Project 7: Symbolic Math Simplifier (Algebraic Rule Systems)

Build a rule-based system that simplifies algebraic expressions using rewrite rules.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 10-16 hours
Language Python
Prerequisites Parsing basics, recursion
Key Topics expression trees, rewrite rules

1. Learning Objectives

By completing this project, you will:

  1. Parse expressions into ASTs.
  2. Apply rewrite rules for simplification.
  3. Handle associative/commutative rules.
  4. Avoid infinite rewrite loops.
  5. Compare simplified forms.

2. Theoretical Foundation

2.1 Rewrite Systems

Symbolic simplification uses rewrite rules to transform expressions into equivalent forms.

3. Project Specification

3.1 What You Will Build

A symbolic simplifier that takes algebraic expressions and returns simplified equivalents.

3.2 Functional Requirements

  1. Parser for algebraic expressions.
  2. AST representation with operators.
  3. Rewrite rules (e.g., x*1 -> x).
  4. Rewrite engine with termination checks.
  5. Comparison of original vs simplified.

3.3 Non-Functional Requirements

  • Deterministic simplification.
  • Configurable rule sets.
  • Readable output formatting.

4. Solution Architecture

4.1 Components

Component Responsibility
Parser Build AST
Rule Engine Apply rewrite rules
Simplifier Iterate until fixed point
Formatter Render expressions

5. Implementation Guide

5.1 Project Structure

SYMBOLIC_AI_AND_EXPERT_SYSTEMS_MASTERY/P07-symbolic-math/
├── src/
│   ├── parse.py
│   ├── rules.py
│   ├── simplify.py
│   └── format.py

5.2 Implementation Phases

Phase 1: Parsing + AST (4-6h)

  • Parse expressions into trees.
  • Checkpoint: AST renders correctly.

Phase 2: Rule engine (4-6h)

  • Implement rewrite rules.
  • Checkpoint: simple simplifications work.

Phase 3: Termination (2-4h)

  • Avoid infinite loops.
  • Checkpoint: fixed point reached.

6. Testing Strategy

6.1 Test Categories

Category Purpose Examples
Unit parser AST correctness
Integration simplifier expected simplifications
Regression loops termination guaranteed

6.2 Critical Test Cases

  1. x*1 simplifies to x.
  2. x+0 simplifies to x.
  3. Rewrites terminate without loops.

7. Common Pitfalls & Debugging

Pitfall Symptom Fix
Infinite rewrites no termination track rule applications
Wrong precedence incorrect AST enforce operator precedence
Non-determinism inconsistent results order rules consistently

8. Extensions & Challenges

Beginner

  • Add more rewrite rules.
  • Add pretty-print output.

Intermediate

  • Add factoring and expansion.
  • Add rule priorities.

Advanced

  • Add simplification with assumptions.
  • Add symbolic differentiation.

9. Real-World Connections

  • Computer algebra systems rely on rewrite rules.
  • Compiler optimizers use similar transformations.

10. Resources

  • Term rewriting references
  • Symbolic algebra tutorials

11. Self-Assessment Checklist

  • I can parse expressions into ASTs.
  • I can apply rewrite rules safely.
  • I can ensure termination.

12. Submission / Completion Criteria

Minimum Completion:

  • Parser + rewrite rules

Full Completion:

  • Termination handling

Excellence:

  • Differentiation or advanced rules

This guide was generated from project_based_ideas/AI_AGENTS_LLM_RAG/SYMBOLIC_AI_AND_EXPERT_SYSTEMS_MASTERY.md.