Data.List.NonEmpty.Compat

This backports the modern Data.Semigroup interface back to base-4.9/GHC 8.0.

The type of non-empty streams

data NonEmpty a

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

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5

Instances

Foldable NonEmpty

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m

foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m

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

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b

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

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b

foldr1 :: (a -> a -> a) -> NonEmpty a -> a

foldl1 :: (a -> a -> a) -> NonEmpty a -> a

toList :: NonEmpty a -> [a]

null :: NonEmpty a -> Bool

length :: NonEmpty a -> Int

elem :: Eq a => a -> NonEmpty a -> Bool

maximum :: Ord a => NonEmpty a -> a

minimum :: Ord a => NonEmpty a -> a

sum :: Num a => NonEmpty a -> a

product :: Num a => NonEmpty a -> a

Foldable1 NonEmpty

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => NonEmpty m -> m

foldMap1 :: Semigroup m => (a -> m) -> NonEmpty a -> m

foldMap1' :: Semigroup m => (a -> m) -> NonEmpty a -> m

toNonEmpty :: NonEmpty a -> NonEmpty a

maximum :: Ord a => NonEmpty a -> a

minimum :: Ord a => NonEmpty a -> a

head :: NonEmpty a -> a

last :: NonEmpty a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> NonEmpty a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> NonEmpty a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> NonEmpty a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> NonEmpty a -> b

Traversable NonEmpty

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b)

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a)

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b)

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a)

Applicative NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

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

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a

Functor NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

(<$) :: a -> NonEmpty b -> NonEmpty a

Monad NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

return :: a -> NonEmpty a

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Read a => Read (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (NonEmpty a)

readList :: ReadS [NonEmpty a]

readPrec :: ReadPrec (NonEmpty a)

readListPrec :: ReadPrec [NonEmpty a]

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS

show :: NonEmpty a -> String

showList :: [NonEmpty a] -> ShowS

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool

(/=) :: NonEmpty a -> NonEmpty a -> Bool

Ord a => Ord (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

compare :: NonEmpty a -> NonEmpty a -> Ordering

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

(<=) :: NonEmpty a -> NonEmpty a -> Bool

(>) :: NonEmpty a -> NonEmpty a -> Bool

(>=) :: NonEmpty a -> NonEmpty a -> Bool

max :: NonEmpty a -> NonEmpty a -> NonEmpty a

min :: NonEmpty a -> NonEmpty a -> 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.

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

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

sortBy for NonEmpty, behaves the same as sortBy

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

sortWith for NonEmpty, behaves the same as:

sortBy . comparing

Basic functions

length :: NonEmpty a -> Int

Number of elements in NonEmpty list.

compareLength :: NonEmpty a -> Int -> Ordering

Use compareLength xs n as a safer and faster alternative to compare (length xs) n. Similarly, it's better to write compareLength xs 10 == LT instead of length xs < 10.

While length would force and traverse the entire spine of xs (which could even diverge if xs is infinite), compareLength traverses at most n elements to determine its result.

>>> compareLength ('a' :| []) 1
EQ
>>> compareLength ('a' :| ['b']) 3
LT
>>> compareLength (0 :| [1..]) 100
GT
>>> compareLength undefined 0
GT
>>> compareLength ('a' :| 'b' : undefined) 1
GT

Since: 4.21.0.0

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.

singleton :: a -> NonEmpty a

Construct a NonEmpty list from a single element.

Since: base-4.15

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

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

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

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

Sort a stream.

sortOn :: Ord b => (a -> b) -> NonEmpty a -> NonEmpty a

Sort a NonEmpty on a user-supplied projection of its elements. See sortOn for more detailed information.

Examples

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

>>> sortOn length $ "jim" :| ["creed", "pam", "michael", "dwight", "kevin"]
"jim" :| ["pam","creed","kevin","dwight","michael"]

Performance notes

This function minimises the projections performed, by materialising the projections in an intermediate list.

For trivial projections, you should prefer using sortBy with comparing, for example:

>>> sortBy (comparing fst) $ (3, 1) :| [(2, 2), (1, 3)]
(1,3) :| [(2,2),(3,1)]

Or, for the exact same API as sortOn, you can use `sortBy . comparing`:

>>> (sortBy . comparing) fst $ (3, 1) :| [(2, 2), (1, 3)]
(1,3) :| [(2,2),(3,1)]

sortWith is an alias for `sortBy . comparing`.

Since: 4.20.0.0

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, starting with the shortest. The result is NonEmpty because the result always contains the empty list as the first element.

inits [1,2,3] == [] :| [[1], [1,2], [1,2,3]]
inits [1] == [] :| [[1]]
inits [] == [] :| []

inits1 :: NonEmpty a -> NonEmpty (NonEmpty a)

The inits1 function takes a NonEmpty stream xs and returns all the NonEmpty finite prefixes of xs, starting with the shortest.

inits1 (1 :| [2,3]) == (1 :| []) :| [1 :| [2], 1 :| [2,3]]
inits1 (1 :| []) == (1 :| []) :| []

Since: base-4.18

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

The tails function takes a stream xs and returns all the suffixes of xs, starting with the longest. The result is NonEmpty because the result always contains the empty list as the last element.

tails [1,2,3] == [1,2,3] :| [[2,3], [3], []]
tails [1] == [1] :| [[]]
tails [] == [] :| []

tails1 :: NonEmpty a -> NonEmpty (NonEmpty a)

The tails1 function takes a NonEmpty stream xs and returns all the non-empty suffixes of xs, starting with the longest.

tails1 (1 :| [2,3]) == (1 :| [2,3]) :| [2 :| [3], 3 :| []]
tails1 (1 :| []) == (1 :| []) :| []

Since: base-4.18

append :: NonEmpty a -> NonEmpty a -> NonEmpty a

A monomorphic version of <> for NonEmpty.

>>> append (1 :| []) (2 :| [3])
1 :| [2,3]

Since: base-4.16

appendList :: NonEmpty a -> [a] -> NonEmpty a

Attach a list at the end of a NonEmpty.

>>> appendList (1 :| [2,3]) []
1 :| [2,3]

>>> appendList (1 :| [2,3]) [4,5]
1 :| [2,3,4,5]

Since: base-4.16

prependList :: [a] -> NonEmpty a -> NonEmpty a

Attach a list at the beginning of a NonEmpty.

>>> prependList [] (1 :| [2,3])
1 :| [2,3]

>>> prependList [negate 1, 0] (1 :| [2, 3])
-1 :| [0,1,2,3]

Since: base-4.16

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.

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

some1 x sequences x one or more times.

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 ==.

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

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

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

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)

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.

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

groupWith1 is to group1 as groupWith is to group

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

groupAllWith1 is to groupWith1 as groupAllWith is to groupWith

permutations :: [a] -> NonEmpty [a]

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

Since: 4.20.0.0

permutations1 :: NonEmpty a -> NonEmpty (NonEmpty a)

permutations1 operates like permutations, but uses the knowledge that its input is non-empty to produce output where every element is non-empty.

permutations1 = fmap fromList . permutations . toList

Since: 4.20.0.0

Sublist predicates

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

The isPrefixOf 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 occurrence 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

(!!) :: HasCallStack => NonEmpty a -> Int -> a infixl 9

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.

Converting to and from a list

fromList :: HasCallStack => [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

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