Data.List.NonEmpty

base-4.9.1.0: Basic libraries

Copyright | (C) 2011-2015 Edward Kmett (C) 2010 Tony Morris Oliver Taylor Eelis van der Weegen
License | BSD-style (see the file LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.List.NonEmpty

Contents

- The type of non-empty streams
- Non-empty stream transformations
- Basic functions
- Building streams
- Extracting sublists
- Sublist predicates
- "Set" operations
- Indexing streams
- Zipping and unzipping streams
- Converting to and from a list

Description

A `NonEmpty` list is one which always has at least one element, but is otherwise identical to the traditional list type in complexity and in terms of API. You will almost certainly want to import this module `qualified`.

Since: 4.9.0.0

Synopsis

- data NonEmpty a = a :| [a]
- map :: (a -> b) -> NonEmpty a -> NonEmpty b
- intersperse :: a -> NonEmpty a -> NonEmpty a
- scanl :: Foldable f => (b -> a -> b) -> b -> f a -> NonEmpty b
- scanr :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b
- scanl1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
- scanr1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
- transpose :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
- sortBy :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a
- sortWith :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a
- length :: NonEmpty a -> Int
- head :: NonEmpty a -> a
- tail :: NonEmpty a -> [a]
- last :: NonEmpty a -> a
- init :: NonEmpty a -> [a]
- (<|) :: a -> NonEmpty a -> NonEmpty a
- cons :: a -> NonEmpty a -> NonEmpty a
- uncons :: NonEmpty a -> (a, Maybe (NonEmpty a))
- unfoldr :: (a -> (b, Maybe a)) -> a -> NonEmpty b
- sort :: Ord a => NonEmpty a -> NonEmpty a
- reverse :: NonEmpty a -> NonEmpty a
- inits :: Foldable f => f a -> NonEmpty [a]
- tails :: Foldable f => f a -> NonEmpty [a]
- iterate :: (a -> a) -> a -> NonEmpty a
- repeat :: a -> NonEmpty a
- cycle :: NonEmpty a -> NonEmpty a
- unfold :: (a -> (b, Maybe a)) -> a -> NonEmpty b
- insert :: (Foldable f, Ord a) => a -> f a -> NonEmpty a
- some1 :: Alternative f => f a -> f (NonEmpty a)
- take :: Int -> NonEmpty a -> [a]
- drop :: Int -> NonEmpty a -> [a]
- splitAt :: Int -> NonEmpty a -> ([a], [a])
- takeWhile :: (a -> Bool) -> NonEmpty a -> [a]
- dropWhile :: (a -> Bool) -> NonEmpty a -> [a]
- span :: (a -> Bool) -> NonEmpty a -> ([a], [a])
- break :: (a -> Bool) -> NonEmpty a -> ([a], [a])
- filter :: (a -> Bool) -> NonEmpty a -> [a]
- partition :: (a -> Bool) -> NonEmpty a -> ([a], [a])
- group :: (Foldable f, Eq a) => f a -> [NonEmpty a]
- groupBy :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a]
- groupWith :: (Foldable f, Eq b) => (a -> b) -> f a -> [NonEmpty a]
- groupAllWith :: Ord b => (a -> b) -> [a] -> [NonEmpty a]
- group1 :: Eq a => NonEmpty a -> NonEmpty (NonEmpty a)
- groupBy1 :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty (NonEmpty a)
- groupWith1 :: Eq b => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a)
- groupAllWith1 :: Ord b => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a)
- isPrefixOf :: Eq a => [a] -> NonEmpty a -> Bool
- nub :: Eq a => NonEmpty a -> NonEmpty a
- nubBy :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty a
- (!!) :: NonEmpty a -> Int -> a
- zip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b)
- zipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c
- unzip :: Functor f => f (a, b) -> (f a, f b)
- fromList :: [a] -> NonEmpty a
- toList :: NonEmpty a -> [a]
- nonEmpty :: [a] -> Maybe (NonEmpty a)
- xor :: NonEmpty Bool -> Bool

