Exercise 10      Name    ____________________   Points __/22

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G4:
    <exp> ::= <exp> + <exp> | <exp> * <exp> | (<exp>) | a | b | c

G5:
    <exp> ::= <exp> + <exp> | <mulexp>
    <mulexp> ::= <mulexp> * <mulexp> | (<exp>) | a | b | c

G6:
    <exp> ::= <mulexp> + <exp>  | <mulexp>
    <mulexp> ::=  <rootexp> * <mulexp> | <rootexp>
    <rootexp> ::= (<exp>) | a | b | c

1. (6) Give the parse tree for a*b+c*a using:
   1. Grammar G4.
   2. Grammar G5.
   3. Grammar G6.
       
2. (4) Give the ASTs for:
     a.
   2. 

       

3. (4) Give the RPN for the two above ASTs.
4. (8) Modify G6 to include an operation called:
   1. some : precedence between * and +, right-associative.
   2. thing : lowest precedence, right-associative.