Grammars and Parsing - Crafting a Compiler - page 140

9. Compute First and Follow sets for the nonterminals of the following
grammar.

1 S → aSe

2 | B

3 B → bBe

4 | C

5 C → cCe

6 | d

10. Compute First and Follow sets for each nonterminal in ac grammar from
Chapter 2, reprised as follows.

1 Prog → Dcls Stmts $

2 Dcls → Dcl Dcls

3 | λ

4 Dcl → floatdcl id

5 | intdcl id

6 Stmts → Stmt Stmts

7 | λ

8 Stmt → id assign Val ExprTail

9 | print id

10 ExprTail → plus Val ExprTail

11 | minus Val ExprTail

12 | λ

13 Val → id

14 | num

11. Compute First and Follow sets for each nonterminal in Exercise 3.

12. As discussed in Section 4.3, the algorithm in Figure 4.4 could use left
or right recursion to transform a repeated sequence of symbols into
standard grammar form. A production of the form A → A α is said to

be left recursive . Similarly, a production of the form A A is said

to be right recursive . Show that any grammar that contains left- and
right-recursive rules for the same LHS nonterminal must be ambiguous.

→β