A simple selection algorithm for finding the maximum integer option in an integer list is given below :

max.sml

fun max_case (xs) =
    case xs of
	[] => NONE
      | x::xs' => let fun non_empty_max (ys) =
			  case ys of 
			      [] => x
			    | y::ys' => let val tl_ans = non_empty_max (ys')
					in 
					    if y > tl_ans
					    then y
					    else tl_ans
					end
		  in SOME (non_empty_max (xs'))
		  end


val test_max_case = max_case ([1,2,3,4,5,6,7,8,9,10])