# The type of non-empty streams

data NonEmpty a Source #

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

Since: 4.9.0.0

Constructors

a :| [a] infixr 5 |

Instances

Monad NonEmpty # |
Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # return :: a -> NonEmpty a Source # fail :: String -> NonEmpty a Source #
Functor NonEmpty # |
Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
MonadFix NonEmpty # |
Methods mfix :: (a -> NonEmpty a) -> NonEmpty a Source #
Applicative NonEmpty # |
Methods pure :: a -> NonEmpty a Source # (<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # (*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Foldable NonEmpty # |
Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # sum :: Num a => NonEmpty a -> a Source # product :: Num a => NonEmpty a -> a Source #
Traversable NonEmpty # |
Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source #
Generic1 NonEmpty # |
Associated Types type Rep1 (NonEmpty :: * -> *) :: * -> * Source # Methods from1 :: NonEmpty a -> Rep1 NonEmpty a Source # to1 :: Rep1 NonEmpty a -> NonEmpty a Source #
MonadZip NonEmpty # |
Methods mzip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b) Source # mzipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # munzip :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b) Source #
IsList (NonEmpty a) # |
Associated Types type Item (NonEmpty a) :: * Source # Methods fromList :: [Item (NonEmpty a)] -> NonEmpty a Source # fromListN :: Int -> [Item (NonEmpty a)] -> NonEmpty a Source # toList :: NonEmpty a -> [Item (NonEmpty a)] Source #
Eq a => Eq (NonEmpty a) # |
Methods (==) :: NonEmpty a -> NonEmpty a -> Bool Source # (/=) :: NonEmpty a -> NonEmpty a -> Bool Source #
Data a => Data (NonEmpty a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NonEmpty a -> c (NonEmpty a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NonEmpty a) Source # toConstr :: NonEmpty a -> Constr Source # dataTypeOf :: NonEmpty a -> DataType Source # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (NonEmpty a)) Source # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NonEmpty a)) Source # gmapT :: (forall b. Data b => b -> b) -> NonEmpty a -> NonEmpty a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> NonEmpty a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> NonEmpty a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source #
Ord a => Ord (NonEmpty a) # |
Methods compare :: NonEmpty a -> NonEmpty a -> Ordering Source # (<) :: NonEmpty a -> NonEmpty a -> Bool Source # (<=) :: NonEmpty a -> NonEmpty a -> Bool Source # (>) :: NonEmpty a -> NonEmpty a -> Bool Source # (>=) :: NonEmpty a -> NonEmpty a -> Bool Source # max :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # min :: NonEmpty a -> NonEmpty a -> NonEmpty a Source #
Read a => Read (NonEmpty a) # |
Methods readsPrec :: Int -> ReadS (NonEmpty a) Source # readList :: ReadS [NonEmpty a] Source # readPrec :: ReadPrec (NonEmpty a) Source # readListPrec :: ReadPrec [NonEmpty a] Source #
Show a => Show (NonEmpty a) # |
Methods showsPrec :: Int -> NonEmpty a -> ShowS Source # show :: NonEmpty a -> String Source # showList :: [NonEmpty a] -> ShowS Source #
Generic (NonEmpty a) # |
Associated Types type Rep (NonEmpty a) :: * -> * Source # Methods from :: NonEmpty a -> Rep (NonEmpty a) x Source # to :: Rep (NonEmpty a) x -> NonEmpty a Source #
Semigroup (NonEmpty a) # |
Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source #
type Rep1 NonEmpty # |
type Rep1 NonEmpty = D1 (MetaData "NonEmpty" "Data.List.NonEmpty" "base" False) (C1 (MetaCons ":|" (InfixI RightAssociative 5) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 []))))
type Rep (NonEmpty a) # |
type Rep (NonEmpty a) = D1 (MetaData "NonEmpty" "Data.List.NonEmpty" "base" False) (C1 (MetaCons ":|" (InfixI RightAssociative 5) False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [a]))))
type Item (NonEmpty a) # |
type Item (NonEmpty a) = a

