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 | Trustworthy
Language | Haskell2010

Data.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

Operations on lists.

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 :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- map :: (a -> b) -> [a] -> [b]
- reverse :: [a] -> [a]
- intersperse :: a -> [a] -> [a]
- intercalate :: [a] -> [[a]] -> [a]
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- foldl :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b
- foldl1 :: Foldable t => (a -> a -> a) -> t a -> a
- foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a
- foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
- foldr1 :: Foldable t => (a -> a -> a) -> t a -> a
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- sum :: (Foldable t, Num a) => t a -> a
- product :: (Foldable t, Num a) => t a -> a
- maximum :: forall a. (Foldable t, Ord a) => t a -> a
- minimum :: forall a. (Foldable t, Ord a) => t a -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- mapAccumL :: forall t s a b. Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- mapAccumR :: forall t s a b. Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- 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
- 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])
- (!!) :: 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 :: Foldable t => (a -> a -> Ordering) -> t a -> a
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- genericLength :: Num i => [a] -> i
- genericTake :: Integral i => i -> [a] -> [a]
- genericDrop :: Integral i => i -> [a] -> [a]
- genericSplitAt :: Integral i => i -> [a] -> ([a], [a])
- genericIndex :: Integral i => [a] -> i -> a
- genericReplicate :: Integral i => i -> a -> [a]

# Basic functions

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

Append two lists, i.e.,

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

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

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

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 Source #

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

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

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 Source #

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

This ensures that each step of the fold is forced to Weak Head Normal Form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite 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

foldl1 :: Foldable t => (a -> a -> a) -> t a -> a Source #

A variant of `foldl` that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

    foldl1 f = foldl1 f . toList

#### Examples

Expand

Basic usage:

    >>> foldl1 (+) [1..4]
    10

    >>> foldl1 (+) []
    *** Exception: Prelude.foldl1: empty list

    >>> foldl1 (+) Nothing
    *** Exception: foldl1: empty structure

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

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]

foldr1 :: Foldable t => (a -> a -> a) -> t a -> a Source #

A variant of `foldr` that has no base case, and thus may only be applied to non-empty structures.

This function is non-total and will raise a runtime exception if the structure happens to be empty.

#### Examples

Expand

Basic usage:

    >>> foldr1 (+) [1..4]
    10

    >>> foldr1 (+) []
    Exception: Prelude.foldr1: empty list

    >>> foldr1 (+) Nothing
    *** Exception: foldr1: empty structure

    >>> foldr1 (-) [1..4]
    -2

    >>> foldr1 (&&) [True, False, True, True]
    False

    >>> foldr1 (||) [False, False, True, True]
    True

    >>> foldr1 (+) [1..]
    * Hangs forever *

## Special folds

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

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] Source #

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 Source #

`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 Source #

`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 Source #

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 Source #

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 Source #

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 Source #

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

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

The largest element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

#### Examples

Expand

Basic usage:

    >>> maximum [1..10]
    10

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

    >>> maximum Nothing
    *** Exception: maximum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

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

The least element of a non-empty structure.

This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

#### Examples

Expand

Basic usage:

    >>> minimum [1..10]
    1

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

    >>> minimum Nothing
    *** Exception: minimum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

Since: base-4.8.0.0

# 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 :: forall t s a b. Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b) Source #

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 :: forall t s a b. Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b) Source #

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] 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 *

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

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

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

    >>> isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
    True
    >>> isSubsequenceOf ['a','d'..'z'] ['a'..'z']
    True
    >>> isSubsequenceOf [1..10] [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*

Since: base-4.8.0.0

# Searching lists

## Searching by equality

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

Does the element occur in the structure?

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 Source #

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

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

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

#### Examples

Expand

Basic usage:

    >>> maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
    "Longest"

WARNING: This function is partial for possibly-empty structures like lists.

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

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

#### Examples

Expand

Basic usage:

    >>> minimumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]
    "!"

WARNING: This function is partial for possibly-empty structures like lists.

## 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.