Exercise 9      Name       ____________________   Points __/25

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<!ELEMENT exp ( (exp, plus, exp) | (exp, times, exp) | (lparen, exp, rparen) | a | b | c )>

1. (9) For the above EBNF DTD give the parse trees for the following XML.

   i. a + b

   <exp>
       <exp><a/></exp>
       <plus/>
       <exp><b/></exp>
   </exp>

   ii. a * b + c

   <exp>
       <exp>
           <exp><a/></exp>
           <times/>
           <exp><b/></exp>
       </exp>
       <plus/>
       <exp><c/></exp>
   </exp>

   iii. (a + b) * c

<exp>
    <exp>
        <lparen/>
        <exp>
            <exp><a/></exp>
            <plus/>
            <exp><b/></exp>
        </exp>
        <rparen/>
     </exp>
    <times/>
    <exp><c/></exp>
</exp>

2. (6) Give the XML for the following using the definition of exp above:
   1. a * (b + c)
   2. (a + b) * (b + c)

    

    

   <!ELEMENT digit (zero | one | two | three)>
   <!ELEMENT unsigned (digit+)>                                            Iterative
   <!ELEMENT unsigned (digit | (unsigned, digit))>                    Recursive
   <!ELEMENT signed ((plus, unsigned) | (minus, unsigned))>
   <!ELEMENT plus EMPTY>
   <!ELEMENT minus EMPTY>
   <!ELEMENT zero EMPTY>
   <!ELEMENT one EMPTY>
   <!ELEMENT two EMPTY>
   <!ELEMENT three EMPTY>

    

3. (6) Complete the above DTD of a grammar with the following rules:
   1. <integer> as the set of all strings of <signed> or <unsigned>.
   2. <decimal> as the set of all strings of <integer> followed by a ‘.’ and optionally followed by an <unsigned>.
   3. <twoorthreedigits> as the set of all strings of two or three <digit>.

    

4. (4) The following is XML for an <unsigned> 123:

   <!DOCTYPE unsigned SYSTEM "ex9.dtd">                 Using iterative
       <unsigned>
           <digit>
               <one/>
           </digit>
           <digit>
               <two/>
           </digit>
           <digit>
               <three/>
           </digit>
       </unsigned>

   <!DOCTYPE unsigned SYSTEM "ex9.dtd">                 Using Recursive
   <unsigned>
       <unsigned>
           <unsigned>
               <digit><one/></digit>
           </unsigned>
           <digit><two/></digit>
        </unsigned>
        <digit><three/></digit>
   </unsigned>

   1. Give the XML for a <signed> +123.
   2. Give the XML for a <decimal> -12.4.