Just some scribblings. Carry on. :)

automaton.hs

import qualified Data.Set as S

type State  = String
type Letter = String
type Alphabet = S.Set Letter

{-
data Automaton = Automaton { auto_state    :: S.Set State
                           , auto_alphabet :: Alphabet
                           , auto_delta    :: (State -> Letter -> State)
                           , auto_start    :: State
                           , auto_final    :: S.Set State
                           } 
                           -}

data Automaton = Automaton (S.Set State) Alphabet (State -> Letter -> State) State (S.Set State)

delta1 :: State -> Letter -> State
delta1 "q0" "0" = "q1"
delta1 "q0" "1" = "q0"
delta1 "q1" "0" = "q0"
delta1 "q1" "1" = "q1"

a1 = (Automaton (S.fromList ["q0", "q1"]) (S.fromList ["0", "1"]) delta1 (S.fromList ["q0"]))

-- Applies the product between to Automatons and returns a new one.
product' :: Automaton -> Automaton -> Automaton
product' (Automaton states1 alphabet1 delta1 start1 final1) (Automaton states2 alphabet2 delta2 start2 final2) = (Automaton states1 alphabet1 delta1 start1 final1)