Copyright | (c) The University of Glasgow 1994-2002 |
---|---|

License | see libraries/base/LICENSE |

Maintainer | ghc-devs@haskell.org |

Stability | internal |

Portability | non-portable (GHC Extensions) |

Safe Haskell | Safe |

Language | Haskell2010 |

The List data type and its operations

## Synopsis

- data List a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr' :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: HasCallStack => (a -> a -> a) -> [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
- null :: [a] -> Bool
- length :: [a] -> Int
- elem :: Eq a => a -> [a] -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- maximum :: (Ord a, HasCallStack) => [a] -> a
- minimum :: (Ord a, HasCallStack) => [a] -> a
- sum :: Num a => [a] -> a
- product :: Num a => [a] -> a
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- all :: (a -> Bool) -> [a] -> Bool
- foldl1' :: HasCallStack => (a -> a -> a) -> [a] -> a
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- map :: (a -> b) -> [a] -> [b]
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- head :: HasCallStack => [a] -> a
- last :: HasCallStack => [a] -> a
- tail :: HasCallStack => [a] -> [a]
- init :: HasCallStack => [a] -> [a]
- uncons :: [a] -> Maybe (a, [a])
- unsnoc :: [a] -> Maybe ([a], a)
- (!?) :: [a] -> Int -> Maybe a
- (!!) :: HasCallStack => [a] -> Int -> a
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl' :: (b -> a -> b) -> b -> [a] -> [b]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- iterate' :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: HasCallStack => [a] -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- reverse :: [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- errorEmptyList :: HasCallStack => String -> a
- augment :: (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a]
- build :: (forall b. (a -> b -> b) -> b -> b) -> [a]

# The list data type

The builtin linked list type.

In Haskell, lists are one of the most important data types as they are often used analogous to loops in imperative programming languages. These lists are singly linked, which makes them unsuited for operations that require \(\mathcal{O}(1)\) access. Instead, they are intended to be traversed.

You can use `List a`

or `[a]`

in type signatures:

length :: [a] -> Int

or

length :: List a -> Int

They are fully equivalent, and `List a`

will be normalised to `[a]`

.

#### Usage

Lists are constructed recursively using the right-associative constructor operator (or *cons*)
`(:) :: a -> [a] -> [a]`

, which prepends an element to a list,
and the empty list `[]`

.

(1 : 2 : 3 : []) == (1 : (2 : (3 : []))) == [1, 2, 3]

Lists can also be constructed using list literals
of the form `[x_1, x_2, ..., x_n]`

which are syntactic sugar and, unless `-XOverloadedLists`

is enabled,
are translated into uses of `(:)`

and `[]`

`String`

literals, like `"I 💜 hs"`

, are translated into
Lists of characters, `['I', ' ', '💜', ' ', 'h', 's']`

.

#### Implementation

Internally and in memory, all the above are represented like this, with arrows being pointers to locations in memory.

╭───┬───┬──╮ ╭───┬───┬──╮ ╭───┬───┬──╮ ╭────╮ │(:)│ │ ─┼──>│(:)│ │ ─┼──>│(:)│ │ ─┼──>│ [] │ ╰───┴─┼─┴──╯ ╰───┴─┼─┴──╯ ╰───┴─┼─┴──╯ ╰────╯ v v v 1 2 3

#### Examples

>>> ['H', 'a', 's', 'k', 'e', 'l', 'l'] "Haskell"

>>> 1 : [4, 1, 5, 9] [1,4,1,5,9]

>>> [] : [] : [] [[],[]]

*Since: ghc-prim-0.10.0*

#### Instances

MonadZip [] Source # |
| ||||

Eq1 [] Source # |
| ||||

Ord1 [] Source # |
| ||||

Defined in Data.Functor.Classes liftCompare :: (a -> b -> Ordering) -> [a] -> [b] -> Ordering Source # | |||||

Read1 [] Source # |
| ||||

Defined in Data.Functor.Classes | |||||

Show1 [] Source # |
| ||||

Alternative [] | Combines lists by concatenation, starting from the empty list. @since base-2.01 | ||||

Applicative [] | @since base-2.01 | ||||

Functor [] | @since base-2.01 | ||||

Monad [] | @since base-2.01 | ||||

MonadPlus [] | Combines lists by concatenation, starting from the empty list. @since base-2.01 | ||||

