1. (a) There are now a number of programming paradigms available to us,
       such as procedural, declarative, object-oriented, and functional 
       (sometimes referred to as "applicative") programming.
       Suggest a number of reasons why functional programming
       languages are worthy of study. You should address this question 
       from both a theoretical and a practical perspective.

                                                               (5 marks)

   (b) It might be said that "All functions in ML take a single argument". 
       This statement appears to be incorrect when we look at the 
       definitions of the two functions below, mult and prod, both of
       which deliver as a result x times y. 

         fun mult (x,y) = x*y:int;
         fun prod  x y  = x*y:int;
 
       Explain why the above statement is true, namely that all functions
       in ML do indeed have a single argument. You should use the functions
       mult and prod to clarify your answer.
                                                               (4 marks)

   (c) We can represent a binary number as a list of zeros and ones, with 
       the least significant bit as the head of the list. For example the 
       binary representation of 8 would be the list [0,0,0,1]. Write a 
       function in ML, called convert, that takes an integer and delivers 
       its binary equivalent as a list of zeros and ones. 
                                                               (4 marks)

   (d) Write a function in ML, called add_bin, that adds together two 
       numbers, where those numbers are binary numbers represented as 
       lists of zero's and one's (ie. numbers that might have been produced 
       by the function convert above, such that the least significant digit 
       is the head of the list). HINT: you might find it is helpful
       to define a function called add_digits (c,x,y), where add_digits 
       adds the carry c, the x, and y, and delivers as a result 
       the pair (result,new_carry). This may then be used to construct 
       the function add_bin.
      
                                                               (12 marks)