tasks a-s

Task/Power-set/Haskell/power-set-1.hs

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+import Data.Set
+import Control.Monad
+
+powerset :: Ord a => Set a -> Set (Set a)
+powerset = fromList . fmap fromList . listPowerset . toList
+
+listPowerset :: [a] -> [[a]]
+listPowerset = filterM (const [True, False])

Task/Power-set/Haskell/power-set-2.hs

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+powerset [] = [[]]
+powerset (head:tail) = acc ++ map (head:) acc where acc = powerset tail

Task/Power-set/Haskell/power-set-3.hs

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+powerset = foldr (\x acc -> acc ++ map (x:) acc) [[]]

Task/Power-set/Haskell/power-set-4.hs

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+import qualified Data.Set as Set
+type Set=Set.Set
+unionAll :: (Ord a) => Set (Set a) -> Set a
+unionAll = Set.fold Set.union Set.empty
+
+--slift is the analogue of liftA2 for sets.
+slift :: (Ord a, Ord b, Ord c) => (a->b->c) -> Set a -> Set b -> Set c
+slift f s0 s1 = unionAll (Set.map (\e->Set.map (f e) s1) s0)
+
+--a -> {{},{a}}
+makeSet :: (Ord a) => a -> Set (Set a)
+makeSet = (Set.insert Set.empty) . Set.singleton.Set.singleton
+
+powerSet :: (Ord a) => Set a -> Set (Set a)
+powerSet = (Set.fold (slift Set.union) (Set.singleton Set.empty)) . Set.map makeSet

Task/Power-set/Haskell/power-set-5.hs

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+Prelude Data.Set> powerSet fromList [1,2,3]
+fromList [fromList [], fromList [1], fromList [1,2], fromList [1,2,3], fromList [1,3], fromList [2], fromList [2,3], fromList [3]]