Decompose, Don't Analogize: First-Principles Programming

01 Sep, 2025

Inspired by Casey Handmer's "How to reason from first principles" and his Seven Ds method for physics problem-solving, adapted here for programming and software architecture.

Introduction

When physicists solve complex problems, they decompose them to fundamental laws rather than reasoning by analogy. Casey Handmer's Seven Ds method provides a systematic approach to physics problem-solving that starts from first principles. This same rigor can transform how we understand code and build software systems.

This framework adapts Handmer's methodology for programmers who need to reason about complex codebases, debug mysterious issues, or architect robust systems from scratch.

The Seven Cs Method

Context (Diagram analog)

Build a hierarchical mental model of the system:

• Map data flow: "User input → Parser → AST → Compiler → Bytecode → VM"
• Identify boundaries: "Module A owns data X, exposes interface Y to Module B"
• Trace dependencies: "Component C requires services D, E; provides capability F"
• State invariants: "Queue must maintain FIFO ordering, capacity never exceeds N"

Components

Decompose system into atomic, composable units:

• Pure functions (no side effects)
• State containers (explicit mutations)
• I/O boundaries (clearly marked effects)
• Interface contracts (type signatures, preconditions)

Constraints

Identify fundamental limitations:

• Computational complexity bounds
• Memory/space requirements
• Concurrency/synchronization requirements
• Platform/environment dependencies

Core Principle

Name the governing abstraction:

• "This is fundamentally a graph traversal problem"
• "State machine with N states and M transitions"
• "Producer-consumer with backpressure"
• "Recursive descent parser"

Construction

Build from primitives upward:

1. Start with simplest possible working implementation
2. Add complexity only when proven necessary
3. Each layer should be independently testable
4. Compose solutions from smaller verified components

Correctness

Prove implementation satisfies requirements:

• Type checking (static guarantees)
• Property-based testing (invariant verification)
• Complexity analysis (time/space bounds)
• Edge case enumeration

Concrete Implementation

Final working code with:

• Minimal viable feature set
• Clear extension points
• Performance characteristics documented

Analyzing Complex Codebases

Discovery Phase

1. Entry points: main(), initialization, API surfaces
2. Data structures: Core types and their relationships
3. Control flow: Execution paths, state transitions
4. Side effects: I/O, mutations, external dependencies

Comprehension Strategies

• Bottom-up: Understand primitives → Compose into modules → System behavior
• Top-down: Trace user actions → Follow execution → Identify subsystems
• Lateral: Find similar patterns → Extract commonalities → Understand design philosophy

Navigation Heuristics

• Start at tests to understand intent
• Follow data, not control flow
• Identify "god objects" and trace their usage
• Find the "main loop" or event dispatcher
• Locate configuration/initialization for system boundaries

Problem-Solving Algorithms

For Debugging

1. Reproduce: Minimal failing case
2. Bisect: Binary search for introduction point
3. Isolate: Remove variables until core issue remains
4. Hypothesize: Form specific, testable theory
5. Verify: Confirm fix addresses root cause

For Design

1. Define interface before implementation
2. Write usage examples before API
3. Consider failure modes before success paths
4. Design for deletion, not modification
5. Make illegal states unrepresentable

Technical Reasoning Rules

Complexity Management

• Cyclomatic complexity < 10 per function
• Dependency depth < 5 levels
• Interface width < 7±2 parameters
• Module cohesion > module coupling

Performance Principles

• Measure before optimizing
• Algorithmic improvements > micro-optimizations
• Cache locality > parallelization (usually)
• Lazy evaluation for expensive computations

Abstraction Guidelines

• Zero-cost abstractions preferred
• Leaky abstractions explicitly documented
• Two implementations before generalizing
• Composition over inheritance

Example: Analyzing a Web Server

Context Mapping

Request → Router → Middleware Stack → Handler → Response
         ↓         ↓                   ↓
    Route Table  Auth/Logging    Business Logic
                                       ↓
                                  Database/Cache

Core Principle Identification

"This is a pipeline architecture with request/response transformation"

Component Analysis

# Primitive: Request handler
def handle(request: Request) -> Response:
    # Pure transformation
    return Response(transform(request.data))

# Composition: Middleware chain
def compose(*middlewares):
    def handler(request):
        for mw in middlewares:
            request = mw(request)
            if request.terminated:
                break
        return request
    return handler

# State boundary: Database interaction
async def fetch_user(id: int) -> User:
    # Explicit I/O boundary
    async with db.transaction() as tx:
        return await tx.query_one(User, id=id)

Common Anti-Patterns to Avoid

• Premature optimization: Optimizing before measuring
• Speculative generality: Building for imagined future needs
• God objects/functions: Entities doing too much
• Circular dependencies: A depends on B depends on A
• Hidden side effects: Mutations not visible in signatures
• Implicit state coupling: Relying on execution order
• Synchronous I/O in hot paths: Blocking the main thread
• Unbounded resource consumption: No limits on memory/CPU

Advanced Techniques

Reasoning About Concurrency

1. Identify shared state
2. Map synchronization points
3. Prove absence of deadlock
4. Verify atomicity requirements
5. Consider failure ordering

Memory Model Analysis

Stack: [Local variables, function calls]
  ↓
Heap: [Dynamic allocations, objects]
  ↓
Static: [Global state, constants]

Optimization Decision Tree

Is it slow? → Profile
  ↓
Where? → Hotspot analysis
  ↓
Why? → Algorithm vs Implementation
  ↓
Fix: O(n²)→O(n log n) vs Cache miss→Cache hit

Practical Application: Code Review Checklist

When reviewing code through this lens, consider:

Critical Issues

• Does it violate fundamental constraints?
• Are there O(n²) or worse algorithms where O(n log n) exists?
• Does it introduce circular dependencies?

Design Concerns

• Can the core principle be stated in one sentence?
• Are components properly isolated?
• Does each abstraction justify its cost?

Implementation Quality

• Are side effects contained at boundaries?
• Can another developer understand the code in < 5 minutes?
• Is the simplest solution that works being used?

Conclusion

Just as physicists don't solve problems by pattern-matching to similar problems they've seen before, we shouldn't approach programming by blindly applying design patterns or copying Stack Overflow solutions. Instead, decompose problems to their fundamental operations—assignment, comparison, iteration, recursion—and build up from there.

Every abstraction has a cost. Make that cost explicit and justified by the value it provides. When in doubt, choose the simpler solution that solves today's problem, not tomorrow's hypothetical.

The Seven Cs framework forces us to think systematically:

1. Context establishes the problem space
2. Components breaks it into manageable pieces
3. Constraints defines the boundaries
4. Core Principle identifies the fundamental challenge
5. Construction builds the solution methodically
6. Correctness verifies it works
7. Concrete Implementation delivers working code

By reasoning from first principles rather than analogies, we write more robust, maintainable, and correct software. The next time you face a complex codebase or architectural decision, try applying this framework—you might be surprised how much clarity emerges from systematic decomposition.