Parse trees and derivations in Compiler Design - Mini Project: Build & Apply

Understanding Parse Trees and Derivations

📖 Scenario: You are learning how programming languages are understood by computers. One key idea is how sentences in a language are broken down into parts using parse trees. These trees show how a sentence is built step-by-step from basic rules called grammar productions. This helps computers check if sentences are correct and understand their meaning.

🎯 Goal: Build a simple parse tree for a small sentence using a given grammar. Then, write the steps (derivations) that show how the sentence is formed from the grammar rules.

📋 What You'll Learn

Create a dictionary representing grammar rules with exact keys and values

Add a variable for the sentence to be parsed

Write code to build a parse tree structure for the sentence using the grammar

List the derivation steps that show how the sentence is generated from the grammar

💡 Why This Matters

🌍 Real World

Parse trees and derivations are used by compilers and interpreters to understand and check programming languages and natural languages.

💼 Career

Understanding parse trees is essential for jobs in compiler design, language processing, and software development tools.

1

Set up the grammar rules dictionary

Create a dictionary called grammar with these exact entries: 'S': ['NP VP'], 'NP': ['Det N'], 'VP': ['V NP'], 'Det': ['the'], 'N': ['cat'], 'V': ['chased'].

Compiler Design

# Create the grammar dictionary with the given rules
# Your code here

Need a hint?

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

2

Define the sentence to parse

Create a variable called sentence and set it to the string 'the cat chased the cat'.

Compiler Design

grammar = {
    'S': ['NP VP'],
    'NP': ['Det N'],
    'VP': ['V NP'],
    'Det': ['the'],
    'N': ['cat'],
    'V': ['chased']
}

# Define the sentence string
# Your code here

Need a hint?

Assign the exact sentence string to the variable sentence.

3

Build the parse tree structure

Create a dictionary called parse_tree that represents the parse tree for the sentence. Use this exact nested structure: {'S': {'NP': {'Det': 'the', 'N': 'cat'}, 'VP': {'V': 'chased', 'NP': {'Det': 'the', 'N': 'cat'}}}}.

Compiler Design

grammar = {
    'S': ['NP VP'],
    'NP': ['Det N'],
    'VP': ['V NP'],
    'Det': ['the'],
    'N': ['cat'],
    'V': ['chased']
}

sentence = 'the cat chased the cat'

# Build the parse tree dictionary
# Your code here

Need a hint?

Use nested dictionaries to show how each part of the sentence breaks down by grammar rules.

4

Write the derivation steps

Create a list called derivations with these exact strings in order: 'S', 'NP VP', 'Det N VP', 'the N VP', 'the cat VP', 'the cat V NP', 'the cat chased NP', 'the cat chased Det N', 'the cat chased the N', 'the cat chased the cat'.

Compiler Design

grammar = {
    'S': ['NP VP'],
    'NP': ['Det N'],
    'VP': ['V NP'],
    'Det': ['the'],
    'N': ['cat'],
    'V': ['chased']
}

sentence = 'the cat chased the cat'

parse_tree = {
    'S': {
        'NP': {'Det': 'the', 'N': 'cat'},
        'VP': {
            'V': 'chased',
            'NP': {'Det': 'the', 'N': 'cat'}
        }
    }
}

# Write the derivation steps list
# Your code here

Need a hint?

List each step showing how the sentence is formed by replacing non-terminals with their productions.