# Non-empty stream transformations

map :: (a -> b) -> NonEmpty a -> NonEmpty b Source #

Map a function over a `NonEmpty` stream.

intersperse :: a -> NonEmpty a -> NonEmpty a Source #

'intersperse x xs' alternates elements of the list with copies of `x`.

    intersperse 0 (1 :| [2,3]) == 1 :| [0,2,0,3]

scanl :: Foldable f => (b -> a -> b) -> b -> f a -> NonEmpty b Source #

`scanl` is similar to `foldl`, but returns a stream 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.

scanr :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b Source #

`scanr` is the right-to-left dual of `scanl`. Note that

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

scanl1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a Source #

`scanl1` is a variant of `scanl` that has no starting value argument:

    scanl1 f [x1, x2, ...] == x1 :| [x1 `f` x2, x1 `f` (x2 `f` x3), ...]

scanr1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a Source #

`scanr1` is a variant of `scanr` that has no starting value argument.

transpose :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a) Source #

`transpose` for `NonEmpty`, behaves the same as `transpose` The rows/columns need not be the same length, in which case > transpose . transpose /= id

sortBy :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a Source #

`sortBy` for `NonEmpty`, behaves the same as `sortBy`

sortWith :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a Source #

`sortWith` for `NonEmpty`, behaves the same as:

    sortBy . comparing

# Basic functions

length :: NonEmpty a -> Int Source #

Number of elements in `NonEmpty` list.

head :: NonEmpty a -> a Source #

Extract the first element of the stream.

tail :: NonEmpty a -> [a] Source #

Extract the possibly-empty tail of the stream.

last :: NonEmpty a -> a Source #

Extract the last element of the stream.

init :: NonEmpty a -> [a] Source #

Extract everything except the last element of the stream.

(<|) :: a -> NonEmpty a -> NonEmpty a infixr 5 Source #

Prepend an element to the stream.

cons :: a -> NonEmpty a -> NonEmpty a Source #

Synonym for `<|`.

uncons :: NonEmpty a -> (a, Maybe (NonEmpty a)) Source #

`uncons` produces the first element of the stream, and a stream of the remaining elements, if any.

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

The `unfoldr` function is analogous to Data.List's `unfoldr` operation.

sort :: Ord a => NonEmpty a -> NonEmpty a Source #

Sort a stream.

reverse :: NonEmpty a -> NonEmpty a Source #

`reverse` a finite NonEmpty stream.

inits :: Foldable f => f a -> NonEmpty [a] Source #

The `inits` function takes a stream `xs` and returns all the finite prefixes of `xs`.

tails :: Foldable f => f a -> NonEmpty [a] Source #

The `tails` function takes a stream `xs` and returns all the suffixes of `xs`.

# Building streams

iterate :: (a -> a) -> a -> NonEmpty a Source #

``iterate` f x` produces the infinite sequence of repeated applications of `f` to `x`.

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

repeat :: a -> NonEmpty a Source #

``repeat` x` returns a constant stream, where all elements are equal to `x`.

cycle :: NonEmpty a -> NonEmpty a Source #

``cycle` xs` returns the infinite repetition of `xs`:

    cycle (1 :| [2,3]) = 1 :| [2,3,1,2,3,...]

unfold :: (a -> (b, Maybe a)) -> a -> NonEmpty b Source #

`unfold` produces a new stream by repeatedly applying the unfolding function to the seed value to produce an element of type `b` and a new seed value. When the unfolding function returns `Nothing` instead of a new seed value, the stream ends.

insert :: (Foldable f, Ord a) => a -> f a -> NonEmpty a Source #

``insert` x xs` inserts `x` into the last position in `xs` where it is still less than or equal to the next element. In particular, if the list is sorted beforehand, the result will also be sorted.

some1 :: Alternative f => f a -> f (NonEmpty a) Source #

``some1` x` sequences `x` one or more times.

