(* 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) = sum(n-1) + n;

 

(* 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));


(* list examples from the text *)

fun repeatEach([]) = []
  | repeatEach(a::rest) = a::a::repeatEach(rest);

fun sum([]) = 0
  | sum(a::rest) = a + sum(rest);

fun switchPair([]) = []
  | switchPair((a,b)::rest) = (b, a)::switchPair(rest);