CS 3304 Homework #2

1. (15 points) Problem 23 of Chapter 3 in your textbook.
   
   
2. (10 points) Show that the following grammar does not satisfy the rules of predictive parsing.

   
   <stmt> -> <if-stmt> | <other>
   <if-stmt> -> if <stmt> [ else <stmt> ]
   

   
   
3. (25 points) The following grammar generates declarations for a single identifier:

   
   <stmt> -> declare <id> <option_list>
   <option_list> -> <option_list> <option> | epsilon
   <option> -> <mode> | <scale> | <precision> | <base>
   <mode> -> real | complex
   <scale> -> fixed | floating
   <precision> -> single | double
   <base> -> binary | decimal
   

   where "epsilon" is the empty symbol.
   
   As you can see, this grammar permits redundant or contradictory declarations such as:

   
   declare zippy real fixed real floating
   

   Our goal is to revise the grammar so that it forbids such obviously incorrect declarations. Write a grammar for legal declarations, where legal means each option appearing at most once (so there can be at most one mode, one scale, one precision, and one base). It is legal to not have anything specified for one or more (or all) of the options. So, just

   
   declare zippy
   

   is legal.