Demonstration of Ambiguity in Context-Free Grammars
Getting Started
The simulation interface consists of three main components:
- Control Panel: Contains buttons to navigate through different ambiguous grammars and derivation steps
- Derivation Panels: Left and right panels showing two different derivations of the same string
- Parse Tree Visualization: Side-by-side comparison of parse trees demonstrating ambiguity
Step-by-Step Instructions
1. Selecting an Ambiguous Grammar
Click the "Change Grammar" button to cycle through three different ambiguous grammar examples. Each grammar demonstrates a specific type of ambiguity commonly found in programming languages.
2. Understanding the Interface
- Input String: Displayed at the center, showing the string being derived by both parse trees
- Production Rules: Listed below the input string, showing all available grammar rules
- Derivation A & B: Left and right panels showing two different derivations of the same string
- Parse Trees: Visual representations updating as you step through derivations
3. Stepping Through Derivations
Auto Step Mode
Click the "Auto Step" button to automatically advance through both derivations simultaneously. The simulation alternates between the left and right derivations, showing how the same string can be derived differently.
Manual Navigation
- "Previous Step": Go back one step in the current derivation
- "Show Hint": Get guidance about the next step or the difference between derivations
4. Observing the Derivation Process
As you step through the derivations:
- Derivation Steps: Watch how each panel shows different sequences of rule applications
- Parse Tree Growth: Observe how the trees develop differently for the same input string
- Rule Applications: Notice which production rules are applied at each step
5. Comparing Parse Trees
After completing both derivations:
- Structure Differences: Compare the final tree structures side-by-side
- Semantic Implications: Understand how different parse trees can lead to different interpretations
- Ambiguity Visualization: See clearly how one string has multiple valid parse trees
6. Exploring Different Grammar Types
The simulation includes three types of ambiguous grammars:
- Arithmetic Expressions: Demonstrates operator precedence ambiguity
- String Concatenation: Shows grouping ambiguity in sequence operations
- If-Then-Else Statements: Illustrates the classic dangling else problem
7. Understanding Results
A successful exploration involves:
- Completing both derivations for the same input string
- Observing the structural differences between the resulting parse trees
- Understanding why the grammar is considered ambiguous
- Recognizing the practical implications of each type of ambiguity