-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Haskell 98 semigroups
--
-- Haskell 98 semigroups
--
-- In mathematics, a semigroup is an algebraic structure consisting of a
-- set together with an associative binary operation. A semigroup
-- generalizes a monoid in that there might not exist an identity
-- element. It also (originally) generalized a group (a monoid with all
-- inverses) to a type where every element did not have to have an
-- inverse, thus the name semigroup.
@package semigroups
@version 0.9.2
-- | A NonEmpty list forms a monad as per list, but always contains at
-- least one element.
module Data.List.NonEmpty
data NonEmpty a
(:|) :: a -> [a] -> NonEmpty a
-- | Map a function over a NonEmpty stream.
map :: (a -> b) -> NonEmpty a -> NonEmpty b
-- | 'intersperse x xs' alternates elements of the list with copies of
-- x.
--
--
-- intersperse 0 (1 :| [2,3]) == 1 :| [0,2,0,3]
--
intersperse :: a -> NonEmpty a -> NonEmpty a
-- | 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.
--
scanl :: Foldable f => (b -> a -> 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.
--
scanr :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b
-- | 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), ...]
--
scanl1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
-- | scanr1 is a variant of scanr that has no starting value
-- argument.
scanr1 :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
-- | Extract the first element of the stream.
head :: NonEmpty a -> a
-- | Extract the possibly-empty tail of the stream.
tail :: NonEmpty a -> [a]
-- | Extract the last element of the stream.
last :: NonEmpty a -> a
-- | Extract everything except the last element of the stream.
init :: NonEmpty a -> [a]
-- | Prepend an element to the stream.
(<|) :: a -> NonEmpty a -> NonEmpty a
-- | Synonym for <|.
cons :: a -> NonEmpty a -> NonEmpty a
-- | uncons produces the first element of the stream, and a stream
-- of the remaining elements, if any.
uncons :: NonEmpty a -> (a, Maybe (NonEmpty a))
-- | Sort a stream.
sort :: Ord a => NonEmpty a -> NonEmpty a
-- | reverse a finite NonEmpty stream.
reverse :: NonEmpty a -> NonEmpty a
-- | The inits function takes a stream xs and returns all
-- the finite prefixes of xs.
inits :: Foldable f => f a -> NonEmpty [a]
-- | The tails function takes a stream xs and returns all
-- the suffixes of xs.
tails :: Foldable f => f 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), ..]
--
iterate :: (a -> a) -> a -> NonEmpty a
-- | repeat x returns a constant stream, where all elements
-- are equal to x.
repeat :: a -> NonEmpty a
-- | cycle xs returns the infinite repetition of
-- xs:
--
--
-- cycle [1,2,3] = 1 :| [2,3,1,2,3,...]
--
cycle :: NonEmpty a -> NonEmpty a
-- | 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.
unfold :: (a -> (b, Maybe a)) -> a -> NonEmpty b
-- | 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.
insert :: (Foldable f, Ord a) => a -> f a -> NonEmpty a
-- | take n xs returns the first n elements of
-- xs.
take :: Int -> NonEmpty a -> [a]
-- | drop n xs drops the first n elements off the
-- front of the sequence xs.
drop :: Int -> NonEmpty 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
--
splitAt :: Int -> NonEmpty a -> ([a], [a])
-- | takeWhile p xs returns the longest prefix of the
-- stream xs for which the predicate p holds.
takeWhile :: (a -> Bool) -> NonEmpty a -> [a]
-- | dropWhile p xs returns the suffix remaining after
-- takeWhile p xs.
dropWhile :: (a -> Bool) -> NonEmpty 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
--
span :: (a -> Bool) -> NonEmpty a -> ([a], [a])
-- | The break p function is equivalent to span
-- (not . p).
break :: (a -> Bool) -> NonEmpty a -> ([a], [a])
-- | filter p xs removes any elements from xs that
-- do not satisfy p.
filter :: (a -> Bool) -> NonEmpty 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)
--
partition :: (a -> Bool) -> NonEmpty a -> ([a], [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" : ...
--
group :: (Foldable f, Eq a) => f a -> [NonEmpty a]
-- | groupBy operates like group, but uses the provided
-- equality predicate instead of ==.
groupBy :: Foldable f => (a -> a -> Bool) -> f a -> [NonEmpty a]
-- | group1 operates like group, but uses the knowledge that
-- its input is non-empty to produce guaranteed non-empty output.
group1 :: Eq a => NonEmpty a -> NonEmpty (NonEmpty a)
-- | groupBy1 is to group1 as groupBy is to
-- group.
groupBy1 :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty (NonEmpty a)
-- | The isPrefix function returns True if the first
-- argument is a prefix of the second.
isPrefixOf :: Eq a => [a] -> NonEmpty a -> Bool
-- | 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.
