# List transformations

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

\(\mathcal{O}(n)\). `map` `f xs` is the list obtained by applying `f` to each element of `xs`, i.e.,

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

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

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

`reverse` `xs` returns the elements of `xs` in reverse order. `xs` must be finite.

    >>> reverse []
    []
    >>> reverse [42]
    [42]
    >>> reverse [2,5,7]
    [7,5,2]
    >>> reverse [1..]
    * Hangs forever *

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

\(\mathcal{O}(n)\). The `intersperse` function takes an element and a list and `intersperses' that element between the elements of the list. For example,

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

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

`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.

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

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

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]]

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

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

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

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

    >>> 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]] Source #

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

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

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`.

This function is productive on infinite inputs:

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

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]

# Reducing lists (folds)

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

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

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

The list must be finite.

    >>> foldl (+) 0 [1..4]
    10
    >>> foldl (+) 42 []
    42
    >>> foldl (-) 100 [1..4]
    90
    >>> foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
    "dcbafoo"
    >>> foldl (+) 0 [1..]
    * Hangs forever *

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

A strict version of `foldl`.

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

`foldl1` is a variant of `foldl` that has no starting value argument, and thus must be applied to non-empty lists. Note that unlike `foldl`, the accumulated value must be of the same type as the list elements.

    >>> foldl1 (+) [1..4]
    10
    >>> foldl1 (+) []
    *** Exception: Prelude.foldl1: empty list
    >>> foldl1 (-) [1..4]
    -8
    >>> foldl1 (&&) [True, False, True, True]
    False
    >>> foldl1 (||) [False, False, True, True]
    True
    >>> foldl1 (+) [1..]
    * Hangs forever *

foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a Source #

A strict version of `foldl1`.

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

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

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

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

`foldr1` is a variant of `foldr` that has no starting value argument, and thus must be applied to non-empty lists. Note that unlike `foldr`, the accumulated value must be of the same type as the list elements.

    >>> foldr1 (+) [1..4]
    10
    >>> foldr1 (+) []
    *** Exception: Prelude.foldr1: empty list
    >>> foldr1 (-) [1..4]
    -2
    >>> foldr1 (&&) [True, False, True, True]
    False
    >>> foldr1 (||) [False, False, True, True]
    True
    >>> force $ foldr1 (+) [1..]
    *** Exception: stack overflow

## Special folds

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

Concatenate a list of lists.

    >>> concat []
    []
    >>> concat [[42]]
    [42]
    >>> concat [[1,2,3], [4,5], [6], []]
    [1,2,3,4,5,6]

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

Map a function returning a list over a list and concatenate the results. `concatMap` can be seen as the composition of `concat` and `map`.

    concatMap f xs == (concat . map f) xs

    >>> concatMap (\i -> [-i,i]) []
    []
    >>> concatMap (\i -> [-i,i]) [1,2,3]
    [-1,1,-2,2,-3,3]

and :: [Bool] -> Bool Source #

`and` returns the conjunction of a Boolean list. For the result to be `True`, the list must be finite; `False`, however, results from a `False` value at a finite index of a finite or infinite list.

    >>> and []
    True
    >>> and [True]
    True
    >>> and [False]
    False
    >>> and [True, True, False]
    False
    >>> and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True...
    False
    >>> and (repeat True)
    * Hangs forever *

or :: [Bool] -> Bool Source #

`or` returns the disjunction of a Boolean list. For the result to be `False`, the list must be finite; `True`, however, results from a `True` value at a finite index of a finite or infinite list.

    >>> or []
    False
    >>> or [True]
    True
    >>> or [False]
    False
    >>> or [True, True, False]
    True
    >>> or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False...
    True
    >>> or (repeat False)
    * Hangs forever *

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

Applied to a predicate and a list, `any` determines if any element of the list satisfies the predicate. For the result to be `False`, the list must be finite; `True`, however, results from a `True` value for the predicate applied to an element at a finite index of a finite or infinite list.

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

Applied to a predicate and a list, `all` determines if all elements of the list satisfy the predicate. For the result to be `True`, the list must be finite; `False`, however, results from a `False` value for the predicate applied to an element at a finite index of a finite or infinite list.

