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diff --git a/2020/21-Allergen_Assessment/second.hs b/2020/21-Allergen_Assessment/second.hs
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+-- requires cabal install --lib megaparsec parser-combinators
+module Main (main) where
+import Control.Monad (void, when)
+import Data.List qualified as L
+import Data.Map qualified as M
+import Data.Maybe (catMaybes)
+import Data.Set qualified as S
+import Data.Void (Void)
+import Text.Megaparsec
+import Text.Megaparsec.Char
+import System.Exit (die)
+
+exampleExpectedOutput = "mxmxvkd,sqjhc,fvjkl"
+
+newtype Ingredient = Ingredient String deriving (Eq, Ord, Read, Show)
+newtype Allergen = Allergen String deriving (Eq, Ord, Read, Show)
+type Rule = ([Ingredient], [Allergen])
+type Input = [Rule]
+
+type Parser = Parsec Void String
+
+parseRule :: Parser Rule
+parseRule = do
+  ingredients <- some ((Ingredient <$> some letterChar) <* char ' ')
+  void $ string "(contains "
+  allergens <- some ((Allergen <$> some letterChar) <* optional (string ", "))
+  void $ string ")\n"
+  return $ (ingredients, allergens)
+
+parseInput' :: Parser Input
+parseInput' = some parseRule <* eof
+
+parseInput :: String -> IO Input
+parseInput filename = do
+  input <- readFile filename
+  case runParser parseInput' filename input of
+    Left bundle -> die $ errorBundlePretty bundle
+    Right input' -> return input'
+
+compute :: Input -> String
+compute rules = L.intercalate "," . map (\(_, Ingredient i) -> i) $ M.assocs allergensMap
+  where
+    candidatesMap :: M.Map Allergen [Ingredient]
+    candidatesMap = L.foldl' appendIngredientsForRule M.empty rules
+    appendIngredientsForRule :: M.Map Allergen [Ingredient] -> Rule -> M.Map Allergen [Ingredient]
+    appendIngredientsForRule m (is, as) = L.foldl' (appendIngredientsForAllergen is) m as
+    appendIngredientsForAllergen :: [Ingredient] -> M.Map Allergen [Ingredient] -> Allergen -> M.Map Allergen [Ingredient]
+    appendIngredientsForAllergen is m a = case M.lookup a m of
+      Nothing -> M.insert a is m
+      Just is' -> M.insert a (L.intersect is is') m
+    allergensMap :: M.Map Allergen Ingredient
+    allergensMap = allergensMap' candidatesMap M.empty
+    allergensMap' :: M.Map Allergen [Ingredient] -> M.Map Allergen Ingredient -> M.Map Allergen Ingredient
+    allergensMap' m acc
+      | M.size m == 0 = acc
+      | otherwise = allergensMap' (M.map (L.delete (head oneI)) $ M.delete oneK m) $ M.insert oneK (head oneI) acc
+      where
+        one = M.filter (\is -> length is == 1) m
+        (oneK, oneI) = head $ M.assocs one
+
+main :: IO ()
+main = do
+  example <- parseInput "example"
+  let exampleOutput = compute example
+  when  (exampleOutput /= exampleExpectedOutput)  (die $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
+  input <- parseInput "input"
+  print $ compute input