Predictive parsing in Compiler Design - Step-by-Step Execution

Concept Flow - Predictive parsing

Start: Input string

↓

Initialize stack with start symbol

↓

Read next input token

↓

Check top of stack

↓

If terminal

↓

Match with input token?

↓

Error: Mismatch

↓

If non-terminal

↓

Use parsing table to find production

↓

Production found?

Yes↓

Replace non-terminal with production RHS

↓

Error: No rule

↓

Stack empty and input consumed?

Yes↓

Accept

No↓

Error

Predictive parsing reads input tokens and uses a stack and parsing table to decide which grammar rules to apply, matching input step-by-step until the input is accepted or an error occurs.

Execution Sample

Compiler Design

Stack = [S]
Input = id + id * id $
While stack not empty:
  top = stack.pop()
  if top is terminal:
    match input token
  else:
    use table to expand top

This code simulates a predictive parser processing an input string using a stack and parsing table.

Analysis Table

Step	Stack (top right)	Input Token	Action	Output/Notes
1	[S]	id	Expand S using table: S -> id E	Stack becomes [E, id]
2	[E, id]	id	Top is terminal 'id', matches input 'id'	Pop 'id', advance input
3	[E]	+	Expand E using table: E -> + id E | ε	Choose production based on lookahead '+'; expand E -> + id E
4	[E, id, +]	+	Top is terminal '+', matches input '+'	Pop '+', advance input
5	[E, id]	id	Top is terminal 'id', matches input 'id'	Pop 'id', advance input
6	[E]	*	Expand E using table: E -> * id E | ε	Lookahead '*', expand E -> * id E
7	[E, id, *]	*	Top is terminal '*', matches input '*'	Pop '*', advance input
8	[E, id]	id	Top is terminal 'id', matches input 'id'	Pop 'id', advance input
9	[E]	$	Lookahead '$', no expansion needed, E -> ε	Pop E (epsilon), no input advance
10	[]	$	Stack empty and input is '$'	Accept input string
11	-	-	-	Parsing complete successfully

💡 Stack empty and input fully matched, parsing accepted

State Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	After 7	After 8	After 9	Final
Stack	[S]	[E, id]	[E]	[E, id, +]	[E, id]	[E]	[E, id, *]	[E, id]	[E]	[]	[]
Input Token	id	id	+	+	id	*	*	id	$	$	$

Key Insights - 3 Insights

Why do we expand a non-terminal using the parsing table instead of just guessing?

The parsing table uses the current input token (lookahead) to choose the correct production, ensuring the parser follows the grammar rules correctly (see execution_table steps 1, 3, 6).

What happens if the top of the stack is a terminal but does not match the input token?

This causes a parsing error because the input does not follow the grammar; the parser expects a specific token but found another (see execution_table step 2 for a successful match, opposite would be error).

How does the parser know when to stop expanding non-terminals?

When the lookahead token does not require further expansion, the parser uses epsilon (empty) productions to pop non-terminals without consuming input (see execution_table step 9).

Visual Quiz - 3 Questions

Look at the execution_table at step 4. What is the top of the stack and input token?

A Top of stack: '+', Input token: '+'

B Top of stack: 'E', Input token: '+'

C Top of stack: 'id', Input token: 'id'

D Top of stack: 'S', Input token: 'id'

💡 Hint

Refer to execution_table row 4 under 'Stack' and 'Input Token' columns.

At which step does the parser accept the input string?

A Step 9

B Step 10

C Step 11

D Step 8

💡 Hint

Check execution_table rows where stack is empty and input token is '$'.

If the input token at step 5 was '*', what would happen?

A The parser would match '*' and continue normally.

B The parser would expand E using epsilon production.

C The parser would raise an error due to mismatch.

D The parser would pop 'id' without matching input.

💡 Hint

Look at execution_table step 5 where 'id' is expected but input token differs.

Concept Snapshot

Predictive parsing uses a stack and input tokens.
It expands non-terminals using a parsing table based on lookahead.
Terminals on stack must match input tokens exactly.
Epsilon productions allow popping without consuming input.
Parsing succeeds if stack empties and input is fully read.
Errors occur on mismatches or missing table entries.

Full Transcript

Predictive parsing is a method to analyze input strings using a stack and a parsing table. The parser starts with the start symbol on the stack and reads input tokens one by one. If the top of the stack is a terminal, it must match the current input token to continue. If it is a non-terminal, the parser uses the parsing table and the lookahead token to decide which production rule to apply, replacing the non-terminal with the right side of the rule. This process repeats until the stack is empty and the input is fully consumed, meaning the input string is accepted. If a mismatch or missing rule occurs, the parser reports an error. Epsilon productions allow the parser to pop non-terminals without consuming input when appropriate. This step-by-step process ensures the input follows the grammar rules.

