Standard ML

fibonacci.sml

(* Traditional (not tail-recursive) *)
fun fibonacci n =
    case n of
        0 => 0
      | 1 => 1
      | _ => fibonacci(n-1) + fibonacci(n-2)

(* tail-recursive *)
fun fbnc_tail n =
    let fun aux (n, n_1, n_2) =
            case n of
                0 => n_2
              | 1 => n_1
              | _ => aux(n-1, n_1+n_2, n_1)
    in aux(n, 1, 0)
    end