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FIRST and FOLLOW in Compiler Design

Introduction

In the context of compiler design, FIRST and FOLLOW sets are essential for determining which production rules should be applied during parsing. These sets help in predictive parsing and constructing LL(k) parsers, ensuring the correctness of the parsing table.

1. FIRST Set

Definition

The FIRST set of a non-terminal is the set of all terminals that begin the strings derivable from that non-terminal. It helps in deciding which terminal symbol can appear first in the derivation of a production.

• A symbol c is in FIRST(α) if and only if α ⇒ cβ for some sequence β of grammar symbols.

Steps to Compute FIRST Set

• For every terminal X, FIRST(X) is X.
• If a production is of the form A → α, then add all terminals from FIRST(α) to FIRST(A).
• If α derives ε (empty string), then add ε to FIRST(A).

Example

If A → BCD and FIRST(B) = {a}, then FIRST(A) = {a}.

If B → ε, then FIRST(A) must also include FIRST(C).

2. FOLLOW Set

Definition