Data.HashSet.Internal

WARNING

This module is considered internal.

The Package Versioning Policy does not apply.

The contents of this module may change in any way whatsoever and without any warning between minor versions of this package.

Authors importing this module are expected to track development closely.

Description

A set of hashable values. A set cannot contain duplicate items. A HashSet makes no guarantees as to the order of its elements.

The implementation is based on hash array mapped tries. A HashSet is often faster than other tree-based set types, especially when value comparison is expensive, as in the case of strings.

Many operations have a average-case complexity of O(log n). The implementation uses a large base (i.e. 16) so in practice these operations are constant time.

Documentation

data HashSet a

A set of values. A set cannot contain duplicate values.

Instances

Foldable HashSet

Defined in Data.HashSet.Internal

Methods

fold :: Monoid m => HashSet m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> HashSet a -> a

foldl1 :: (a -> a -> a) -> HashSet a -> a

toList :: HashSet a -> [a]

null :: HashSet a -> Bool

length :: HashSet a -> Int

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

maximum :: Ord a => HashSet a -> a

minimum :: Ord a => HashSet a -> a

sum :: Num a => HashSet a -> a

product :: Num a => HashSet a -> a

Eq1 HashSet

Defined in Data.HashSet.Internal

Methods

liftEq :: (a -> b -> Bool) -> HashSet a -> HashSet b -> Bool

Ord1 HashSet

Defined in Data.HashSet.Internal

Methods

liftCompare :: (a -> b -> Ordering) -> HashSet a -> HashSet b -> Ordering

Show1 HashSet

Defined in Data.HashSet.Internal

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashSet a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashSet a] -> ShowS

Hashable1 HashSet

Defined in Data.HashSet.Internal

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashSet a -> Int

(Eq a, Hashable a) => IsList (HashSet a)

Defined in Data.HashSet.Internal

Associated Types

type Item (HashSet a) :: Type

Methods

fromList :: [Item (HashSet a)] -> HashSet a

fromListN :: Int -> [Item (HashSet a)] -> HashSet a

toList :: HashSet a -> [Item (HashSet a)]

Eq a => Eq (HashSet a)

Note that, in the presence of hash collisions, equal HashSets may behave differently, i.e. substitutivity may be violated:

>>> data D = A | B deriving (Eq, Show)
>>> instance Hashable D where hashWithSalt salt _d = salt

>>> x = fromList [A, B]
>>> y = fromList [B, A]

>>> x == y
True
>>> toList x
[A,B]
>>> toList y
[B,A]

In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals.

Defined in Data.HashSet.Internal

Methods

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

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

(Data a, Eq a, Hashable a) => Data (HashSet a)

Defined in Data.HashSet.Internal

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashSet a -> c (HashSet a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashSet a)

toConstr :: HashSet a -> Constr

dataTypeOf :: HashSet a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (HashSet a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashSet a))

gmapT :: (forall b. Data b => b -> b) -> HashSet a -> HashSet a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r

gmapQ :: (forall d. Data d => d -> u) -> HashSet a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> HashSet a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a)

Ord a => Ord (HashSet a)

Defined in Data.HashSet.Internal

Methods

compare :: HashSet a -> HashSet a -> Ordering

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

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

(>) :: HashSet a -> HashSet a -> Bool

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

max :: HashSet a -> HashSet a -> HashSet a

min :: HashSet a -> HashSet a -> HashSet a

(Eq a, Hashable a, Read a) => Read (HashSet a)

Defined in Data.HashSet.Internal

Methods

readsPrec :: Int -> ReadS (HashSet a)

readList :: ReadS [HashSet a]

readPrec :: ReadPrec (HashSet a)

readListPrec :: ReadPrec [HashSet a]

Show a => Show (HashSet a)

Defined in Data.HashSet.Internal

Methods

showsPrec :: Int -> HashSet a -> ShowS

show :: HashSet a -> String

showList :: [HashSet a] -> ShowS

(Hashable a, Eq a) => Semigroup (HashSet a)

<> = union

O(n+m)

To obtain good performance, the smaller set must be presented as the first argument.

Examples

>>> fromList [1,2] <> fromList [2,3]
fromList [1,2,3]

Defined in Data.HashSet.Internal

Methods

(<>) :: HashSet a -> HashSet a -> HashSet a

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

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

(Hashable a, Eq a) => Monoid (HashSet a)

mempty = empty

mappend = union

O(n+m)

To obtain good performance, the smaller set must be presented as the first argument.

Examples

>>> mappend (fromList [1,2]) (fromList [2,3])
fromList [1,2,3]

Defined in Data.HashSet.Internal

Methods

mempty :: HashSet a

mappend :: HashSet a -> HashSet a -> HashSet a

mconcat :: [HashSet a] -> HashSet a

NFData a => NFData (HashSet a)

Defined in Data.HashSet.Internal

Methods

rnf :: HashSet a -> ()

Hashable a => Hashable (HashSet a)

Defined in Data.HashSet.Internal

Methods

hashWithSalt :: Int -> HashSet a -> Int

hash :: HashSet a -> Int

type Item (HashSet a)

Defined in Data.HashSet.Internal

type Item (HashSet a) = a

Construction

empty :: HashSet a

O(1) Construct an empty set.