MonadFail [] | @since base-4.9.0.0 | ||||

Defined in GHC.Internal.Control.Monad.Fail | |||||

MonadFix [] | @since base-2.01 | ||||

Defined in GHC.Internal.Control.Monad.Fix | |||||

Foldable [] | @since base-2.01 | ||||

Defined in GHC.Internal.Data.Foldable fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # | |||||

Traversable [] | @since base-2.01 | ||||

Generic1 [] | |||||

Defined in GHC.Internal.Generics
| |||||

IsChar c => PrintfArg [c] Source # |
| ||||

Defined in Text.Printf formatArg :: [c] -> FieldFormatter Source # parseFormat :: [c] -> ModifierParser Source # | |||||

IsChar c => PrintfType [c] Source # |
| ||||

Defined in Text.Printf | |||||

Monoid [a] | @since base-2.01 | ||||

Semigroup [a] | @since base-4.9.0.0 | ||||

Data a => Data [a] | For historical reasons, the constructor name used for @since base-4.0.0.0 | ||||

Defined in GHC.Internal.Data.Data gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> [a] -> c [a] Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c [a] Source # toConstr :: [a] -> Constr Source # dataTypeOf :: [a] -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c [a]) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c [a]) Source # gmapT :: (forall b. Data b => b -> b) -> [a] -> [a] Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> [a] -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> [a] -> r Source # gmapQ :: (forall d. Data d => d -> u) -> [a] -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> [a] -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> [a] -> m [a] Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> [a] -> m [a] Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> [a] -> m [a] Source # | |||||

a ~ Char => IsString [a] |
@since base-2.01 | ||||

Defined in GHC.Internal.Data.String fromString :: String -> [a] Source # | |||||

Generic [a] | |||||

Defined in GHC.Internal.Generics
| |||||

IsList [a] | @since base-4.7.0.0 | ||||

Read a => Read [a] | @since base-2.01 | ||||

Show a => Show [a] | @since base-2.01 | ||||

Eq a => Eq [a] | |||||

Ord a => Ord [a] | |||||

type Rep1 [] | @since base-4.6.0.0 | ||||

Defined in GHC.Internal.Generics type Rep1 [] = D1 ('MetaData "List" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "[]" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))) | |||||

type Rep [a] | @since base-4.6.0.0 | ||||

Defined in GHC.Internal.Generics type Rep [a] = D1 ('MetaData "List" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "[]" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons ":" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) | |||||

type Item [a] | |||||

Defined in GHC.Internal.IsList type Item [a] = a |

# List-monomorphic Foldable methods and misc functions

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)...)

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

`foldr'`

is a variant of `foldr`

that begins list reduction from the last
element and evaluates the accumulator strictly as it unwinds the stack back
to the beginning of the list. The input list *must* be finite, otherwise
`foldr'`

runs out of space (*diverges*).

Note that if the function that combines the accumulated value with each
element is strict in the accumulator, other than a possible improvement
in the constant factor, you get the same \(\mathcal{O}(n)\) space cost
as with just `foldr`

.

If you want a strict right fold in constant space, you need a structure
that supports faster than \(\mathcal{O}(n)\) access to the right-most
element, such as `Seq`

from the `containers`

package.

Use of this function is a hint that the `[]`

structure may be a poor fit
for the task at hand. If the order in which the elements are combined is
not important, use `foldl'`

instead.

`>>>`

10`foldr' (+) [1..4] -- Use foldl' instead!`

`>>>`

False`foldr' (&&) [True, False, True, True] -- Use foldr instead!`

`>>>`

True`foldr' (||) [False, False, True, True] -- Use foldr instead!`

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.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

*** Exception: stack overflow`force $ foldr1 (+) [1..]`

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.

`>>>`

10`foldl (+) 0 [1..4]`

`>>>`

42`foldl (+) 42 []`

`>>>`

90`foldl (-) 100 [1..4]`

`>>>`

"dcbafoo"`foldl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']`

`>>>`

* Hangs forever *`foldl (+) 0 [1..]`

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.

`>>>`

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

`>>>`

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

`>>>`

-8`foldl1 (-) [1..4]`

`>>>`

False`foldl1 (&&) [True, False, True, True]`

`>>>`

True`foldl1 (||) [False, False, True, True]`

`>>>`

* Hangs forever *`foldl1 (+) [1..]`

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

`>>>`

True`null []`

`>>>`

False`null [1]`

`>>>`

False`null [1..]`

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

`>>>`

0`length []`

`>>>`

3`length ['a', 'b', 'c']`

`>>>`

* Hangs forever *`length [1..]`

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.

