Music.Theory.Set.List

Set operations on lists.

Documentation

set :: Ord a => [a] -> [a]

Remove duplicate elements with nub and then sort.

set_l [3,3,3,2,2,1] == [1,2,3]

n_powerset :: Integral n => n -> n

Size of powerset of set of cardinality n, ie. 2 ^ n.

map n_powerset [6..9] == [64,128,256,512]

powerset :: [a] -> [[a]]

Powerset, ie. set of all subsets.

sort (powerset [1,2]) == [[],[1],[1,2],[2]]
map length (map (\n -> powerset [1..n]) [6..9]) == [64,128,256,512]

pairs :: [a] -> [(a, a)]

Two element subsets.

pairs [1,2,3] == [(1,2),(1,3),(2,3)]

triples :: [a] -> [(a, a, a)]

Three element subsets.

triples [1..4] == [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]

let f n = genericLength (triples [1..n]) == nk_combinations n 3
in all f [1..15]

expand_set :: Ord a => Int -> [a] -> [[a]]

Set expansion (ie. to multiset of degree n).

expand_set 4 [1,2,3] == [[1,1,2,3],[1,2,2,3],[1,2,3,3]]

partitions :: Eq a => [a] -> [[[a]]]

All distinct multiset partitions, see partitions.

partitions "aab" == [["aab"],["a","ab"],["b","aa"],["b","a","a"]]

partitions "abc" == [["abc"]
                    ,["bc","a"],["b","ac"],["c","ab"]
                    ,["c","b","a"]]

cartesian_product :: [a] -> [b] -> [(a, b)]

Cartesian product of two sets.

let r = [('a',1),('a',2),('b',1),('b',2),('c',1),('c',2)]
in cartesian_product "abc" [1,2] == r