CS321 Prog Lang & Compilers          Assignment # 3
Assigned: Mon. Jan 22, 2007       Due: Wed. Jan 24, 2007

Turn in a listing, and a transcript that shows you have tested your code. A
minimum of 3 tests is necessary. Some functions may require more than 3 tests
to receive full credit.

1) Write the following functions over lists. You must
use pattern matching and recursion.

A. reverse a list so that its elements appear in the oposite order.
reverse [1,2,3,4]  ---->  [4,3,2,1]

B. Count the number of occurrences of an element in a list
count 4 [1,2,3,4,5,4] ---> 2
count 4 [1,2,3,2,1]   ---> 0

C. concatenate together a list of lists
concat [[1,2],[],[5,6]] ----> [1,2,5,6]

2) Using the datatype for Regular Expressions we defined in class

datatype RE
  = Empty
  | Union of RE * RE
  | Concat of RE * RE
  | Star of RE
  | C of char;

Write a function that turns a RE into a string, so that it can be
printed. Minimize the number of parenthesis, but keep the string
unambigouous by using the following rules.
        1) Star has highest precedence so:  ab*  means a(b*)
        2) Concat has the next highest precedence so: a+bc   means   a+(bc)
        3) Union has lowest precedence so: a+bc+c*   means   a+(bc)+(c*)
        4) Use the hash mark (#) as the empty string.
        5) Special characters *+()\ should be escaped by using a
           preceeding backslash.
              So (Concat (C #"+") (C #"a"))  should be   "\+a"

Hints:
1) The string concatenation operator is usefull:
   "abc" ^ "zx" -----> "abczx"
2) Write this is two steps.
  First, fully paranethesize every RE
  Second, Change the function to not add the parenthesis which
  the rules don't require.