#### Examples

`>>>`

False`3 `elem` []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

* Hangs forever *`3 `elem` [4..]`

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.

`>>>`

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

`>>>`

42`maximum [42]`

`>>>`

55`maximum [55, -12, 7, 0, -89]`

`>>>`

* Hangs forever *`maximum [1..]`

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.

`>>>`

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

`>>>`

42`minimum [42]`

`>>>`

-89`minimum [55, -12, 7, 0, -89]`

`>>>`

* Hangs forever *`minimum [1..]`

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

The `sum`

function computes the sum of a finite list of numbers.

`>>>`

0`sum []`

`>>>`

42`sum [42]`

`>>>`

55`sum [1..10]`

`>>>`

7.8`sum [4.1, 2.0, 1.7]`

`>>>`

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

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

The `product`

function computes the product of a finite list of numbers.

`>>>`

1`product []`

`>>>`

42`product [42]`

`>>>`

3628800`product [1..10]`

`>>>`

13.939999999999998`product [4.1, 2.0, 1.7]`

`>>>`

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

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.

#### Examples

`>>>`

True`and []`

`>>>`

True`and [True]`

`>>>`

False`and [False]`

`>>>`

False`and [True, True, False]`

`>>>`

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

`>>>`

* Hangs forever *`and (repeat True)`

`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.

#### Examples

`>>>`

False`or []`

`>>>`

True`or [True]`

`>>>`

False`or [False]`

`>>>`

True`or [True, True, False]`

`>>>`

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

`>>>`

* Hangs forever *`or (repeat False)`

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.

#### Examples

`>>>`

False`any (> 3) []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

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.

#### Examples

`>>>`

True`all (> 3) []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

# Other functions

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

A strict version of `foldl1`

.

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

Concatenate a list of lists.

#### Examples

`>>>`

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

`>>>`

[]`concat []`

`>>>`

[42]`concat [[42]]`

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

#### Examples

`>>>`

[]`concatMap (\i -> [-i,i]) []`

`>>>`

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

`>>>`

[0,0,0,2,2,2,4,4,4]`concatMap ('replicate' 3) [0, 2, 4]`

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, ...]

this means that `map id == id`

#### Examples

`>>>`

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

`>>>`

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

`>>>`

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

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

`(++)`

appends two lists, i.e.,

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

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

#### Performance considerations

This function takes linear time in the number of elements of the
**first** list. Thus it is better to associate repeated
applications of `(++)`

to the right (which is the default behaviour):
`xs ++ (ys ++ zs)`

or simply `xs ++ ys ++ zs`

, but not `(xs ++ ys) ++ zs`

.
For the same reason `concat`

`=`

`foldr`

`(++)`

`[]`

has linear performance, while `foldl`

`(++)`

`[]`

is prone
to quadratic slowdown

#### Examples

`>>>`

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

`>>>`

[1,2,3]`[] ++ [1, 2, 3]`

`>>>`

[3,2,1]`[3, 2, 1] ++ []`

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]

#### Examples

`>>>`

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

`>>>`

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

`>>>`

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

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

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

To disable the warning about partiality put `{-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}`

at the top of the file. To disable it throughout a package put the same
options into `ghc-options`

section of Cabal file. To disable it in GHCi
put `:set -Wno-x-partial -Wno-unrecognised-warning-flags`

into `~/.ghci`

config file.
See also the migration guide.

##### Examples

`>>>`

1`head [1, 2, 3]`

`>>>`

1`head [1..]`

`>>>`

*** Exception: Prelude.head: empty list`head []`

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

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

WARNING: This function is partial. Consider using `unsnoc`

instead.

#### Examples

`>>>`

3`last [1, 2, 3]`

`>>>`

* Hangs forever *`last [1..]`

`>>>`

*** Exception: Prelude.last: empty list`last []`

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

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

To disable the warning about partiality put `{-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}`

at the top of the file. To disable it throughout a package put the same
options into `ghc-options`

section of Cabal file. To disable it in GHCi
put `:set -Wno-x-partial -Wno-unrecognised-warning-flags`

into `~/.ghci`

config file.
See also the migration guide.

#### Examples

`>>>`

[2,3]`tail [1, 2, 3]`

`>>>`

[]`tail [1]`

`>>>`

*** Exception: Prelude.tail: empty list`tail []`

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.

WARNING: This function is partial. Consider using `unsnoc`

instead.

