> makeInverseIndex ["hello world", "world test", "hello test"]
fromList [("hello",fromList [0,2]),("test",fromList [1,2]),("world",fromList [0,1])]

> orSearch ["hello", "world"] $ makeInverseIndex ["hello world", "world test", "hello test"]
fromList [0,1,2]

> andSearch ["hello", "world"] $ makeInverseIndex ["hello world", "world test", "hello test"]
fromList [0]

import Data.List as L
import Data.Map.Strict as M
import Data.Set as S

makeInverseIndex :: [String] -> Map String (Set Int)
makeInverseIndex = L.foldr (unionWith S.union . uncurry group) M.empty . zipWithIndex . L.map words
  where
    zipWithIndex :: [a] -> [(Int, a)]
    zipWithIndex xs = zip [0..length xs] xs

    group :: Ord k => v -> [k] -> Map k (Set v)
    group n = M.fromList . L.map (w -> (w, S.singleton n))

orSearch :: [String] -> Map String (Set Int) -> Set Int
orSearch words =
  M.foldr S.union S.empty . pick words

andSearch :: [String] -> Map String (Set Int) -> Set Int
andSearch words =
  M.foldr S.intersection (S.fromList [0..length words]) . pick words

pick :: Ord k => [k] -> Map k v -> Map k v
pick keys m =
  restrictKeys m $ S.fromList keys