nit: Shouldn't your route definition be type Route instead of type alias Route ? I think your old route function would work just fine with your new custom type definition.

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But assuming that you want to do some useful pattern matching based on AuthenticatedRoute or UnauthenticatedRoute later on, you might want to change your Route type a little to allow nested pattern matching. perhaps like this

type Route
    = UnAuthed UnAuthenticatedRoute
    | Authed AuthenticatedRoute
    | NotFound

After this your route method can be something like this I believe

route : Parser (Route -> a) a
route =
    oneOf
        [ map (Authed Index) top
        , map (Authed New) (s "todos" </> s "new")
        , map (Authed Edit) (s "todos" </> int </> s "edit")
        , map (Authed Show) (s "todos" </> int)
        , map (UnAuthed Login) (s "sign-in")
        , map (UnAuthed Signup) (s "sign-up")
        ]

-- (or alternatively you can also split this into two parsers for authed routes and unauthed routes as well)

Now say you want to figure out what page to show based on the route:

processRoute : Route -> Model -> (Model, Cmd msg)
processRoute route model =    
    case route of 
        Authed authRoute ->
            -- do stuff with your authRoute (e.g. pattern matching, go to login page if not authed )

        UnAuthed unauthRoute ->
            -- do stuff with your unauthroute

        NotFound ->                     
            -- do stuff with 

I didn't try to compile anything above so there might be some errors, but hopefully this gives you some idea!