2023-13 part 2 in haskell

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diff --git a/2023/13-Point_of_Incidence/second.hs b/2023/13-Point_of_Incidence/second.hs
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+-- requires cabal install --lib megaparsec parser-combinators
+module Main (main) where
+
+import Control.Applicative.Permutations
+import Control.Monad (void, when)
+import Data.Char qualified as C
+import Data.Either
+import Data.Functor
+import Data.List qualified as L
+import Data.Map qualified as M
+import Data.Maybe
+import Data.Set qualified as S
+import Data.Vector qualified as V
+import Data.Void (Void)
+import Text.Megaparsec
+import Text.Megaparsec.Char
+
+import Debug.Trace
+
+exampleExpectedOutput = 400
+
+data Tile = Ash | Rock deriving (Eq)
+instance Show Tile where
+  show Ash = "."
+  show Rock = "#"
+type Row = [Tile]
+type Pattern = [Row]
+type Input = [Pattern]
+
+type Parser = Parsec Void String
+
+parseTile :: Parser Tile
+parseTile = char '.' $> Ash
+        <|> char '#' $> Rock
+
+parseRow :: Parser Row
+parseRow = some parseTile <* eol
+
+parsePattern :: Parser Pattern
+parsePattern = some parseRow <* eol
+
+parseInput' :: Parser Input
+parseInput' = some parsePattern <* eof
+
+parseInput :: String -> IO Input
+parseInput filename = do
+  input <- readFile filename
+  case runParser parseInput' filename input of
+    Left bundle -> error $ errorBundlePretty bundle
+    Right input' -> return input'
+
+compute :: Input -> Int
+compute = sum . map findMirror
+  where
+    findMirror :: Pattern -> Int
+    findMirror xs = 100 * findMirrors xs 1 + findMirrors (L.transpose xs) 1
+    findMirrors :: Pattern -> Int -> Int
+    findMirrors xs i | i == length xs = 0
+                     | diffs == 1 = i
+                     | otherwise = next
+      where
+        (is, ts) = L.splitAt i xs
+        next = findMirrors xs (i+1)
+        is' = reverse is -- we need to flip the left side
+        diffs = sum $ zipWith diff is' ts
+        diff :: Row -> Row -> Int
+        diff as bs = length . L.filter id $ zipWith (/=) as bs
+
+main :: IO ()
+main = do
+  example <- parseInput "example"
+  let exampleOutput = compute example
+  when  (exampleOutput /= exampleExpectedOutput)  (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
+  input <- parseInput "input"
+  print $ compute input