LL(1) parser implementation in Compiler Design - Mini Project: Build & Apply

LL(1) Parser Implementation

📖 Scenario: You are building a simple LL(1) parser for a tiny programming language. This parser will read a grammar, create parsing tables, and then parse input strings to check if they follow the grammar rules.This project will guide you through the key steps of implementing an LL(1) parser, a fundamental concept in compiler design.

🎯 Goal: Build a basic LL(1) parser that can parse input strings using a given grammar and parsing table.You will create the grammar data structure, define the parsing table, implement the parsing logic, and complete the parser to accept or reject input strings.

📋 What You'll Learn

Create a grammar dictionary with non-terminals and their productions

Define the LL(1) parsing table as a dictionary

Implement the parsing algorithm using a stack and input string

Complete the parser to return acceptance or rejection of input

💡 Why This Matters

🌍 Real World

LL(1) parsers are used in compilers and interpreters to analyze source code and check if it follows the language grammar.

💼 Career

Understanding LL(1) parsing is essential for compiler developers, language designers, and software engineers working on language tools.

1

Create the Grammar Dictionary

Create a dictionary called grammar with these exact entries:
'E': ['T E\''], 'E\'': ['+ T E\'', 'ε'], 'T': ['F T\''], 'T\'': ['* F T\'', 'ε'], 'F': ['( E )', 'id'].
Use exact string formatting including quotes and escape characters.

Compiler Design

# Create the grammar dictionary with the specified productions
# Your code here

Hint

Use a Python dictionary with keys as non-terminals and values as lists of production strings.

2

Define the LL(1) Parsing Table

Create a dictionary called parsing_table representing the LL(1) parsing table with these exact entries:
('E', 'id'): 'T E\'', ('E', '('): 'T E\'', ('E\'', '+'): '+ T E\'', ('E\'', ')'): 'ε', ('E\'', '$'): 'ε', ('T', 'id'): 'F T\'', ('T', '('): 'F T\'', ('T\'', '+'): 'ε', ('T\'', '*'): '* F T\'', ('T\'', ')'): 'ε', ('T\'', '$'): 'ε', ('F', 'id'): 'id', ('F', '('): '( E )'.

Compiler Design

grammar = {
    'E': ['T E\''],
    'E\'': ['+ T E\'', 'ε'],
    'T': ['F T\''],
    'T\'': ['* F T\'', 'ε'],
    'F': ['( E )', 'id']
}
# Define the LL(1) parsing table as specified
# Your code here

Hint

Use a dictionary with keys as tuples (non-terminal, terminal) and values as production strings.

3

Implement the Parsing Algorithm

Write a function called parse_input that takes a string input_string and parses it using the grammar and parsing_table. Inside the function, initialize a stack with ['$', 'E'] and append '$' to the end of input_string. Use a while loop to process the stack and input tokens. Use variables stack, input_tokens, top, and current_token. Implement the logic to match terminals, expand non-terminals using the parsing table, and handle epsilon 'ε'. Return True if the input is accepted, otherwise False.

Compiler Design

grammar = {
    'E': ['T E\''],
    'E\'': ['+ T E\'', 'ε'],
    'T': ['F T\''],
    'T\'': ['* F T\'', 'ε'],
    'F': ['( E )', 'id']
}

parsing_table = {
    ('E', 'id'): 'T E\'',
    ('E', '('): 'T E\'',
    ('E\'', '+'): '+ T E\'',
    ('E\'', ')'): 'ε',
    ('E\'', '$'): 'ε',
    ('T', 'id'): 'F T\'',
    ('T', '('): 'F T\'',
    ('T\'', '+'): 'ε',
    ('T\'', '*'): '* F T\'',
    ('T\'', ')'): 'ε',
    ('T\'', '$'): 'ε',
    ('F', 'id'): 'id',
    ('F', '('): '( E )'
}

# Write the parse_input function as described
# Your code here

Hint

Use a stack to hold grammar symbols and process input tokens one by one. Expand non-terminals using the parsing table. Handle epsilon by not pushing anything.

4

Complete the Parser with Acceptance Check

Add a final line to the parse_input function to return False if the stack is empty but the input is not fully parsed. Ensure the function returns True only when the entire input string is successfully parsed and the stack is empty. The function should be complete and ready to use.

Compiler Design

grammar = {
    'E': ['T E\''],
    'E\'': ['+ T E\'', 'ε'],
    'T': ['F T\''],
    'T\'': ['* F T\'', 'ε'],
    'F': ['( E )', 'id']
}

parsing_table = {
    ('E', 'id'): 'T E\'',
    ('E', '('): 'T E\'',
    ('E\'', '+'): '+ T E\'',
    ('E\'', ')'): 'ε',
    ('E\'', '$'): 'ε',
    ('T', 'id'): 'F T\'',
    ('T', '('): 'F T\'',
    ('T\'', '+'): 'ε',
    ('T\'', '*'): '* F T\'',
    ('T\'', ')'): 'ε',
    ('T\'', '$'): 'ε',
    ('F', 'id'): 'id',
    ('F', '('): '( E )'
}

def parse_input(input_string):
    stack = ['$','E']
    input_tokens = input_string.split() + ['$']
    index = 0
    while stack:
        top = stack.pop()
        current_token = input_tokens[index]
        if top == current_token == '$':
            return True
        elif top == current_token:
            index += 1
        elif top in grammar:
            production = parsing_table.get((top, current_token))
            if production is None:
                return False
            if production != 'ε':
                symbols = production.split()[::-1]
                stack.extend(symbols)
        else:
            return False
    # Return false if input not fully parsed
    # Your code here

Hint

After the loop ends, if parsing is incomplete, return false to reject the input.

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