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 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: 
    </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 Scheme. Here is one of them:

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

  A 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

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

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

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.