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

The `sum` function computes the sum of a finite list of numbers.

    >>> sum []
    0
    >>> sum [42]
    42
    >>> sum [1..10]
    55
    >>> sum [4.1, 2.0, 1.7]
    7.8
    >>> sum [1..]
    * Hangs forever *

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

The `product` function computes the product of a finite list of numbers.

    >>> product []
    1
    >>> product [42]
    42
    >>> product [1..10]
    3628800
    >>> product [4.1, 2.0, 1.7]
    13.939999999999998
    >>> product [1..]
    * Hangs forever *

maximum :: (Ord a, HasCallStack) => [a] -> a Source #

`maximum` returns the maximum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of `maximumBy`, which allows the programmer to supply their own comparison function.

    >>> maximum []
    *** Exception: Prelude.maximum: empty list
    >>> maximum [42]
    42
    >>> maximum [55, -12, 7, 0, -89]
    55
    >>> maximum [1..]
    * Hangs forever *

minimum :: (Ord a, HasCallStack) => [a] -> a Source #

`minimum` returns the minimum value from a list, which must be non-empty, finite, and of an ordered type. It is a special case of `minimumBy`, which allows the programmer to supply their own comparison function.

    >>> minimum []
    *** Exception: Prelude.minimum: empty list
    >>> minimum [42]
    42
    >>> minimum [55, -12, 7, 0, -89]
    -89
    >>> minimum [1..]
    * Hangs forever *

# Building lists

## Scans

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

\(\mathcal{O}(n)\). `scanl` is similar to `foldl`, but returns a list of successive reduced values from the left:

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

Note that

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

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

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

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

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

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

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

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

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

\(\mathcal{O}(n)\). `scanr` is the right-to-left dual of `scanl`. Note that the order of parameters on the accumulating function are reversed compared to `scanl`. Also note that

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

    >>> 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

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

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

    >>> 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 :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) Source #

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

mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) Source #

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

## Infinite lists

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

`iterate` `f x` returns an infinite list of repeated applications of `f` to `x`:

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

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

    >>> take 10 $ iterate not True
    [True,False,True,False...
    >>> take 10 $ iterate (+3) 42
    [42,45,48,51,54,57,60,63...

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

`iterate'` is the strict version of `iterate`.

It forces the result of each application of the function to weak head normal form (WHNF) before proceeding.

repeat :: a -> [a] Source #

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

    >>> repeat 17
    [17,17,17,17,17,17,17,17,17...

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

`replicate` `n x` is a list of length `n` with `x` the value of every element. It is an instance of the more general `genericReplicate`, in which `n` may be of any integral type.

    >>> replicate 0 True
    []
    >>> replicate (-1) True
    []
    >>> replicate 4 True
    [True,True,True,True]

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

`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.

    >>> cycle []
    *** Exception: Prelude.cycle: empty list
    >>> cycle [42]
    [42,42,42,42,42,42,42,42,42,42...
    >>> cycle [2, 5, 7]
    [2,5,7,2,5,7,2,5,7,2,5,7...

## Unfolding

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

The `unfoldr` function is a `dual' to `foldr`: while `foldr` reduces a list to a summary value, `unfoldr` builds a list from a seed value. The function takes the element and returns `Nothing` if it is done producing the list or returns `Just` `(a,b)`, in which case, `a` is a prepended to the list and `b` is used as the next element in a recursive call. For example,

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

In some cases, `unfoldr` can undo a `foldr` operation:

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

if the following holds:

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

A simple use of unfoldr:

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

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

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

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

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

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

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

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

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

`splitAt` `n xs` returns a tuple where first element is `xs` prefix of length `n` and second element is the remainder of the list:

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

It is equivalent to `(`take` n xs, `drop` n xs)` when `n` is not `_|_` (`splitAt _|_ xs = _|_`). `splitAt` is an instance of the more general `genericSplitAt`, in which `n` may be of any integral type.

