LL(1) parser implementation in Compiler Design - Step-by-Step Execution

Concept Flow - LL(1) parser implementation

Start: Input string

↓

Initialize stack with start symbol

↓

Read next input token

↓

Check top of stack

↓

If terminal and matches input token

↓

Pop stack, advance input

↓

Continue

↓

If non-terminal

↓

Use parsing table to find production

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Replace non-terminal with production RHS

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Continue

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If mismatch or no rule

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Error: Reject input

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If stack empty and input consumed

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Accept input

The LL(1) parser reads input tokens and uses a stack and parsing table to decide which grammar rules to apply, matching input step-by-step until acceptance or error.

Execution Sample

Compiler Design

stack = ['S']
input = ['id', '+', 'id', '$']
while stack not empty:
  top = stack.pop()
  if top is terminal:
    if top == input_token: advance
    else: error
  else:
    production = table[top, input_token]
    if production: push RHS
    else: error

This code simulates an LL(1) parser processing an input string using a stack and parsing table.

Analysis Table

Step	Stack (top on right)	Input Token	Top of Stack	Action	Output/Result
1	[S]	id	S	Use table[S, id] -> S -> id + E	Pop S, push E + id
2	[E, +, id]	id	id	id is terminal and matches input	Pop id, advance input
3	[E, +]	+	+	+ is terminal and matches input	Pop +, advance input
4	[E]	id	E	Use table[E, id] -> E -> id	Pop E, push id
5	[id]	id	id	id is terminal and matches input	Pop id, advance input
6	[]	$	Stack empty	Input consumed	Accept input
7	-	-	-	-	Parsing complete, input accepted

💡 Stack empty and input token is end marker $, so input is accepted

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6
stack	['S']	['E', '+', 'id']	['E', '+']	['E']	['id']	[]	[]
input_token	id	id	+	id	id	$	$

Key Insights - 3 Insights

Why do we push the right-hand side of the production in reverse order onto the stack?

Because the stack processes symbols from top to bottom, pushing the right-hand side in reverse ensures the leftmost symbol is on top to be processed next, as shown in Step 1 of the execution_table.

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

The parser reports an error and rejects the input, as the matching condition fails (see the 'error' action in the concept_flow). This is not shown in the sample but is critical for correctness.

How does the parser know which production to use for a non-terminal?

It uses the parsing table indexed by the non-terminal and current input token, as in Step 1 and Step 4 of the execution_table where table entries guide which production to apply.

Visual Quiz - 3 Questions

Look at the execution_table at Step 3. What is the top of the stack and what action is taken?

A Top is 'id', mismatch error

B Top is 'E', use parsing table to find production

C Top is '+', it matches input token '+', so pop and advance input

D Stack is empty, accept input

💡 Hint

Check the 'Top of Stack' and 'Action' columns at Step 3 in execution_table

At which step does the parser pop the last 'id' terminal from the stack?

A Step 5

B Step 2

C Step 4

D Step 6

💡 Hint

Look at the 'Stack' and 'Action' columns in execution_table for when 'id' is popped

If the input token after Step 2 was 'id' instead of '+', what would happen at Step 3?

A Parser would pop '+' and advance input

B Parser would report an error due to mismatch

C Parser would use table to expand 'E'

D Parser would accept input

💡 Hint

Refer to key_moments about terminal mismatch and error handling

Concept Snapshot

LL(1) parser uses a stack and input tokens.
Start with stack holding start symbol.
At each step, check top of stack:
- If terminal, match input token and pop.
- If non-terminal, use parsing table to find production.
Push production RHS in reverse order.
Accept if stack empty and input consumed.

Full Transcript

An LL(1) parser reads an input string from left to right and uses a stack to keep track of expected grammar symbols. It starts with the start symbol on the stack. At each step, it looks at the top of the stack and the current input token. If the top is a terminal symbol and matches the input token, it pops the stack and moves to the next input token. If the top is a non-terminal, it consults the parsing table to find the correct production rule to apply, pops the non-terminal, and pushes the right-hand side of the production onto the stack in reverse order. If there is a mismatch or no rule, it reports an error. The parser accepts the input if the stack is empty and all input tokens have been consumed. The execution table shows a step-by-step example parsing the input "id + id". Key moments include understanding why the production is pushed in reverse, handling terminal mismatches, and using the parsing table to select productions.

Practice

1. What does the 1 in LL(1) parser stand for?

easy

A. One stack is used for parsing

B. One left recursion is allowed in the grammar

C. One lookahead token is used to decide parsing steps

D. One grammar rule is applied at a time

Solution

1. Step 1: Understand LL(1) parser basics

   LL(1) parser reads input Left to right (L), produces Leftmost derivation (L), and uses 1 lookahead token.

