Explanation of why `filterM (const [True, False])` maps list to its power set(list)

Powerset_by_filterM.hs

import Control.Monad
import Control.Applicative


-- filterM (const [True, False])

-- filterM :: (Applicative m) => (a -> m Bool) -> [a] -> m [a]
-- filterM p = foldr (\x -> liftA2 (\flg -> if flg then (x:) else id) (p x)) (pure [])

-- (<*>) :: [a -> b] -> [a] -> [b]
-- fs <*> xs = [f x | f <- fs, x <- xs]

-- foldr (\x -> (<*>) $ (\flg -> if flg then (x:) else id) <$> [True, False]) (pure []) [1,4,3]

-- diverge :: a -> [[a]] -> [[a]]
-- diverge x as = [f a | f <- map (\flg -> if flg then (x:) else id) [True, False], a <- as]

-- diverge :: a -> [[a]] -> [[a]]
-- diverge x as = [f a | f <- [(x:), id], a <- as]

diverge' :: a -> [[a]] -> [[[a]]]
diverge' x = map (\a -> [x:a, a])

diverge :: a -> [[a]] -> [[a]]
diverge x = concat . (diverge' x)

powerR :: [a] -> [[a]]
powerR xs = foldr diverge [[]] xs

powerL :: [a] -> [[a]]
powerL xs = foldl (flip diverge) [[]] xs

main :: IO ()
main = do
  print $ filterM (const [True, False]) [4,3,6]
  print $ diverge 6 [[]] -- > [[6],[]]
  print $ diverge 3 [[6],[]] -- > [[3,6], [6], [3], []]
  print $ diverge 4 [[3,6],[6],[3],[]]  -- > [[4,3,6],[3,6],[4,6],[6],[4,3],[3],[4],[]]
  print $ powerR [4,3,6]  -- > [[4,3,6],[3,6],[4,6],[6],[4,3],[3],[4],[]]
  print $ powerL [4,3,6]  -- > [[6,3,4],[3,4],[6,4],[4],[6,3],[3],[6],[]]