Comp 372 Program 2	Sept 22, 2004	Peter Dordal
Due: Wed, Sept 29

The following functions are to be defined in Haskell. 
If you use another implementation than Hugs, please let me know.

These can all be defined by (primitive) recursion. Alternatively,
you can sometimes express these as a combination of existing
functions.


1. Define the function
	sumcubes :: Int -> Int
sumcubes(n) should return the sum 1^3 + 2^3 + ... + n^3.


2. Define the function 
	divisors :: Int -> Int
which returns the list of positive divisors of a positive integer
(and the empty list when the argument is <= 0). For example,
	divisors 12 -->  [1,2,3,4,6,12]
Hint: use a list comprehension!


3. Define the list function
	unique :: [a] -> [a]
that returns the list with duplicates eliminated. For example,
unique [1, 2, 1, 3, 2, 4] should return [1, 2, 3, 4].
(Returning [1, 3, 2, 4], where we keep the elements in order of
their *last* occurrence, is also acceptable.)


4. Define the function countwhat, as in the first (lisp) assignment.  
This should take a list and a predicate, and return the count of the 
number of elements of the list that satisfy the predicate. For example,
	countwhat isEven [1, 2, 3, 4, 5, 7]  should return 2.
Note that all the elements must have the same type!


5. Define a function iterate n f x that applies the function f to x n times:
f(f(...f(x))). For example, iterate 3 sqr 2 should return 256, the result
of squaring 2 three times. You may need to call it "myiterate" or "iterate2"


6. *Using* the iterate function from number 5, define a function
pow(x,n) = x^n. Iterate the function 
	\y -> y*x
applied n times to the value 1.