Comp 372 program 3-ml: ML exercises 	Dordal, Nov 3, 1999

Due: Friday, Nov 12

Turn in your function definition together with a few sample tests


1. Write a function sumfun(n, f) that takes an int n and a function 
f:int->int and returns the sum f(1)+f(2)+...f(n). If n=0, return 0.



2. Write a function iterate(n, f, x) that applies function f to x n times:
f(f(...f(x))).


3. *Using* iterate, write pow(x,n) = x^n (x to the nth power). 
Iterate the function fn y => x*y; if you apply this n times to 1
then you calculate x^n.


4. Using the mywhile function defined in class, implement the following
while loop:
	x=1;
	y=20;
	z=0;
	w=0;
	while (x<y) {
	    x = x*2;
	    y = y+20;
	    z = x + y;
	    if (x<100) w = w+1;
	}

Here is mywhile:
    fun mywhile (state, pred, update) = 
	if pred(state) then mywhile(update(state), pred, update)
	else state;