automatonarrow.elm

type Automaton a b = Automaton (a -> (b, Automaton a b))

arr : (a -> b) -> Automaton a b
arr f = 
  Automaton (\a -> (f a, arr f))
  
(>>>) : Automaton a b -> Automaton b c -> Automaton a c
(>>>) (Automaton f) (Automaton g) = 
  Automaton <|
    \a ->
      case f a of 
        (b, autoA) ->
          case g b of 
            (c, autoB) ->
              (c, autoA >>> autoB)
              
              
first : Automaton a b -> Automaton (a, c) (b, c)
first (Automaton f) = 
  Automaton <|
    \(a,c) -> 
      case f a of 
        (b, autoAb) ->
          ((b,c), first autoAb)