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

`takeWhile`, applied to a predicate `p` and a list `xs`, returns the longest prefix (possibly empty) of `xs` of elements that satisfy `p`.

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

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

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

    >>> 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] Source #

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: base-4.5.0.0

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

`span`, applied to a predicate `p` and a list `xs`, returns a tuple where first element is longest prefix (possibly empty) of `xs` of elements that satisfy `p` and second element is the remainder of the list:

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

`span` `p xs` is equivalent to `(`takeWhile` p xs, `dropWhile` p xs)`

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

`break`, applied to a predicate `p` and a list `xs`, returns a tuple where first element is longest prefix (possibly empty) of `xs` of elements that do not satisfy `p` and second element is the remainder of the list:

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

`break` `p` is equivalent to ``span` (`not` . p)`.

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

\(\mathcal{O}(\min(m,n))\). The `stripPrefix` function drops the given prefix from a list. It returns `Nothing` if the list did not start with the prefix given, or `Just` the list after the prefix, if it does.

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

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

    >>> stripPrefix "foo" "barfoo"
    Nothing

    >>> stripPrefix "foo" "barfoobaz"
    Nothing

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

The `group` function takes a list and returns a list of lists such that the concatenation of the result is equal to the argument. Moreover, each sublist in the result is non-empty and all elements are equal to the first one. For example,

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

`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.

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

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

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

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

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

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

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

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

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

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

## Predicates

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

\(\mathcal{O}(\min(m,n))\). The `isPrefixOf` function takes two lists and returns `True` iff the first list is a prefix of the second.

    >>> "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 *

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

The `isSuffixOf` function takes two lists and returns `True` iff the first list is a suffix of the second.

    >>> "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 Source #

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

    >>> 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 *

# Searching lists

## Searching by equality

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

`elem` is the list membership predicate, usually written in infix form, e.g., `x `elem` xs`. For the result to be `False`, the list must be finite; `True`, however, results from an element equal to `x` found at a finite index of a finite or infinite list.

    >>> 3 `elem` []
    False
    >>> 3 `elem` [1,2]
    False
    >>> 3 `elem` [1,2,3,4,5]
    True
    >>> 3 `elem` [1..]
    True
    >>> 3 `elem` [4..]
    * Hangs forever *

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

`notElem` is the negation of `elem`.

    >>> 3 `notElem` []
    True
    >>> 3 `notElem` [1,2]
    True
    >>> 3 `notElem` [1,2,3,4,5]
    False
    >>> 3 `notElem` [1..]
    False
    >>> 3 `notElem` [4..]
    * Hangs forever *

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

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

    >>> lookup 2 []
    Nothing
    >>> lookup 2 [(1, "first")]
    Nothing
    >>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
    Just "second"

## Searching with a predicate

find :: (a -> Bool) -> [a] -> Maybe a Source #

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

    >>> find (> 4) [1..]
    Just 5

    >>> find (< 0) [1..10]
    Nothing

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

\(\mathcal{O}(n)\). `filter`, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

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

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

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

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

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

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

# Indexing lists

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

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

List index (subscript) operator, starting from 0. It is an instance of the more general `genericIndex`, which takes an index of any integral type.

    >>> ['a', 'b', 'c'] !! 0
    'a'
    >>> ['a', 'b', 'c'] !! 2
    'c'
    >>> ['a', 'b', 'c'] !! 3
    *** Exception: Prelude.!!: index too large
    >>> ['a', 'b', 'c'] !! (-1)
    *** Exception: Prelude.!!: negative index

WARNING: This function is partial. You can use atMay instead.

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

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.

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

elemIndices :: Eq a => a -> [a] -> [Int] Source #

The `elemIndices` function extends `elemIndex`, by returning the indices of all elements equal to the query element, in ascending order.

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

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

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.

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

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

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

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

# Zipping and unzipping lists

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

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

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

If one input list is 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..] []
    []

`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.

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

`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)] Source #

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)] Source #

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)] Source #

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)] Source #

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] Source #

\(\mathcal{O}(\min(m,n))\). `zipWith` generalises `zip` by zipping with the function given as the first argument, instead of a tupling function.

