Computer Science 5641
Compiler Design
Homework Assignment 2 (20 points)
Due October 20, 2004

Consider a language defined by the following syntax:

• Any integer constant is an expression
• If e1 and e2 are expressions, then so are:
  • +++ e1
  • e1 ---
  • e1 +-- e2
  • e1 --+ e2
  • e1 ++- e2
  • e1 -++ e2
  • ( e1 )
• Nothing else is an expression

Answer the following questions:

1. [2] Write a context-free grammar for the language using only one nonterminal.
2. [1] Is your grammar ambiguous? Explain your answer.
3. [3] Update your grammar to make a grammar that accounting for the following precedence/associativity information. Operators in order of precedence from highest to lowest are (two operators at the same bullet have highest precedence):
   • +--, --+ (right associative)
   • ++-, -++ (left associative)
   • --- (left associative)
   • +++ (right associative)
4. [1] Show a right-most derivation and corresponding parse tree for +++ 5 --+ 3 +-- 4 ++- 6 +-- 2 ---
5. [3] Determine the first and follow sets for your grammar. Using your sets construct a parse table for a predictive parser.