XML: Foundations, Techniques, Applications; Summer 2000
 
Solution to Problem 7:                Harold Boley <boley@informatik.uni-kl.de>
July 13, 2000


a)

Not well-formed, since <def><theorem>1st definition</def> contains
start-tag <theorem> without end-tag </theorem>. Easiest correction:
Remove <theorem>, obtaining <def>1st definition</def>.


b)

Not valid w.r.t. Mathpaper DTD -- after well-formedness correction
in a): Element

  <coro>
    <stat>1st corollary's statement</stat>
    <proof>1st corollary's proof</proof>
  </coro>

contains stat and proof subelements, but for coro the DTD defined none.

Easiest correction (for fixed DTD): Remove stat and proof *as tags* in
the coro element, leaving only PCDATA inside, as in

  <coro>
    stat: 1st corollary's statement
    proof: 1st corollary's proof
  </coro>

Easiest correction (for flexible DTD): Insert new DTD declaration

<!ELEMENT coro          (stat, proof?)>


c)

         apply
         / | \
        /  |  \
       /   |   \
      /    |    \
     /     |     \
    /      |      \
   /       |       \
  /        |        \
 /         |         \
eq      apply        apply
        / | \        / | \
    times ci ci  times ci ci
          |  |         |  |
          |  |         |  |
          x  y         y  x


d)

apply(
  eq(),
  apply(
    times(),
    ci("x"),
    ci("y")),
  apply(
    times(),
    ci("y"),
    ci("x")))


e)

  <theopro>
    <theorem> <apply> <eq/> . . . </apply> </theorem>
    <proof>easy</proof>
  </theopro>


f)

<!ELEMENT theorem       (apply)>