(* ----- From Section 1.12 ----- *)

(* Examples with numbers *)

fun factorial(0) = 1
  | factorial(n) = n * factorial(n-1);


(* Ex 1.12.4. Homemade multiply  *)
fun multiply(x, 0) = 0
  | multiply(x, y) = x + multiply(x, y-1);


(* Ex 1.12.6.  Summation. *)
fun sum(1) = 1
  | sum(n) = n + sum(n-1);

(* Examples with strings *)
fun capitalizeAll("") = ""
   | capitalizeAll(s) =
       str(Char.toUpper(String.sub(s, 0))) ^ 
       capitalizeAll(substring(s, 1, size(s) - 1));

(* 1.12.2. Reverse a string. *)
fun reverse("") = "" 
  | reverse(s) = reverse(substring(s, 1, size(s) -1)) ^ str(String.sub(s, 0));


(* 1.12.8. --- Homework *)
(* The book doesn't say what to name the function, but the grading
    system expects the name "fib" (not "fibonacci"). Also index the
    Fibonacci sequence starting at 0 (0 is the 0th Fibonacci number). *)
fun fib(0) = 
   | fib(1) = 
   | fib(n) =