Safe Haskell | Safe |
---|---|

Language | Haskell98 |

Set operations on lists.

- set :: Ord a => [a] -> [a]
- n_powerset :: Integral n => n -> n
- powerset :: [a] -> [[a]]
- powerset' :: Ord a => [a] -> [[a]]
- pairs :: [a] -> [(a, a)]
- triples :: [a] -> [(a, a, a)]
- expand_set :: Ord a => Int -> [a] -> [[a]]
- partitions :: Eq a => [a] -> [[[a]]]
- cartesian_product :: [a] -> [b] -> [(a, b)]
- nfold_cartesian_product :: [[a]] -> [[a]]

# Documentation

n_powerset :: Integral n => n -> n Source #

Size of powerset of set of cardinality *n*, ie. `2`

`^`

*n*.

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

powerset :: [a] -> [[a]] Source #

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]

powerset' :: Ord a => [a] -> [[a]] Source #

Variant where result is sorted and the empty set is not given.

powerset' [1,2,3] == [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]

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

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]] Source #

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]]] Source #

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)] Source #

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

cartesian_product "abc" "" == []

nfold_cartesian_product :: [[a]] -> [[a]] Source #

List form of n-fold cartesian product.

length (nfold_cartesian_product [[1..13],[1..4]]) == 52 length (nfold_cartesian_product ["abc","de","fgh"]) == 3 * 2 * 3