Exercise: Parsing Variable Declarations and Assignments

Consider the following context$-$free grammar for variable declarations and assignments in a hypothetical programming language:

$S$ DECL $||$ ASSIGN

DECL $$ TYPE ID ;

ASSIGN $$ ID $=$ EXPR ;

TYPE $$ int $||$ float $||$ char

EXPR $$ ID $||$ NUM

ID $\text{'}$a$\text{'}|\text{'}$b$\text{'}|\text{'}$c$\text{'}$

NUM $\text{'}0\text{'}|\text{'}1\text{'}|\text{'}2\text{'}$

Compute the First and Follow sets for each non$-$terminal in the grammar.

Construct the $LL(1)$ parsing table for the grammar based on the First and Follow sets.

Use the $LL(1)$ parsing table to parse the following strings:

int a;

$b=1$