((if is_zero(((fn y => pred y)1)) then succ else pred) ((fn y => (pred(pred y)))8))
fun char_to_num c = ord c - ord "0"; fun calc_list (,n) = n | calc_list ((fst::rest),n) = calc_list(rest,10 * n + char_to_num fst); fun string_to_num s = calc_list(explode s, 0);For instance, string_to_num "3405" returns the integer, 3405. Unfortunately, calc_list returns a spurious result if the string contains any non-digits. For instance, string_to_num "3a05" returns 7905, while string_to_num " 405" returns ~15595. This occurs because char_to_num will convert any character, not just digits. We can attempt to fix this by having char_to_num raise an exception if it is applied to a non-digit.
a. Please revise the definition of char_to_num to raise this exception, and then modify the function string_to_num so that it handles the exception, returning ~1 if there is a non-digit in the string. You should make no changes to calc_list.
b. Please rewrite these ML functions to provide the same behavior (including returning ~1 if the string includes a non-digit) as in (a), but without using exceptions. While you may change any function, try to preserve as much of the structure of the original program as possible.