Obtained by defunctionalizing match', thus obtaining a 2-state PDA.

match0n1n-3.hs

-- Defunctionalizing match' -- we obtain a 2-state push-down automaton!
-- 1) https://gist.github.com/suhorng/5204442
-- 2) https://gist.github.com/suhorng/5204636

data Cont = Cont0
          | Cont1 Cont

match'' :: String -> Bool
match'' s = trace s Cont0
            where trace :: String -> Cont -> Bool
                  trace ('0':xs) k = trace xs (Cont1 k)
                  trace xs k       = applyCont k xs

                  applyCont :: Cont -> String -> Bool
                  applyCont Cont0 xs            = null xs
                  applyCont (Cont1 k) ('1':xs') = applyCont k xs'
                  applyCont _ _                 = False

-- Note that Cont is isomorphic to nat -- which represents the count of 0s!