Memoized fibonacci using closures in Standard ML

fib_memo.sml

(* Regular fibonacci *)
fun fib 0 = 0
  | fib 1 = 1
  | fib n = fib (n-1) + fib (n-2);

(* Fibonacci using closures for memoization *)
local
    fun fib_c f n =
        case f n of
            SOME v => (v, f)
          | NONE   =>
            let val (v', f')   = fib_c f (n-1)
                val (v'', f'') = fib_c f' (n-2)
                val res = v' + v''
            in (res, fn x => if x = n then SOME res else f'' x) end

    fun fib_init 0 = SOME 0
      | fib_init 1 = SOME 1
      | fib_init _ = NONE
in
    val fib' = #1 o fib_c fib_init
end