2. Step 2: Identify what '1' means

   The '1' specifically means the parser looks ahead by one token to decide which grammar rule to apply next.

3. Final Answer:

   One lookahead token is used to decide parsing steps -> Option C

4. Quick Check:

   LL(1) = 1 lookahead token [OK]

Hint: Remember LL(1) means 1 token lookahead [OK]

Common Mistakes:

• Confusing '1' with number of grammar rules
• Thinking '1' means one stack or recursion
• Assuming '1' means one parsing step

2. Which of the following is the correct syntax to represent the parsing table entry for non-terminal A and terminal a in LL(1) parser?

easy

A. parsing_table(a, A) = production_rule

B. parsing_table.a.A = production_rule

C. parsing_table[A, a] = production_rule

D. parsing_table[A][a] = production_rule

Solution

1. Step 1: Understand parsing table structure

   Parsing table is usually a two-dimensional structure indexed by non-terminal and terminal symbols.

2. Step 2: Identify correct syntax

   Using bracket notation with parsing_table[A][a] is the standard way to access or assign entries in a 2D table or dictionary of dictionaries.

3. Final Answer:

   parsing_table[A][a] = production_rule -> Option D

4. Quick Check:

   Use parsing_table[non-terminal][terminal] [OK]

Hint: Use double brackets for 2D table access [OK]

Common Mistakes:

• Using parentheses instead of brackets
• Swapping terminal and non-terminal order
• Using dot notation which is invalid here

3. Given the grammar rules:
S -> a A
A -> b
and the input string ab, what will be the output of an LL(1) parser?

medium

A. Parsing successful

B. Syntax error at 'b'

C. Parsing successful but with warnings

D. Syntax error at 'a'

Solution

1. Step 1: Trace parsing steps with input 'ab'

   Start with stack containing S. Input is 'a b'. Match 'a' with S -> a A, pop S, push A. Next input 'b' matches A -> b.

2. Step 2: Confirm all input consumed and stack empty

   After matching 'b', stack is empty and input is fully consumed, so parsing is successful.

3. Final Answer:

   Parsing successful -> Option A

4. Quick Check:

   Input matches grammar rules fully [OK]

Hint: Match input tokens stepwise with grammar rules [OK]

Common Mistakes:

• Assuming error on matching terminal 'b'
• Confusing input order
• Not popping stack correctly

4. Identify the error in this LL(1) parser snippet:

stack = ['$', 'S']
input = list('ab$')
while stack:
    top = stack.pop()
    current = input[0]
    if top == current:
        input.pop(0)
    else:
        rule = parsing_table[top][current]
        stack.extend(reversed(rule))

medium

A. Stack is popped before checking if top is terminal

B. Input is not consumed correctly

C. Parsing table lookup uses wrong indices

D. Stack is extended without reversing the rule

Solution

1. Step 1: Analyze stack popping logic

   The code pops the stack before checking if the top is a terminal matching the input token, which can cause loss of needed symbol if mismatch occurs.

2. Step 2: Explain correct approach

   Correct approach is to peek at the top of the stack first, then decide to pop if it matches input or replace using parsing table if non-terminal.

3. Final Answer:

   Stack is popped before checking if top is terminal -> Option A

4. Quick Check:

   Pop after checking top symbol type [OK]

Hint: Peek stack top before popping [OK]

Common Mistakes:

• Popping stack too early
• Not reversing rule before pushing
• Incorrect input token consumption

5. You want to implement an LL(1) parser for a grammar with left recursion. What is the best approach to handle this?

hard

A. Use a stack to store left recursive calls

B. Eliminate left recursion from the grammar before building the parser

C. Increase lookahead tokens to LL(2) or more

D. Ignore left recursion and parse as usual

Solution

1. Step 1: Understand LL(1) parser limitations

   LL(1) parsers cannot handle left recursion because it causes infinite recursion or parsing conflicts.

2. Step 2: Apply grammar transformation

   To use LL(1) parsing, left recursion must be removed by rewriting grammar rules into right-recursive or iterative forms.

3. Final Answer:

   Eliminate left recursion from the grammar before building the parser -> Option B

4. Quick Check:

   Remove left recursion for LL(1) compatibility [OK]

Hint: Remove left recursion before LL(1) parsing [OK]

Common Mistakes:

• Trying to parse left recursion directly
• Assuming more lookahead solves left recursion
• Ignoring grammar transformation needs