(!!) :: NonEmpty a -> Int -> a
-- | The zip function takes two streams and returns a stream of
-- corresponding pairs.
zip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b)
-- | The zipWith function generalizes zip. Rather than
-- tupling the elements, the elements are combined using the function
-- passed as the first argument.
zipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c
-- | The unzip function is the inverse of the zip function.
unzip :: Functor f => f (a, b) -> (f a, f b)
-- | 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.
words :: NonEmpty Char -> NonEmpty String
-- | The unwords function is an inverse operation to words.
-- It joins words with separating spaces.
--
-- Beware: the input ("" :| []) will cause an error.
unwords :: NonEmpty String -> NonEmpty Char
-- | The lines function breaks a stream of characters into a stream
-- of strings at newline characters. The resulting strings do not contain
-- newlines.
lines :: NonEmpty Char -> NonEmpty String
-- | The unlines function is an inverse operation to lines.
-- It joins lines, after appending a terminating newline to each.
unlines :: NonEmpty String -> NonEmpty Char
-- | Converts a normal list to a NonEmpty stream.
--
-- Raises an error if given an empty list.
fromList :: [a] -> NonEmpty a
-- | Convert a stream to a normal list efficiently.
toList :: NonEmpty a -> [a]
-- | nonEmpty efficiently turns a normal list into a NonEmpty
-- stream, producing Nothing if the input is empty.
nonEmpty :: [a] -> Maybe (NonEmpty a)
xor :: NonEmpty Bool -> Bool
instance Typeable1 NonEmpty
instance Eq a => Eq (NonEmpty a)
instance Ord a => Ord (NonEmpty a)
instance Show a => Show (NonEmpty a)
instance Read a => Read (NonEmpty a)
instance Data a => Data (NonEmpty a)
instance Foldable NonEmpty
instance Traversable NonEmpty
instance Monad NonEmpty
instance Applicative NonEmpty
instance Functor NonEmpty
-- | In mathematics, a semigroup is an algebraic structure consisting of a
-- set together with an associative binary operation. A semigroup
-- generalizes a monoid in that there might not exist an identity
-- element. It also (originally) generalized a group (a monoid with all
-- inverses) to a type where every element did not have to have an
-- inverse, thus the name semigroup.
--
-- The use of (<>) in this module conflicts with an
-- operator with the same name that is being exported by Data.Monoid.
-- However, this package re-exports (most of) the contents of
-- Data.Monoid, so to use semigroups and monoids in the same package just
--
--
-- import Data.Semigroup
--
module Data.Semigroup
class Semigroup a where <> = mappend sconcat (a :| as) = go a as where go b (c : cs) = b <> go c cs go b [] = b times1p y0 x0 = f x0 (1 + y0) where f x y | even y = f (x <> x) (y `quot` 2) | y == 1 = x | otherwise = g (x <> x) (unsafePred y `quot` 2) x g x y z | even y = g (x <> x) (y `quot` 2) z | y == 1 = x <> z | otherwise = g (x <> x) (unsafePred y `quot` 2) (x <> z)
(<>) :: Semigroup a => a -> a -> a
sconcat :: Semigroup a => NonEmpty a -> a
times1p :: (Semigroup a, Whole n) => n -> a -> a
newtype Min a
Min :: a -> Min a
getMin :: Min a -> a
newtype Max a
Max :: a -> Max a
getMax :: Max a -> a
-- | Use Option (First a) -- to get the behavior of
-- First
newtype First a
First :: a -> First a
getFirst :: First a -> a
-- | Use Option (Last a) -- to get the behavior of
-- Last
newtype Last a
Last :: a -> Last a
getLast :: Last a -> a
-- | Provide a Semigroup for an arbitrary Monoid.
newtype WrappedMonoid m
WrapMonoid :: m -> WrappedMonoid m
unwrapMonoid :: WrappedMonoid m -> m
-- | Repeat a value n times.
--
--
-- times n a = a <> a <> ... <> a -- using <> (n-1) times
--
--
-- Implemented using times1p.
timesN :: (Whole n, Monoid a) => n -> a -> a
-- | The class of monoids (types with an associative binary operation that
-- has an identity). Instances should satisfy the following laws:
--
--
--
-- The method names refer to the monoid of lists under concatenation, but
-- there are many other instances.
--
-- Minimal complete definition: mempty and mappend.
--
-- Some types can be viewed as a monoid in more than one way, e.g. both
-- addition and multiplication on numbers. In such cases we often define
-- newtypes and make those instances of Monoid, e.g.
