{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances,
  UndecidableInstances, FlexibleContexts, EmptyDataDecls, ScopedTypeVariables,
  TypeOperators, TypeSynonymInstances, TypeFamilies, NoMonomorphismRestriction #-}

module Automata where

----- I can't understand why doesn't automata representation as typeclasses work?

{-
class Eq a => DFA a b where
  start :: a
  delta :: b -> a -> a
  finals :: [a]  
  
  dfa :: [b] -> a
  dfa = foldl (flip delta) start
-}  
  -- dfaAccept :: [b] -> Bool
  -- dfaAccept xs = (dfa xs) `elem` finals


-- dfa ()
  
--  = foldl (flip delta) (start :: State t)

class IsDFA t where
  data State t
  data Trans t
  start  :: State t
  delta  :: Trans t -> State t -> State t
  finals :: [State t]
  
  dfa :: [Trans t] -> State t
  dfa = foldl (flip delta) start

  -- members


instance IsDFA () where
  data State () = S Int
  data Trans () = B Bool
  start = S 1
  delta (B b) (S s) = if b then S s else S (s+1)
  finals =  [S 3, S 4]


t = dfa []