1. (a) The factorial function, which is shown below in ML, is a 
       standard example of recursion. It includes a base case, n=0, 
       where evaluation stops.

           fun fact n = if n=0 then 1 else n * fact(n-1)

       Show how ML evaluates the function call fact(4), and
       comment on the computational costs associated with that
       evaluation.
                                                               (5 marks)

   (b) Write a more efficient version of the factorial function,
       and explain why your version is more efficient, and
       describe the principle that you have employed.
                                                               (5 marks)

   (c) In what follows, you may wish (but are not obliged) to make use
       of the accompanying program segment.
       
       Given a family tree, composed of persons, where a person has a 
       name and a list of immediate descendants:

        datatype 'a person = empty | Person of ('a * 'a person list)

       (i)   Write a function in ML, called find, that takes as arguments 
             the name of a person and a list of Person's. The function 
             delivers as a result the corresponding person, or empty. 

       (ii) Give an informal assessment of function find,
            stating the assumptions you have made, and the 
            computational costs (space and time) associated 
            with that function.

       (iii) Write a function in ML, called ancestorp, that takes as 
             arguments the names of two people (name_A and name_B)
             and a list of Person's. The function delivers a result of true
             if the person corresponding to name_A is an ancestor of 
             the person corresponding to name_B.

                                                              (15 marks)