Parse trees and derivations in Compiler Design - Step-by-Step Execution

Concept Flow - Parse trees and derivations

Start with Grammar

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Input String

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Apply Production Rules

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Build Parse Tree Step-by-Step

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Derivation Sequence

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Final Parse Tree and Derivation

The process starts with a grammar and an input string, applies production rules step-by-step to build a parse tree, showing the derivation sequence until the final parse tree is complete.

Execution Sample

Compiler Design

Grammar:
S -> a S b | ε
Input: a a b b
Derivation:
S => a S b => a a S b b => a a b b

Shows how the input string 'a a b b' is derived from the start symbol S using production rules, building the parse tree.

Analysis Table

Step	Current String	Production Applied	Resulting String	Parse Tree Node Added
1	S	S -> a S b	a S b	Root S with children 'a', S, 'b'
2	a S b	S -> a S b	a a S b b	Expand S node to 'a', S, 'b'
3	a a S b b	S -> ε	a a b b	Replace S with ε (empty)
4	a a b b	None	a a b b	Parse tree complete

💡 No more non-terminals to expand; input string fully derived.

State Tracker

Variable	Start	After 1	After 2	After 3	Final
Current String	S	a S b	a a S b b	a a b b	a a b b
Parse Tree Nodes	Root S	S with 'a', S, 'b'	Expanded S again	S replaced by ε	Complete tree

Key Insights - 2 Insights

Why do we replace S with ε in step 3?

Because the production S -> ε means S can be empty, which ends the expansion. This is shown in execution_table row 3 where the current string changes from 'a a S b b' to 'a a b b'.

How does the parse tree grow with each production?

Each production adds nodes to the parse tree representing the applied rule. For example, in step 1 and 2, the S node expands to 'a', S, 'b', adding branches as shown in execution_table rows 1 and 2.

Visual Quiz - 3 Questions

Look at the execution_table, what is the Current String after step 2?

A a S b

B a a S b b

C a a b b

D S

💡 Hint

Check the 'Current String' column in row 2 of the execution_table.

At which step is the production S -> ε applied?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Production Applied' column to find where S -> ε is used.

If we did not use S -> ε, what would happen to the parse tree?

A It would be the same

B It would be smaller

C It would keep expanding infinitely

D It would be incomplete

💡 Hint

Refer to variable_tracker showing how S expands and the role of ε in stopping expansions.

Concept Snapshot

Parse trees show how input strings are generated from grammar rules.
Derivations are sequences of rule applications.
Start from start symbol, apply productions stepwise.
Each step expands non-terminals in the string.
Parse tree nodes represent grammar symbols and expansions.
ε means empty string, used to end expansions.

Full Transcript

Parse trees and derivations explain how a string is formed from grammar rules. Starting with the start symbol, we apply production rules step-by-step. Each step replaces a non-terminal with the right side of a rule, building the parse tree. The derivation sequence shows these replacements as strings. When a non-terminal is replaced by ε, it means it produces an empty string, ending that branch. The parse tree visually represents this process, with nodes for symbols and branches for expansions. This helps understand how compilers analyze code structure.