Question

I was looking at Data.Set, and I found out that it has no powerset function. Why?

I can implement it like this:

import Data.Set (Set, empty, fromList, toList, insert)

powerset :: (Ord a) => Set a -> Set (Set a)
powerset s = fromList $ map (fromList) (powerList $ toList s)

powerList :: [a] -> [[a]]
powerList [] = [[]]
powerList (x:xs) = powerList xs ++ map (x:) (powerList xs)

But this doesn’t seem the most efficient way of doing it. OK, I can also write

powerList :: [a] -> [[a]]
powerList = filterM (const [True, False])

but still, I wonder why Data.Set has no powerset function.

Also, what is the best way to write powerset :: (Ord a) => Set a -> Set (Set a)?

Answer 1

Funny, I actually implemented powerset in Haskell the other day just for fun in a comment at /r/python.

import Data.Set
import Prelude hiding (map)

powerset s
    | s == empty = singleton empty
    | otherwise = map (insert x) pxs `union` pxs
        where (x, xs) = deleteFindMin s
              pxs = powerset xs

It is much as camccann described in his comment above. Set‘s fast union should give it a speed boost over the list version.