Data.List.NonEmpty

A NonEmpty list forms a monad as per list, but always contains at least one element.

The type of non-empty streams

data NonEmpty a

Constructors

a :| [a]

Instances

Monad NonEmpty

Functor NonEmpty

Typeable1 NonEmpty

Applicative NonEmpty

Foldable NonEmpty

Traversable NonEmpty

Eq a => Eq (NonEmpty a)

Data a => Data (NonEmpty a)

Ord a => Ord (NonEmpty a)

Read a => Read (NonEmpty a)

Show a => Show (NonEmpty a)

Semigroup (NonEmpty a)

Non-empty stream transformations

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

Map a function over a NonEmpty stream.

intersperse :: a -> NonEmpty a -> NonEmpty a

'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

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

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

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

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

Basic functions

length :: NonEmpty a -> Int

head :: NonEmpty a -> a

Extract the first element of the stream.

tail :: NonEmpty a -> [a]

Extract the possibly-empty tail of the stream.

last :: NonEmpty a -> a

Extract the last element of the stream.

init :: NonEmpty a -> [a]

Extract everything except the last element of the stream.

(<|) :: a -> NonEmpty a -> NonEmpty a

Prepend an element to the stream.

cons :: a -> NonEmpty a -> NonEmpty a

Synonym for <|.

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

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

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

Sort a stream.

reverse :: NonEmpty a -> NonEmpty a

reverse a finite NonEmpty stream.

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

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

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

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

Building streams

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

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

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

cycle :: NonEmpty a -> NonEmpty a

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

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

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.

Extracting sublists

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

take n xs returns the first n elements of xs.

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

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

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

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]

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

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

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

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

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])

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

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

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

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

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]

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]

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

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

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)

groupBy1 is to group1 as groupBy is to group.

Sublist predicates

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

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

"Set" operations

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

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

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

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)

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

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

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)

The unzip function is the inverse of the zip function.

Functions on streams of characters

words :: NonEmpty Char -> NonEmpty String

The words function breaks a stream of characters into a stream of words, which were delimited by white space.

Beware: if the input contains no words (i.e. is entirely whitespace), this will cause an error.

unwords :: NonEmpty String -> NonEmpty Char

The unwords function is an inverse operation to words. It joins words with separating spaces.

Beware: the input ("" :| []) will cause an error.

lines :: NonEmpty Char -> NonEmpty String

The lines function breaks a stream of characters into a stream of strings at newline characters. The resulting strings do not contain newlines.

unlines :: NonEmpty String -> NonEmpty Char

The unlines function is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

Converting to and from a list

fromList :: [a] -> NonEmpty a

Converts a normal list to a NonEmpty stream.

Raises an error if given an empty list.

toList :: NonEmpty a -> [a]

Convert a stream to a normal list efficiently.

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

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

xor :: NonEmpty Bool -> Bool