It turns out to be not that hard to just compute the language of the regex, if it is finite, and otherwise note that it is infinite: import Prelude hiding

It turns out to be not that hard to just compute the language of the regex, if it is finite, and otherwise note that it is infinite: import Prelude hiding (null) import Data.Set (Set, toList, fromList, empty, singleton, isSubsetOf, unions, null) data Regex = Class [Char] -- character class | Seq [Regex] -- sequence, ABC | Choice [Regex] -- choice, A|B|C | Star Regex -- zero or more, A* deriving (Show) -- The language of a regex is either finite or infinite. -- We only care about the finite case. data Lang = Finite (Set String) | Infinite deriving (Show, Eq) zero = Finite empty one = Finite (singleton "") isEmpty (Finite s) = null s isEmpty Infinite = False cat :: Lang -> Lang -> Lang cat x y | isEmpty x || isEmpty y = zero cat (Finite s) (Finite t) = Finite $ fromList [x ++ y | x <- toList s, y <- toList t] cat _ _ = Infinite subsingleton :: Lang -> Bool subsingleton Infinite = False subsingleton (Finite s) = isSubsetOf s (fromList [""]) eval :: Regex -> Lang eval (Class chars) = Finite $ fromList [[c] | c <- chars] eval (Seq rs) = foldr cat one $ map eval rs eval (Choice rs) | any (== Infinite) langs = Infinite | otherwise = Finite $ unions [s | Finite s <- langs] where langs = map eval rs eval (Star r) | subsingleton (eval r) = one | otherwise = Infinite