>>> HashSet.empty
fromList []

singleton :: Hashable a => a -> HashSet a

O(1) Construct a set with a single element.

>>> HashSet.singleton 1
fromList [1]

Basic interface

null :: HashSet a -> Bool

O(1) Return True if this set is empty, False otherwise.

>>> HashSet.null HashSet.empty
True
>>> HashSet.null (HashSet.singleton 1)
False

size :: HashSet a -> Int

O(n) Return the number of elements in this set.

>>> HashSet.size HashSet.empty
0
>>> HashSet.size (HashSet.fromList [1,2,3])
3

member :: (Eq a, Hashable a) => a -> HashSet a -> Bool

O(log n) Return True if the given value is present in this set, False otherwise.

>>> HashSet.member 1 (Hashset.fromList [1,2,3])
True
>>> HashSet.member 1 (Hashset.fromList [4,5,6])
False

insert :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a

O(log n) Add the specified value to this set.

>>> HashSet.insert 1 HashSet.empty
fromList [1]

delete :: (Eq a, Hashable a) => a -> HashSet a -> HashSet a

O(log n) Remove the specified value from this set if present.

>>> HashSet.delete 1 (HashSet.fromList [1,2,3])
fromList [2,3]
>>> HashSet.delete 1 (HashSet.fromList [4,5,6])
fromList [4,5,6]

isSubsetOf :: (Eq a, Hashable a) => HashSet a -> HashSet a -> Bool

O(n*log m) Inclusion of sets.

Examples

>>> fromList [1,3] `isSubsetOf` fromList [1,2,3]
True

>>> fromList [1,2] `isSubsetOf` fromList [1,3]
False

Since: 0.2.12

Transformations

map :: (Hashable b, Eq b) => (a -> b) -> HashSet a -> HashSet b

O(n) Transform this set by applying a function to every value. The resulting set may be smaller than the source.

>>> HashSet.map show (HashSet.fromList [1,2,3])
HashSet.fromList ["1","2","3"]

Combine

union :: (Eq a, Hashable a) => HashSet a -> HashSet a -> HashSet a

O(n+m) Construct a set containing all elements from both sets.

To obtain good performance, the smaller set must be presented as the first argument.

>>> union (fromList [1,2]) (fromList [2,3])
fromList [1,2,3]

unions :: (Eq a, Hashable a) => [HashSet a] -> HashSet a

Construct a set containing all elements from a list of sets.

Difference and intersection

difference :: (Eq a, Hashable a) => HashSet a -> HashSet a -> HashSet a

O(n) Difference of two sets. Return elements of the first set not existing in the second.

>>> HashSet.difference (HashSet.fromList [1,2,3]) (HashSet.fromList [2,3,4])
fromList [1]

intersection :: (Eq a, Hashable a) => HashSet a -> HashSet a -> HashSet a

O(n) Intersection of two sets. Return elements present in both the first set and the second.

>>> HashSet.intersection (HashSet.fromList [1,2,3]) (HashSet.fromList [2,3,4])
fromList [2,3]

Folds

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

O(n) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the right-identity of the operator).

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

O(n) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the right-identity of the operator). Each application of the operator is evaluated before before using the result in the next application. This function is strict in the starting value.

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

O(n) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the left-identity of the operator).

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

O(n) Reduce this set by applying a binary operator to all elements, using the given starting value (typically the left-identity of the operator). Each application of the operator is evaluated before before using the result in the next application. This function is strict in the starting value.

Filter

filter :: (a -> Bool) -> HashSet a -> HashSet a

O(n) Filter this set by retaining only elements satisfying a predicate.

Conversions

Lists

toList :: HashSet a -> [a]

O(n) Return a list of this set's elements. The list is produced lazily.

fromList :: (Eq a, Hashable a) => [a] -> HashSet a

O(n*min(W, n)) Construct a set from a list of elements.

HashMaps

toMap :: HashSet a -> HashMap a ()

O(1) Convert to set to the equivalent HashMap with () values.

>>> HashSet.toMap (HashSet.singleton 1)
fromList [(1,())]

fromMap :: HashMap a () -> HashSet a

O(1) Convert from the equivalent HashMap with () values.

>>> HashSet.fromMap (HashMap.singleton 1 ())
fromList [1]

keysSet :: HashMap k a -> HashSet k

O(n) Produce a HashSet of all the keys in the given HashMap.

>>> HashSet.keysSet (HashMap.fromList [(1, "a"), (2, "b")]
fromList [1,2]

Since: 0.2.10.0