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

For example, ``zipWith` (+)` is applied to two lists to produce the list of corresponding sums:

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

`zipWith` is right-lazy:

    >>> let f = undefined
    >>> zipWith f [] undefined
    []

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

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

The `zipWith3` function takes a function which combines three elements, as well as three lists and returns a list of the function applied to corresponding elements, analogous to `zipWith`. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.

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

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

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] Source #

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] Source #

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] Source #

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]) Source #

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

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

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

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

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

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

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]) Source #

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]) Source #

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]) Source #

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

# Special lists

## Functions on strings

lines :: String -> [String] Source #

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.

For example:

    >>> 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"]

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)

words :: String -> [String] Source #

`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.

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

unlines :: [String] -> String Source #

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

    >>> 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 Source #

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

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

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

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

## "Set" operations

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

\(\mathcal{O}(n^2)\). The `nub` function removes duplicate elements from a list. In particular, it keeps only the first occurrence of each element. (The name `nub` means `essence'.) It is a special case of `nubBy`, which allows the programmer to supply their own equality test.

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

If the order of outputs does not matter and there exists `instance Ord a`, it's faster to use `map` `Data.List.NonEmpty.``head` . `Data.List.NonEmpty.``group` . `sort`, which takes only \(\mathcal{O}(n \log n)\) time.

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

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

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

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

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

The `\\` function is list difference (non-associative). In the result of `xs` `\\` `ys`, the first occurrence of each element of `ys` in turn (if any) has been removed from `xs`. Thus `(xs ++ ys) \\ xs == ys`.

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

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

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] Source #

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. For example,

    >>> "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
    >>> 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.

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

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. For example,

    >>> [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] Source #

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.

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

The argument must be finite.

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

Sort a list by comparing the results of a key function applied to each element. ``sortOn` f` is equivalent to ``sortBy` (`comparing` f)`, but has the performance advantage of only evaluating `f` once for each element in the input list. This is called the decorate-sort-undecorate paradigm, or Schwartzian transform.

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

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

The argument must be finite.

Since: base-4.8.0.0

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

\(\mathcal{O}(n)\). The `insert` function takes an element and a list and inserts the element into the list at the first position where it is less than or equal to the next element. In particular, if the list is sorted before the call, the result will also be sorted. It is a special case of `insertBy`, which allows the programmer to supply their own comparison function.

    >>> 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] Source #

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

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

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

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

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

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

The `deleteFirstsBy` function takes a predicate and two lists and returns the first list with the first occurrence of each element of the second list removed. This is the non-overloaded version of `(\\)`.

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

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

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

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

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]] Source #

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.

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

The function is assumed to define a total ordering.

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

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

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

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.

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

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

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

The `maximumBy` function is the non-overloaded version of `maximum`, which takes a comparison function and a list and returns the greatest element of the list by the comparison function. The list must be finite and non-empty.

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

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

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

The `minimumBy` function is the non-overloaded version of `minimum`, which takes a comparison function and a list and returns the least element of the list by the comparison function. The list must be finite and non-empty.

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

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

## The "`generic`" operations

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

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

\(\mathcal{O}(n)\). The `genericLength` function is an overloaded version of `length`. In particular, instead of returning an `Int`, it returns any type which is an instance of `Num`. It is, however, less efficient than `length`.

    >>> 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] Source #

The `genericTake` function is an overloaded version of `take`, which accepts any `Integral` value as the number of elements to take.

genericDrop :: Integral i => i -> [a] -> [a] Source #

The `genericDrop` function is an overloaded version of `drop`, which accepts any `Integral` value as the number of elements to drop.

genericSplitAt :: Integral i => i -> [a] -> ([a], [a]) Source #

The `genericSplitAt` function is an overloaded version of `splitAt`, which accepts any `Integral` value as the position at which to split.

genericIndex :: Integral i => [a] -> i -> a Source #

The `genericIndex` function is an overloaded version of `!!`, which accepts any `Integral` value as the index.

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

The `genericReplicate` function is an overloaded version of `replicate`, which accepts any `Integral` value as the number of repetitions to make.