Function to Return Datatypes in SML

For homework, I need to design an SML function that returns the type of a custom datatype which matches some input data.

Here's the general idea: we are given a custom datatype typ--

datatype typ = typ1 
              |typ2
              |typ3
              .
              .
              .
              |typn

The function we're supposed to write has this type:

(foo -> typ option)

Since the function isn't returning a string but instead typ option, I understand the function, on the most basic level, as needing to look something like this --

hw_fun x =
  case x of 
    p1 => SOME typ1
   |p2 => SOME typ2
   .
   .
   .
   |pn => SOME typn
   |_  => NONE 

--assuming p1 matches typ1, etc. My question is, how do I make a datatype the return value of a matching case?

Hope that makes sense, thanks in advance for the help!

Type inferencing will take care of you. Consider the following.

datatype foo = Bar | Baz;

fun wooble n =
  case n of
    1 => SOME Bar
  | 2 => SOME Baz
  | _ => NONE;

The wooble function is inferred to have type int → foo option. If I wished to use explicit type nnotations, I might write:

fun wooble (n : int) : foo option =
  case n of
    1 => SOME Bar
  | 2 => SOME Baz
  | _ => NONE;

Of course, in this case the case expression is extraneous.

fun wooble 1 = SOME Bar
  | wooble 2 = SOME Baz
  | wooble _ = NONE

You only get in trouble with type inferencing if you try to return something of a different type from your function. E.g.

fun wooble 1 = SOME Bar
  | wooble 2 = SOME Baz
  | wooble _ = "NONE"