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.

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🧠 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).

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🔍 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)

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✨ Shortcut Flow (for A → α):

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🔢 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 }

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🔢 Example 2:

Then:

• FIRST(A) = { ε }

• FIRST(B) = { ε }

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

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🔢 Example 3:

• FIRST(A) = { c, ε }

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

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📝 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