SML - Failing to compile

mutual-recursion-with-composition__not-working.sml

(* Problem: Write a function that returns true
 * when invoked with list of alternate 1's and 2's
 *
 * Example:
 * matcher [1,2,1,2]
 * matcher [1,2,1]
 * matcher [1,2]
 * matcher [1]
 *
 * all of the above should return true
 *)
 
fun match_one (xs, f) =
  case xs of
       [] => true
     | 1::xs' => f (xs', match_one)
     | _ => false

fun match_two (xs, f) =
  case xs of
       [] => true
     | 2::xs' => f (xs', match_two)
     | _ => false

fun matcher xs = match_one (xs, match_two)

This solution doesn't work.

Both match_one and match_two won't pass the type check, because there is no way to deduce the type of argument f in both functions.