Simple DFA in Haskell

DFA.hs

module DFASpec (spec) where

import Test.Hspec

data State = S1 | S2 deriving (Eq, Show)

data Symbols = Zero | One deriving (Eq, Show)
data Alphabet = Alphabet [Symbols]  deriving (Eq, Show)
data FiniteStates = FiniteStates [State] deriving (Eq, Show)
 
data DFA = DFA FiniteStates Alphabet State deriving (Eq, Show)

data Transitions = Transitions [State] deriving (Eq, Show)

start = S1
finish = S1
dead = S2

transition :: DFA -> State -> Transitions -> String -> State
transition _ S1 _ "" = S1
transition _ S1 _ "0" = S2
transition _ S1 _ "1" = S1
transition _ S2 _ "0" = S1
transition _ S2 _ "1" = S2

spec :: Spec
spec =
  describe "DFA" $ do
    it "a finish state is returned when given a valid input of 0 0 0 0" $ do
      let dfa = DFA (FiniteStates [S1, S2]) (Alphabet [Zero, One]) start
      let transition1 =  transition (dfa) start (Transitions []) "0"
      let transition2 =  transition (dfa) transition1 (Transitions []) "0"
      let transition3 =  transition (dfa) transition2 (Transitions []) "0"
      let transition4 =  transition (dfa) transition3 (Transitions []) "0"
      transition4 `shouldBe` finish
    it "a finish state is returned when given a valid input of 0 0" $ do
      let dfa = DFA (FiniteStates [S1, S2]) (Alphabet [Zero, One]) start
      let transition1 =  transition (dfa) start (Transitions []) "0"
      let transition2 =  transition (dfa) transition1 (Transitions []) "0"
      let transition3 =  transition (dfa) transition2 (Transitions []) "0"
      let transition4 =  transition (dfa) transition3 (Transitions []) "0"
      transition4 `shouldBe` finish
    it "a dead state is returned when given a invalid input of 0 1 0 0" $ do
      let dfa = DFA (FiniteStates [S1, S2]) (Alphabet [Zero, One]) start
      let transition1 =  transition (dfa) start (Transitions []) "0"
      let transition2 =  transition (dfa) transition1 (Transitions []) "1"
      let transition3 =  transition (dfa) transition2 (Transitions []) "0"
      let transition4 =  transition (dfa) transition3 (Transitions []) "0"
      transition4 `shouldBe` dead
    it "a dead state is returned when given a invalid input of 1 1" $ do
      let dfa = DFA (FiniteStates [S1, S2]) (Alphabet [Zero, One]) start
      let transition1 =  transition (dfa) start (Transitions []) "0"
      let transition2 =  transition (dfa) transition1 (Transitions []) "1"
      let transition3 =  transition (dfa) transition2 (Transitions []) "0"
      let transition4 =  transition (dfa) transition3 (Transitions []) "0"
      transition4 `shouldBe` dead