#### Examples

`>>>`

[1,2]`init [1, 2, 3]`

`>>>`

[]`init [1]`

`>>>`

*** Exception: Prelude.init: empty list`init []`

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

, where`Just`

(x, xs)`x`

is the`head`

of the list and`xs`

its`tail`

.

@since base-4.8.0.0

#### Examples

`>>>`

Nothing`uncons []`

`>>>`

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

`>>>`

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

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

\(\mathcal{O}(n)\). Decompose a list into `init`

and `last`

.

- If the list is empty, returns
`Nothing`

. - If the list is non-empty, returns

, where`Just`

(xs, x)`xs`

is the`init`

ial part of the list and`x`

is its`last`

element.

`unsnoc`

is dual to `uncons`

: for a finite list `xs`

unsnoc xs = (\(hd, tl) -> (reverse tl, hd)) <$> uncons (reverse xs)

#### Examples

`>>>`

Nothing`unsnoc []`

`>>>`

Just ([],1)`unsnoc [1]`

`>>>`

Just ([1,2],3)`unsnoc [1, 2, 3]`

#### Laziness

`>>>`

Just []`fst <$> unsnoc [undefined]`

`>>>`

Just *** Exception: Prelude.undefined`head . fst <$> unsnoc (1 : undefined)`

`>>>`

Just 1`head . fst <$> unsnoc (1 : 2 : undefined)`

@since base-4.19.0.0

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

List index (subscript) operator, starting from 0. Returns `Nothing`

if the index is out of bounds

This is the total variant of the partial `!!`

operator.

WARNING: This function takes linear time in the index.

#### Examples

`>>>`

Just 'a'`['a', 'b', 'c'] !? 0`

`>>>`

Just 'c'`['a', 'b', 'c'] !? 2`

`>>>`

Nothing`['a', 'b', 'c'] !? 3`

`>>>`

Nothing`['a', 'b', 'c'] !? (-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.

WARNING: This function is partial, and should only be used if you are
sure that the indexing will not fail. Otherwise, use `!?`

.

WARNING: This function takes linear time in the index.

#### Examples

`>>>`

'a'`['a', 'b', 'c'] !! 0`

`>>>`

'c'`['a', 'b', 'c'] !! 2`

`>>>`

*** Exception: Prelude.!!: index too large`['a', 'b', 'c'] !! 3`

`>>>`

*** Exception: Prelude.!!: negative index`['a', 'b', 'c'] !! (-1)`

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

#### Examples

`>>>`

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

`>>>`

[42]`scanl (+) 42 []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

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, ...]

#### Examples

`>>>`

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

`>>>`

[]`scanl1 (+) []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

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.

#### Examples

`>>>`

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

`>>>`

[42]`scanr (+) 42 []`

`>>>`

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

`>>>`

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

`>>>`

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

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

\(\mathcal{O}(n)\). `scanr1`

is a variant of `scanr`

that has no starting
value argument.

#### Examples

`>>>`

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

`>>>`

[]`scanr1 (+) []`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

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), ...]

#### Laziness

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.

`>>>`

[42]`take 1 $ iterate undefined 42`

#### Examples

`>>>`

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

`>>>`

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

`iterate id == `

:`repeat`

`>>>`

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

`repeat`

`x`

is an infinite list, with `x`

the value of every element.

#### Examples

`>>>`

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

`>>>`

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

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.

#### Examples

`>>>`

[]`replicate 0 True`

`>>>`

[]`replicate (-1) True`

`>>>`

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

#### Examples

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

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

It is an instance of the more general `genericTake`

,
in which `n`

may be of any integral type.

#### Laziness

`>>>`

[]`take 0 undefined`

`>>>`

[1,2]`take 2 (1 : 2 : undefined)`

#### Examples

`>>>`

"Hello"`take 5 "Hello World!"`

`>>>`

[1,2,3]`take 3 [1,2,3,4,5]`

`>>>`

[1,2]`take 3 [1,2]`

`>>>`

[]`take 3 []`

`>>>`

[]`take (-1) [1,2]`

`>>>`

[]`take 0 [1,2]`

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

`drop`

`n xs`

returns the suffix of `xs`

after the first `n`

elements, or `[]`

if `n >= `

.`length`

xs

It is an instance of the more general `genericDrop`

,
in which `n`

may be of any integral type.

#### Examples

`>>>`

"World!"`drop 6 "Hello World!"`

`>>>`

[4,5]`drop 3 [1,2,3,4,5]`

`>>>`

[]`drop 3 [1,2]`

`>>>`

[]`drop 3 []`

`>>>`

[1,2]`drop (-1) [1,2]`

`>>>`

[1,2]`drop 0 [1,2]`

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`

is an instance of the more general `genericSplitAt`

,
in which `n`

may be of any integral type.

