A simple state machine in Elm - http://daniel-levin.github.io/2015/01/19/primitive-state-machine-in-haskell.html

Test.elm

test = 
  describe "State machine"
    [
      test "[A,A,A] should be False" <|
        \() ->
          Expect.equal (decide [A, A, A]) False
    , test "[A,A,A,A,B,B,A,A,A] should be True" <|
        \() ->
          Expect.equal (decide [A,A,A,A,B,B,A,A,A]) True
    , test "[B,A,B,A,B,A] should be False" <|
        \() ->
          Expect.equal (decide [B,A,B,A,B,A]) False
    ]

TheMachine.elm

type State = S0 | S1 | S2
type Event = A | B

accepts : State -> (List Event) -> Bool
accepts state action =
  case state of
    S0 -> case action of
      A :: xs -> accepts S1 xs
      B :: xs -> accepts S2 xs
      _ -> False
    S1 -> case action of
      A :: xs -> accepts S2 xs
      B :: xs -> accepts S0 xs
      _ -> False
    S2 -> case action of
      A :: xs -> accepts S0 xs
      B :: xs -> accepts S2 xs
      _ -> True

decide : (List Event) -> Bool
decide = accepts S0