Computer Science 5641
Compiler Design
Homework Assignment 2 (20 points)
Due October 8, 2002

Consider a language defined by the following syntax:

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

Answer the following questions:

1. [3] Write a context-free grammar for the language using only one nonterminal.
2. [3] Is your grammar ambiguous? Explain your answer.
3. [6] Update your grammar to make a grammar that accounting for the following requirements (you may use as many nonterminals as you like):
   • Precedence (highest to lowest): (1) integer constant, parenthesized expression, unary minus, (2) exponentiation (**), (3) subtraction and division, (4) addition and multiplication
   • ALL of the operations are right
4. [3] Show a right-most derivation and corresponding parse tree for 1/3-4**5--2.
5. [4] Determine the first and follow sets for your grammar. Using your sets construct a parse table for a predictive parser.