Get constructor by value option in Elm (0.19.1) - elm

Question

I have some types:
type alias Type1 = { name : String }
type alias Type2 = { name : String, age : Int }
type S
= S1 Type1
| S2 Type2
So, when I want to build my info I can do the following:
a = S1 { name = "Name1" }
b = S2 { name = "Name2", age = 100 }
Now, I would like to get its constructor (S1 or S2) based on the info passed as parameter to the constructorByData function. Examples:
constructorByData a -- It should be returned `S1`
constructorByData b -- It should be returned `S2`
This is my aproach:
constructorByData : S -> (a -> S)
constructorByData s =
case s of
S1 _ -> S1
S2 _ -> S2
Please, note that the above code does not work. I get the following error:
-- TYPE MISMATCH ---------------------------------------------------------- REPL
Something is off with the 2nd branch of this `case` expression:
14| S2 _ -> S2
^^
This `S2` value is a:
Type2 -> S
But the type annotation on `constructorByData` says it should be:
a -> S
-- TYPE MISMATCH ---------------------------------------------------------- REPL
Something is off with the 1st branch of this `case` expression:
13| S1 _ -> S1
^^
This `S1` value is a:
Type1 -> S
But the type annotation on `constructorByData` says it should be:
a -> S
The main reason I want to do this is because I want to do the following by generalizing the message:
type Field
= Name
| Age
type Msg
= UpdateFieldString S Field String
| UpdateFieldInt S Field Int
update : Msg -> Model -> ( Model, Cmd Msg )
update msg model =
case msg of
UpdateFieldString s field value -> updateFieldString model s field value
UpdateFieldInt s field value -> updateFieldInt model s field value
And is for this I need the constructor in updateField{String, Int} functions