Wrong answer ... but fun

Balance.hs

data Balance =
  Balance !Int
          !Int
  deriving (Eq, Show)

instance Semigroup Balance where
  Balance a b <> Balance c d
    | b <= c = Balance (a + c - b) d
    | otherwise = Balance a (d + b - c)

instance Monoid Balance where
  mempty = Balance 0 0

balanceTotal :: Balance -> Int
balanceTotal (Balance close open) = close + open

balance :: Eq a => a -> a -> a -> Balance
balance open close a
  | a == open = Balance 0 1
  | a == close = Balance 1 0
  | otherwise = Balance 0 0

alphabalance :: NonEmpty (Char -> Balance)
alphabalance = NonEmpty.map (balance <$> id <*> toUpper) ('a' :| ['b' .. 'z'])

runAlphabalance :: Char -> NonEmpty Balance
runAlphabalance = flip NonEmpty.map alphabalance . (&)

stringBalances :: String -> Maybe (NonEmpty (NonEmpty Balance))
stringBalances = (NonEmpty.map runAlphabalance <$>) . NonEmpty.nonEmpty

runStringBalances :: NonEmpty (NonEmpty Balance) -> NonEmpty Balance
runStringBalances = foldr1 (NonEmpty.zipWith (<>))