#### Laziness

It is equivalent to `(`

unless `take`

n xs, `drop`

n xs)`n`

is `_|_`

:
`splitAt _|_ xs = _|_`

, not `(_|_, _|_)`

).

The first component of the tuple is produced lazily:

`>>>`

[]`fst (splitAt 0 undefined)`

`>>>`

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

#### Examples

`>>>`

("Hello ","World!")`splitAt 6 "Hello World!"`

`>>>`

([1,2,3],[4,5])`splitAt 3 [1,2,3,4,5]`

`>>>`

([1],[2,3])`splitAt 1 [1,2,3]`

`>>>`

([1,2,3],[])`splitAt 3 [1,2,3]`

`>>>`

([1,2,3],[])`splitAt 4 [1,2,3]`

`>>>`

([],[1,2,3])`splitAt 0 [1,2,3]`

`>>>`

([],[1,2,3])`splitAt (-1) [1,2,3]`

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`

.

#### Laziness

`>>>`

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

`>>>`

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

`>>>`

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

#### Examples

`>>>`

[1,2]`takeWhile (< 3) [1,2,3,4,1,2,3,4]`

`>>>`

[1,2,3]`takeWhile (< 9) [1,2,3]`

`>>>`

[]`takeWhile (< 0) [1,2,3]`

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

`span`

, applied to a predicate `p`

and a list `xs`

, returns a tuple where
first element is the longest prefix (possibly empty) of `xs`

of elements that
satisfy `p`

and second element is the remainder of the list:

`span`

`p xs`

is equivalent to `(`

, even if `takeWhile`

p xs, `dropWhile`

p xs)`p`

is `_|_`

.

#### Laziness

`>>>`

([],[])`span undefined []`

`>>>`

*** Exception: Prelude.undefined`fst (span (const False) undefined)`

`>>>`

[]`fst (span (const False) (undefined : undefined))`

`>>>`

[1]`take 1 (fst (span (const True) (1 : undefined)))`

`span`

produces the first component of the tuple lazily:

`>>>`

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

#### Examples

`>>>`

([1,2],[3,4,1,2,3,4])`span (< 3) [1,2,3,4,1,2,3,4]`

`>>>`

([1,2,3],[])`span (< 9) [1,2,3]`

`>>>`

([],[1,2,3])`span (< 0) [1,2,3]`

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`

`p`

is equivalent to

and consequently to `span`

(`not`

. p)`(`

,
even if `takeWhile`

(`not`

. p) xs, `dropWhile`

(`not`

. p) xs)`p`

is `_|_`

.

#### Laziness

`>>>`

([],[])`break undefined []`

`>>>`

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

`>>>`

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

`>>>`

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

`break`

produces the first component of the tuple lazily:

`>>>`

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

#### Examples

`>>>`

([1,2,3],[4,1,2,3,4])`break (> 3) [1,2,3,4,1,2,3,4]`

`>>>`

([],[1,2,3])`break (< 9) [1,2,3]`

`>>>`

([1,2,3],[])`break (> 9) [1,2,3]`

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

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

`xs`

returns the elements of `xs`

in reverse order.
`xs`

must be finite.

#### Laziness

`reverse`

is lazy in its elements.

`>>>`

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

`>>>`

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

#### Examples

`>>>`

[]`reverse []`

`>>>`

[42]`reverse [42]`

`>>>`

[7,5,2]`reverse [2,5,7]`

`>>>`

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

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

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

takes two lists and returns a list of
corresponding pairs.

`zip`

is right-lazy:

`>>>`

[]`zip [] undefined`

`>>>`

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

`zip`

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

#### Examples

`>>>`

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

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

`>>>`

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

`>>>`

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

`>>>`

[]`zip [] [1..]`

`>>>`

[]`zip [1..] []`

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..]

`zipWith`

is right-lazy:

`>>>`

`let f = undefined`

`>>>`

[]`zipWith f [] undefined`

`zipWith`

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

#### Examples

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

\(\mathcal{O}(\min(l,m,n))\). The `zipWith3`

function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to `zipWith`

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

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

#### Examples

`>>>`

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

`>>>`

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

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

`unzip`

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

#### Examples

`>>>`

([],[])`unzip []`

`>>>`

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

errorEmptyList :: HasCallStack => String -> a Source #