A set of Word8 numbers.

Implemented using Word256.

Key of Word8Set is Word8.

The empty set.

>>> empty
fromList []

The full set.

>>> full
fromList [0,1,2,3,4,5,6,7,8,9,10,11,12,...,255]

A set of one element.

>>> singleton 127
fromList [127]

A set of inclusive range.

>>> range 10 20
fromList [10,11,12,13,14,15,16,17,18,19,20]

Add a value to the set.

>>> insert 10 (range 15 20)
fromList [10,15,16,17,18,19,20]

>>> insert 10 (range 10 15)
fromList [10,11,12,13,14,15]

Delete a value in the set. Returns the original set when the value was not present.

>>> delete 10 (range 5 15)
fromList [5,6,7,8,9,11,12,13,14,15]

>>> delete 10 (range 1 10)
fromList [1,2,3,4,5,6,7,8,9]

Generalized insetion deletion.

Is the value a member of the set?

>>> member 5 (range 10 20)
False

>>> member 15 (range 10 20)
True

Is the element not in the set?

>>> notMember 5 (range 10 20)
True

>>> notMember 15 (range 10 20)
False

Find largest element smaller than the given one.

>>> lookupLT 3 (fromList [3, 5])
Nothing
>>> lookupLT 5 (fromList [3, 5])
Just 3

>>> lookupLT 0 full
Nothing

Find smallest element greater than the given one.

>>> lookupGT 4 (fromList [3, 5])
Just 5

>>> lookupGT 5 (fromList [3, 5])
Nothing

>>> lookupGT 255 full
Nothing

Find largest element smaller or equal to the given one.

>>> lookupLE 2 (fromList [3, 5])
Nothing

>>> lookupLE 4 (fromList [3, 5])
Just 3

>>> lookupLE 5 (fromList [3, 5])
Just 5

Find smallest element greater or equal to the given one.

>>> lookupGE 3 (fromList [3, 5])
Just 3

>>> lookupGE 4 (fromList [3, 5])
Just 5

>>> lookupGE 6 (fromList [3, 5])
Nothing

Is the set empty?

>>> null empty
True

>>> null (range 10 20)
False

Is the set full?

>>> isFull full
True

>>> isFull (range 1 255)
False

Is set singleton?

>>> isSingleton empty
Nothing

>>> isSingleton full
Nothing

>>> isSingleton (singleton 5)
Just 5

>>> isSingleton (fromList [3, 5])
Nothing

Is set of the form range l r?

>>> isRange empty
Nothing

>>> isRange full
Just (0,255)

>>> isRange (singleton 5)
Just (5,5)

>>> isRange (range 10 20)
Just (10,20)

>>> isRange (fromList [3, 5])
Nothing

Cardinality of the set.

>>> size empty
0

>>> size (union (range 10 20) (range 30 40))
22

Is this a subset? (s1 isSubsetOf s2) tells whether s1 is a subset of s2.

>>> isSubsetOf (range 10 20) (range 5 25)
True

>>> isSubsetOf (range 10 20) (range 10 20)
True

>>> isSubsetOf (range 5 25) (range 10 20)
False

Is this a proper subset? Is this a proper subset? (ie. a subset but not equal).

>>> isProperSubsetOf (range 10 20) (range 5 25)
True

>>> isProperSubsetOf (range 10 20) (range 10 20)
False

>>> isProperSubsetOf (range 5 25) (range 10 20)
False

Check whether two sets are disjoint (i.e. their intersection is empty).

>>> disjoint (range 11 20) (range 21 30)
True

The union of two sets.

The union of a list of sets.

Difference between two sets.

Symmetric difference between two sets

symmetricDifference xs ys = difference (union xs ys) (intersection xs ys)

>>> symmetricDifference (range 10 20) (range 15 25)
fromList [10,11,12,13,14,21,22,23,24,25]

Since: 0.1.1

See difference.

The intersection between two sets.

The complement of the set.

Filter all elements that satisfy some predicate.

>>> filter even (range 10 20)
fromList [10,12,14,16,18,20]

Partition the set according to some predicate.

>>> partition even (range 10 20)
(fromList [10,12,14,16,18,20],fromList [11,13,15,17,19])

map f s is the set obtained by applying f to each element of s.

>>> map (+ 1) (fromList [0, 10, 250, 255])
fromList [0,1,11,251]

Lazy right fold.

>>> foldr (:) [] (unions [range 10 20, range 70 73, range 130 132, range 200 202, singleton 255])
[10,11,12,13,14,15,16,17,18,19,20,70,71,72,73,130,131,132,200,201,202,255]

Lazy left fold.

>>> foldl (flip (:)) [] (unions [range 10 20, range 70 73, range 130 132, range 200 202, singleton 255])
[255,202,201,200,132,131,130,73,72,71,70,20,19,18,17,16,15,14,13,12,11,10]

Strict right fold.

Strict left fold.

The minimal element of the set.

>>> findMin (fromList [3, 5])
3

Returns 0 for empty set.

>>> findMin empty
0

The maximal element of the set.

>>> findMax (fromList [3, 5])
5

Returns 255 for empty set.

>>> findMax empty
255

Delete the minimal element. Returns an empty set if the set is empty.

Delete the maximal element. Returns an empty set if the set is empty.

Retrieves the maximal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

>>> maxView (fromList [3, 5])
Just (5,fromList [3])

>>> maxView empty
Nothing

Retrieves the minimal key of the set, and the set stripped of that element, or Nothing if passed an empty set.

>>> minView (fromList [3, 5])
Just (3,fromList [5])

>>> minView empty
Nothing

The elements of a set in ascending order.

The elements of a set in ascending order.

Create a set from a list of Word8s.

Create a set from a foldable of Word8s.

Convert set to Word256.

Create set from Word256.

Create ASCII string from a set.

>>> toASCII (range 100 120)
"defghijklmnopqrstuvwx"

Create set from ASCII string.

>>> fromASCII "foobar"
fromList [97,98,102,111,114]

Non-ASCII codepoints are truncated:

>>> fromASCII "\1000"
fromList [232]