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

 Short Trick to Find FOLLOW of Any Grammar in Compiler Design 

In Compiler Design, the FOLLOW set of a non-terminal helps in parsing and syntax analysis. It determines the set of terminals that can appear immediately after a given non-terminal in the derivation.

Finding the FOLLOW set can be tricky, but here’s a simple and easy trick to compute it quickly!

 Steps to Find FOLLOW Set Using a Short Trick

 Step 1: Start with the Start Symbol

• Always add $ (EOF symbol) to the FOLLOW of the start symbol.
• Example: If S is the start symbol, then FOLLOW(S) = {$}.

 Step 2: Look at the Right-Hand Side of Productions

• If a non-terminal (A) appears in a production before a terminal or non-terminal, then FOLLOW(A) will contain FIRST of the next symbol.
• Example:
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  S → A B


  Here, FOLLOW(A) ⊇ FIRST(B).

 Step 3: If a Non-Terminal is at the End of a Production

• If A is at the end of a production, then FOLLOW(A) ⊇ FOLLOW of LHS.
• Example:
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  S → A B


  Since B is at the end, FOLLOW(B) ⊇ FOLLOW(S).

 Step 4: If a Nullable Symbol is Present

• If a nullable symbol (ε-production) is after A, then check the next symbol’s FOLLOW or LHS’s FOLLOW.
• Example:
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  S → A B (where FIRST(B) contains ε)


  Then, FOLLOW(A) ⊇ FOLLOW(S).

Shortcut Formula for FOLLOW 

Case	Rule to Follow
A → αBβ	FOLLOW(B) ⊇ FIRST(β) (excluding ε)
A → αB (B is at the end)	FOLLOW(B) ⊇ FOLLOW(A)
A → αBβ, and FIRST(β) contains ε	FOLLOW(B) ⊇ FOLLOW(A)

 Example for Quick Understanding

Grammar:

Step-by-Step Trick to Find FOLLOW

FOLLOW(S) = {$} (Start symbol rule)
FOLLOW(A) ⊇ FIRST(B) = {b, c}
FOLLOW(B) ⊇ FOLLOW(S) = {$}
FOLLOW(C) ⊇ FOLLOW(B) = {$} (Since C → ε)

Final FOLLOW Sets:

 Conclusion:

With this short trick, you can quickly find FOLLOW sets without confusion! 
Start with $ for the start symbol.
Use FIRST of next symbol for FOLLOW.
If at the end, take FOLLOW of LHS.
Handle ε-productions carefully.

Would you like me to explain with more examples?

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

Introduction to Compilers and Language Design

LECTURE NOTES ON COMPILER DESIGN

FIRST and FOLLOW

Sure! Here’s a short-trick method to find the FOLLOW set of any non-terminal in Compiler Design (used in parsing, especially LL(1) parsers):

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Shortcut Method to Find FOLLOW Set in Compiler Design

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What is the FOLLOW set?

The FOLLOW(A) of a non-terminal A is the set of terminals that can appear immediately after A in some “sentential form” (derivation).

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Short Trick to Find FOLLOW(A):

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Step-by-Step Shortcut (Simple Rules):

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Rule 1: Start Symbol Rule

If A is the start symbol, then add $ (end marker) to FOLLOW(A).

If S is start → FOLLOW(S) = { $ }

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Rule 2: A → αBβ Rule (Non-terminal followed by symbols)

If there is a production like:
A → α B β

Then, everything in FIRST(β) (except ε) is added to FOLLOW(B).

FOLLOW(B) += FIRST(β) – { ε }

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Rule 3: A → αB or A → αBβ where β ⇒ ε (Nullable)

If B is at the end, or β ⇒ ε, then
FOLLOW(B) += FOLLOW(A)

This is called “FOLLOW through FOLLOW”
(when nothing follows B, or what follows is nullable)

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Rule 4: Keep Applying Until Stable

Apply all above rules iteratively until no new symbols are added.

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Example Using Shortcut:

Let’s take a simple grammar:

S → A B  
A → a | ε  
B → b

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Step-by-Step:

➤ FIRST Sets:

• FIRST(A) = { a, ε }
• FIRST(B) = { b }

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FOLLOW(S):

• S is start symbol → FOLLOW(S) = { $ }

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FOLLOW(A):

S → A B
→ A is followed by B → so:

FOLLOW(A) += FIRST(B) = { b }

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FOLLOW(B):

S → A B → B is at end → FOLLOW(B) += FOLLOW(S) = { $ }

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Final FOLLOW Sets:

Non-terminal	FOLLOW
S	{ $ }
A	{ b }
B	{ $ }

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Pro Tips:

• Always calculate FIRST sets first — they are used in FOLLOW computation.
• Don’t forget to handle ε (epsilon) carefully.
• Keep applying rules until sets stop changing (fixpoint).

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Would you like:

• PDF cheat sheet of FOLLOW & FIRST shortcuts?
• Animated YouTube script for this?
• Practice problems with solutions?

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