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

\(O(1)\) Construct an empty set.

>>> HashSet.empty
fromList []

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

>>> HashSet.singleton 1
fromList [1]

\(O(n+m)\) 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]

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

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

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

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

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

\(O(\log n)\) 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

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

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

\(O(\log n)\) 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]

\(O(n)\) 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"]

\(O(n)\) 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]

\(O(n)\) 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]

\(O(n)\) 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.

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

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

\(O(n)\) Return a list of this set's elements. The list is produced lazily. The order of its elements is unspecified, and it may change from version to version of either this package or of hashable.

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

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

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

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

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