NOTE: This assignment is due the Tuesday night, after the exam.

This problem set continues the study of self-referential unions. Some of the problems cover functions that process two arguments from classes with complex (self-referential) data definitions. You must follow the design recipe. The graders will look for data definitions, contracts, purpose statements, examples/tests, and properly organized function definitions. For the latter, you must design templates. You do not need to include the templates with your homework, however. If you do, comment them out.

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HtDP Problems:

14.1.4, 14.1.6, 14.2.1, 14.2.2, 14.2.3, 14.2.4, 17.6.4, 17.6.6

Problem A1:

XML is a modern language (really, a family of languages) for encoding data. It uses "named parentheses" to group structured data, and strings for everything else. [Well, it contains a few more things than that, but this is good enough for now.] Here is an example:

     <div>
       <p><b>Problem A1</b>:</p>
  
       <blockquote>
         <p>

           XML is a modern language (really, a
           <i>family</i> of languages) for encoding
           data. It uses "<i>named parentheses</i>" to
           group structured data and strings for everything
           else. [Well, it contains a few more things than that, but
           this is good enough for now.] Here is an example:

         </p> 

         <p> Yes, this example is weird, because it is 
           self-referential but, hey, you should be used to
           this by now.  
         </p>
       </blockquote>
     </div>

Yes, this example is weird, because it is self-referential but, hey, you should be used to this by now.

You should have noticed that the example is not a complete representation of Problem A1. It misses this paragraph and it misses something in the middle. Nevertheless, it is a good example of the kind of XML you will encounter in the real world.

There are many ways to represent XML data in DrRacket. Here is one of them:

     ;; An Xexpr is one of: 
     ;;  - (cons Symbol LoXexpr)
     ;;  - String 

     ;; An LoXexpr is one of: 
     ;;  - empty 
     ;;  - (cons Xexpr LoXexpr)
  

Interpretation: An Xexpr represents a bracketed pair of "named parentheses" and whatever is in between, e.g.,

     <p>
        hello <em>world </em>
     </p>
  

becomes:

     (cons 'p
           (cons "hello "
                 (cons (cons 'em (cons "world " empty))
                       empty)))
  

Or equivalently...

   (list 'p "hello " (list 'em "world "))
  

See DrRacket documentation or the HtDP introduction to the list operator.

(Yes, S-expressions are more compact than XML and 50 years older than XML, but people don't like parentheses. They're so ugly and unreadable...)

In this context solve the following problems:

1. Translate the XML example from above into an Xexpr.
2. Design a function that counts the number of symbols in an Xexpr.
3. Design a function that counts the number of characters in an Xexpr.