# Extracting sublists

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

``take` n xs` returns the first `n` elements of `xs`.

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

``drop` n xs` drops the first `n` elements off the front of the sequence `xs`.

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

``splitAt` n xs` returns a pair consisting of the prefix of `xs` of length `n` and the remaining stream immediately following this prefix.

    'splitAt' n xs == ('take' n xs, 'drop' n xs)
    xs == ys ++ zs where (ys, zs) = 'splitAt' n xs

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

``takeWhile` p xs` returns the longest prefix of the stream `xs` for which the predicate `p` holds.

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

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

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

``span` p xs` returns the longest prefix of `xs` that satisfies `p`, together with the remainder of the stream.

    'span' p xs == ('takeWhile' p xs, 'dropWhile' p xs)
    xs == ys ++ zs where (ys, zs) = 'span' p xs

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

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

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

``filter` p xs` removes any elements from `xs` that do not satisfy `p`.

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

The `partition` function takes a predicate `p` and a stream `xs`, and returns a pair of lists. The first list corresponds to the elements of `xs` for which `p` holds; the second corresponds to the elements of `xs` for which `p` does not hold.

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

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

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

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

groupBy :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a] Source #

`groupBy` operates like `group`, but uses the provided equality predicate instead of `==`.

groupWith :: (Foldable f, Eq b) => (a -> b) -> f a -> [NonEmpty a] Source #

`groupWith` operates like `group`, but uses the provided projection when comparing for equality

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

`groupAllWith` operates like `groupWith`, but sorts the list first so that each equivalence class has, at most, one list in the output

group1 :: Eq a => NonEmpty a -> NonEmpty (NonEmpty a) Source #

`group1` operates like `group`, but uses the knowledge that its input is non-empty to produce guaranteed non-empty output.

groupBy1 :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty (NonEmpty a) Source #

`groupBy1` is to `group1` as `groupBy` is to `group`.

groupWith1 :: Eq b => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a) Source #

`groupWith1` is to `group1` as `groupWith` is to `group`

groupAllWith1 :: Ord b => (a -> b) -> NonEmpty a -> NonEmpty (NonEmpty a) Source #

`groupAllWith1` is to `groupWith1` as `groupAllWith` is to `groupWith`

# Sublist predicates

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

The `isPrefix` function returns `True` if the first argument is a prefix of the second.

# "Set" operations

nub :: Eq a => NonEmpty a -> NonEmpty a Source #

The `nub` function removes duplicate elements from a list. In particular, it keeps only the first occurence of each element. (The name `nub` means 'essence'.) It is a special case of `nubBy`, which allows the programmer to supply their own inequality test.

nubBy :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty a Source #

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

# Indexing streams

(!!) :: NonEmpty a -> Int -> a Source #

`xs !! n` returns the element of the stream `xs` at index `n`. Note that the head of the stream has index 0.

Beware: a negative or out-of-bounds index will cause an error.

# Zipping and unzipping streams

zip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b) Source #

The `zip` function takes two streams and returns a stream of corresponding pairs.

zipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source #

The `zipWith` function generalizes `zip`. Rather than tupling the elements, the elements are combined using the function passed as the first argument.

unzip :: Functor f => f (a, b) -> (f a, f b) Source #

The `unzip` function is the inverse of the `zip` function.

# Converting to and from a list

fromList :: [a] -> NonEmpty a Source #

Converts a normal list to a `NonEmpty` stream.

Raises an error if given an empty list.

toList :: NonEmpty a -> [a] Source #

Convert a stream to a normal list efficiently.

nonEmpty :: [a] -> Maybe (NonEmpty a) Source #

`nonEmpty` efficiently turns a normal list into a `NonEmpty` stream, producing `Nothing` if the input is empty.

xor :: NonEmpty Bool -> Bool Source #

Compute n-ary logic exclusive OR operation on `NonEmpty` list.