Short trick method to find First of any grammar- Compiler Design

Short trick method to find First of any grammar- Compiler Design

Short Trick to Find FIRST of Any Grammar (Compiler Design)

In Compiler Design, computing the FIRST set is essential for parsing table construction in LL(1) parsers. Here’s a short trick method with rules to find the FIRST set quickly and accurately.

What is FIRST?

The FIRST(X) set is the set of terminals that begin the strings derivable from symbol X (where X can be a terminal, non-terminal, or ε).

Short Trick Rules to Find FIRST

Rule 1: For terminals

If X is a terminal, then:

Rule 2: For ε (epsilon)

Rule 3: For non-terminals (A → α1 α2 α3…)

To find FIRST(A):

• Go left to right in production A → α1 α2 α3…

• Add FIRST(α1) to FIRST(A)

• If FIRST(α1) contains ε, then check α2, then α3, etc.

• Continue until a symbol does NOT have ε in its FIRST set.

• If all symbols derive ε, then ε ∈ FIRST(A)

Shortcut Flow (for A → α):

Example 1:

Step-by-step:

• FIRST(A) = { a, ε }

• FIRST(B) = { b }

• FIRST(S):

  • From S → A B

  • FIRST(A) = { a, ε }, so check next

  • FIRST(B) = { b }

  • So FIRST(S) = { a, b }

Example 2:

Then:

• FIRST(A) = { ε }

• FIRST(B) = { ε }

• FIRST(S) = { ε } (since all parts can derive ε)

Example 3:

• FIRST(A) = { c, ε }

• FIRST(S) = { c, b }
  (Because A can be ε, so next terminal b is also considered)

Tips & Tricks Recap:

Go left to right in RHS
If you see a terminal, add it and stop
If you see ε, skip and check next
If all symbols can derive ε, then add ε to FIRST
Don’t forget to union all FIRSTs if multiple rules exist

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Short trick method to find First of any grammar- Compiler Design

LECTURE NOTES ON COMPILER DESIGN

compiler design lecture notes