Practice

1. What is the main purpose of predictive parsing in compiler design?

easy

A. To optimize the runtime performance of a program

B. To analyze sentences using a stack and parsing table without backtracking

C. To generate machine code from source code

D. To translate high-level code into assembly language

Solution

1. Step 1: Understand predictive parsing function

   Predictive parsing analyzes sentences by using a stack and a parsing table to decide the next step without guessing or backtracking.

2. Step 2: Differentiate from other compiler tasks

   Generating machine code, optimizing runtime, and translating to assembly are later compiler stages, not parsing.

3. Final Answer:

   To analyze sentences using a stack and parsing table without backtracking -> Option B

4. Quick Check:

   Predictive parsing = stack + table analysis [OK]

Hint: Parsing means analyzing structure, not generating code [OK]

Common Mistakes:

• Confusing parsing with code generation
• Thinking predictive parsing guesses or backtracks
• Mixing parsing with optimization tasks

2. Which of the following is a correct component used in predictive parsing?

easy

A. Parsing table

B. Backtracking stack

C. Hash map for variables

D. Symbolic debugger

Solution

1. Step 1: Identify key components of predictive parsing

   Predictive parsing uses a parsing table and a stack to decide which grammar rule to apply next.

2. Step 2: Eliminate unrelated options

   Backtracking stack is not used because predictive parsing avoids backtracking. Hash maps and debuggers are unrelated to parsing tables.

3. Final Answer:

   Parsing table -> Option A

4. Quick Check:

   Parsing table is essential in predictive parsing [OK]

Hint: Parsing table guides decisions without guessing [OK]

Common Mistakes:

• Assuming backtracking is part of predictive parsing
• Confusing parsing table with data structures for variables
• Mixing debugging tools with parsing components

3. Given the grammar rules:
S -> a A b
A -> c | ε
and the input string acb, what will the predictive parser do at the point it reads c?

medium

A. Throw a syntax error

B. Apply rule A -> ε and skip c

C. Backtrack to try another rule

D. Apply rule A -> c and consume c

Solution

1. Step 1: Check the input and grammar at A

   The input symbol is c. The grammar allows A -> c or A -> ε.

2. Step 2: Use predictive parsing table logic

   Since the next input is c, the parser chooses A -> c to match the input symbol and consume it.

3. Final Answer:

   Apply rule A -> c and consume c -> Option D

4. Quick Check:

   Input matches rule A -> c [OK]

Hint: Match input symbol with rule start, no backtracking [OK]

Common Mistakes:

• Choosing epsilon rule when input symbol matches
• Thinking parser backtracks on mismatch
• Assuming syntax error without checking rules

4. Identify the error in this predictive parsing step:
Grammar: S -> a S b | ε
Input: a a b b
Parser applies S -> ε immediately at the start.

medium

A. Parser should backtrack after epsilon

B. Input string is invalid for the grammar

C. Incorrect application of epsilon rule too early

D. No error, parsing is correct

Solution

1. Step 1: Analyze grammar and input

   The grammar allows S -> a S b or S -> ε. The input starts with a, so epsilon should not be chosen immediately.

2. Step 2: Understand predictive parsing rules

   Predictive parsing uses lookahead to decide rules. Since input is a, it should apply S -> a S b first, not epsilon.

3. Final Answer:

   Incorrect application of epsilon rule too early -> Option C

4. Quick Check:

   Epsilon only if input doesn't match other rules [OK]

Hint: Check input symbol before choosing epsilon rule [OK]

Common Mistakes:

• Applying epsilon rule without checking input
• Assuming input is invalid without parsing
• Expecting backtracking in predictive parsing

5. You have a grammar with rules:
E -> T E'
E' -> + T E' | ε
T -> int
How would you construct the predictive parsing table entry for non-terminal E' and input symbol +?

hard

A. Use rule E' -> + T E' because input is '+'

B. Use rule E' -> ε because '+' is not in T

C. No entry needed because '+' is terminal

D. Use rule E' -> T E' to start parsing

Solution

1. Step 1: Identify first sets for E'

   The first set of E' includes '+' because of the rule E' -> + T E'.

2. Step 2: Match input symbol '+' with rule

   Since input is '+', the parser uses the rule E' -> + T E' in the parsing table for E' and '+'.

3. Final Answer:

   Use rule E' -> + T E' because input is '+' -> Option A

4. Quick Check:

   Input '+' matches E' -> + T E' [OK]

Hint: Match input with first set of non-terminal rules [OK]

Common Mistakes:

• Choosing epsilon rule when input matches '+'
• Confusing terminals with non-terminals in table
• Ignoring first sets in table construction