-- Sum and Product.
class Monoid a
mempty :: Monoid a => a
mappend :: Monoid a => a -> a -> a
mconcat :: Monoid a => [a] -> a
-- | The dual of a monoid, obtained by swapping the arguments of
-- mappend.
newtype Dual a :: * -> *
Dual :: a -> Dual a
getDual :: Dual a -> a
-- | The monoid of endomorphisms under composition.
newtype Endo a :: * -> *
Endo :: (a -> a) -> Endo a
appEndo :: Endo a -> a -> a
-- | Boolean monoid under conjunction.
newtype All :: *
All :: Bool -> All
getAll :: All -> Bool
-- | Boolean monoid under disjunction.
newtype Any :: *
Any :: Bool -> Any
getAny :: Any -> Bool
-- | Monoid under addition.
newtype Sum a :: * -> *
Sum :: a -> Sum a
getSum :: Sum a -> a
-- | Monoid under multiplication.
newtype Product a :: * -> *
Product :: a -> Product a
getProduct :: Product a -> a
-- | Option is effectively Maybe with a better instance of
-- Monoid, built off of an underlying Semigroup instead of
-- an underlying Monoid. Ideally, this type would not exist at all
-- and we would just fix the Monoid intance of Maybe
newtype Option a
Option :: Maybe a -> Option a
getOption :: Option a -> Maybe a
option :: b -> (a -> b) -> Option a -> b
-- | This lets you use a difference list of a Semigroup as a Monoid.
diff :: Semigroup m => m -> Endo m
-- | A generalization of cycle to an arbitrary Semigroup. May
-- fail to terminate for some values in some semigroups.
cycle1 :: Semigroup m => m -> m
instance Typeable1 Min
instance Typeable1 Max
instance Typeable1 First
instance Typeable1 Last
instance Typeable1 WrappedMonoid
instance Typeable1 Option
instance Eq a => Eq (Min a)
instance Ord a => Ord (Min a)
instance Bounded a => Bounded (Min a)
instance Show a => Show (Min a)
instance Read a => Read (Min a)
instance Data a => Data (Min a)
instance Eq a => Eq (Max a)
instance Ord a => Ord (Max a)
instance Bounded a => Bounded (Max a)
instance Show a => Show (Max a)
instance Read a => Read (Max a)
instance Data a => Data (Max a)
instance Eq a => Eq (First a)
instance Ord a => Ord (First a)
instance Bounded a => Bounded (First a)
instance Show a => Show (First a)
instance Read a => Read (First a)
instance Data a => Data (First a)
instance Eq a => Eq (Last a)
instance Ord a => Ord (Last a)
instance Bounded a => Bounded (Last a)
instance Show a => Show (Last a)
instance Read a => Read (Last a)
instance Data a => Data (Last a)
instance Eq m => Eq (WrappedMonoid m)
instance Ord m => Ord (WrappedMonoid m)
instance Bounded m => Bounded (WrappedMonoid m)
instance Show m => Show (WrappedMonoid m)
instance Read m => Read (WrappedMonoid m)
instance Data m => Data (WrappedMonoid m)
instance Eq a => Eq (Option a)
instance Ord a => Ord (Option a)
instance Show a => Show (Option a)
instance Read a => Read (Option a)
instance Data a => Data (Option a)
instance Ord k => Semigroup (Map k v)
instance Semigroup (IntMap v)
instance Ord a => Semigroup (Set a)
instance Semigroup IntSet
instance Semigroup (Seq a)
instance Semigroup a => Monoid (Option a)
instance Semigroup a => Semigroup (Option a)
instance Traversable Option
instance Foldable Option
instance MonadFix Option
instance MonadPlus Option
instance Alternative Option
instance Monad Option
instance Applicative Option
instance Functor Option
instance Monoid m => Monoid (WrappedMonoid m)
instance Monoid m => Semigroup (WrappedMonoid m)
instance Semigroup (Last a)
instance Semigroup (First a)
instance (Ord a, Bounded a) => Monoid (Max a)
instance Ord a => Semigroup (Max a)
instance (Ord a, Bounded a) => Monoid (Min a)
instance Ord a => Semigroup (Min a)
instance Semigroup (NonEmpty a)
instance Semigroup (Last a)
instance Semigroup (First a)
instance Num a => Semigroup (Product a)
instance Num a => Semigroup (Sum a)
instance Semigroup Any
instance Semigroup All
instance Semigroup (Endo a)
instance Semigroup a => Semigroup (Dual a)
instance Semigroup Ordering
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)
instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)
instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)
instance (Semigroup a, Semigroup b) => Semigroup (a, b)
instance Semigroup (Either a b)
instance Semigroup a => Semigroup (Maybe a)
instance Semigroup [a]
instance Semigroup b => Semigroup (a -> b)
instance Semigroup ()