(* sample.ml

   CS 313   Example ML functions

   To load this file from within sml, type

     use "sample.ml";

   To run ML on this file, use

     sml < sample.ml

*)


(***** list functions *****)

(* sum the numbers in a list *)
fun sumlist1 l =
      if null l then 0
		else hd(l) + sumlist1 (tl(l));

(* same function, defined using cases *)
fun sumlist2 []     = 0                  (* No semicolon here!! *)
|   sumlist2 (a::y) = a + sumlist2 y;

(* sum the numbers in a list - tail-recursive version *)
fun sumlist3 l =
  let fun sumiter(x, res) = 
            if null x then res
		      else sumiter(tl(x), hd(x) + res)
  in sumiter(l, 0)
  end;

(* same function, helper function defined using cases *)
fun sumlist4 l =
  let fun sumiter([], res)   = res
      |   sumiter(n::y, res) = sumiter(y, n+res)
  in sumiter(l, 0)
  end;

(* sample output:  (only for sumlist1 here - the others work too :)
  - sumlist1 [];
  val it = 0 : int
  - sumlist1 [1, 2, 3, 4];
  val it = 10 : int
*)


(***** binary search tree *****)

(* type definition *)
datatype bst = Empty
             | Node of int * bst * bst;

(* useful function to create a leaf node *)
fun leaf n = Node(n, Empty, Empty);

(* compute the height of a tree *)
fun height Empty = 0
|   height (Node(n, left, right)) =
      1 + Int.max(height left, height right);

(* sample output:
  - height Empty;
  val it = 0 : int
  - height(leaf 4);
  val it = 1 : int
  - height (Node(3, leaf(2), Empty));
  val it = 2 : int
  - val t = Node(3, Node(1, Empty, leaf(2)), leaf(4));
  val t = Node (3,Node (1,Empty,Node #),Node (4,Empty,Empty)) : bst
  - height t;
  val it = 3 : int
*)