property-based-testing

# Property-Based Testing

## Overview

Property-based testing (PBT) generates random inputs and verifies that properties hold for all of them. Instead of testing specific examples, you test invariants.

**When PBT beats example-based tests:**
- Serialization pairs (encode/decode)
- Pure functions with clear contracts
- Validators and normalizers
- Data structure operations

## Property Catalog

| Property | Formula | When to Use |
|----------|---------|-------------|
| **Roundtrip** | `decode(encode(x)) == x` | Serialization, conversion pairs |
| **Idempotence** | `f(f(x)) == f(x)` | Normalization, formatting, sorting |
| **Invariant** | Property holds before/after | Any transformation |
| **Commutativity** | `f(a, b) == f(b, a)` | Binary/set operations |
| **Associativity** | `f(f(a,b), c) == f(a, f(b,c))` | Combining operations |
| **Identity** | `f(x, identity) == x` | Operations with neutral element |
| **Inverse** | `f(g(x)) == x` | encrypt/decrypt, compress/decompress |
| **Oracle** | `new_impl(x) == reference(x)` | Optimization, refactoring |
| **Easy to Verify** | `is_sorted(sort(x))` | Complex algorithms |
| **No Exception** | No crash on valid input | Baseline (weakest) |

**Strength hierarchy** (weakest to strongest):
```
No Exception -> Type Preservation -> Invariant -> Idempotence -> Roundtrip
```

Always aim for the strongest property that applies.

## Pattern Detection

**Use PBT when you see:**

| Pattern | Property | Priority |
|---------|----------|----------|
| `encode`/`decode`, `serialize`/`deserialize` | Roundtrip | HIGH |
| `toJSON`/`fromJSON`, `pack`/`unpack` | Roundtrip | HIGH |
| Pure functions with clear contracts | Multiple | HIGH |
| `normalize`, `sanitize`, `canonicalize` | Idempotence | MEDIUM |
| `is_valid`, `validate` with normalizers | Valid after normalize | MEDIUM |
| Sorting, ordering, comparators | Idempotence + ordering | MEDIUM |
| Custom collections (add/remove/get) | Invariants | MEDIUM |
| Builder/factory patterns | Output