Data.HashSet

Introduction

HashSet allows you to store unique elements, providing efficient insertion, lookups, and deletion. A HashSet makes no guarantees as to the order of its elements.

If you are storing sets of Data.Ints consider using Data.IntSet from the containers package.

Examples

All the examples below assume HashSet is imported qualified, and uses the following dataStructures set.

>>> import qualified Data.HashSet as HashSet
>>> let dataStructures = HashSet.fromList ["Set", "Map", "Graph", "Sequence"]

Basic Operations

Check membership in a set:

>>> -- Check if "Map" and "Trie" are in the set of data structures.
>>> HashSet.member "Map" dataStructures
True
>>> HashSet.member "Trie" dataStructures
False

Add a new entry to the set:

>>> let moreDataStructures = HashSet.insert "Trie" dataStructures
>>> HashSet.member "Trie" moreDataStructures
> True

Remove the "Graph" entry from the set of data structures.

>>> let fewerDataStructures = HashSet.delete "Graph" dataStructures
>>> HashSet.toList fewerDataStructures
["Map","Set","Sequence"]

Create a new set and combine it with our original set.

>>> let unorderedDataStructures = HashSet.fromList ["HashSet", "HashMap"]
>>> HashSet.union dataStructures unorderedDataStructures
fromList ["Map","HashSet","Graph","HashMap","Set","Sequence"]

Using custom data with HashSet

To create a HashSet of your custom type, the type must have instances for Eq and Hashable. The Hashable typeclass is defined in the hashable package, see the documentation for information on how to make your type an instance of Hashable.

We'll start by setting up our custom data type:

>>> :set -XDeriveGeneric
>>> import GHC.Generics (Generic)
>>> import Data.Hashable
>>> data Person = Person { name :: String, likesDogs :: Bool } deriving (Show, Eq, Generic)
>>> instance Hashable Person

And now we'll use it!

>>> let people = HashSet.fromList [Person "Lana" True, Person "Joe" False, Person "Simon" True]
>>> HashSet.filter likesDogs people
fromList [Person {name = "Simon", likesDogs = True},Person {name = "Lana", likesDogs = True}]

Performance

The implementation is based on hash array mapped tries. A HashSet is often faster than other Ord-based set types, especially when value comparisons are 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

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

NFData1 HashSet

Since: 0.2.14.0

Defined in Data.HashSet.Internal

Methods

liftRnf :: (a -> ()) -> HashSet a -> ()

Hashable1 HashSet

Defined in Data.HashSet.Internal

Methods

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

Lift a => Lift (HashSet a :: Type)

Since: 0.2.17.0

Defined in Data.HashSet.Internal

Methods

lift :: HashSet a -> Q Exp

liftTyped :: HashSet a -> Q (TExp (HashSet a))

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

Defined in Data.HashSet.Internal

Associated Types

type Item (HashSet a)

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 :: forall r r'. (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]

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.

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"]

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

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.

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).

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]