property-based-testing

Property-Based Testing

An example test asserts one point. A property asserts a rule over the whole input

domain and lets the generator hunt for the counterexample. That trade is worth making

when the code has an algebraic shape — an inverse, an invariant, an oracle — and not

otherwise. Code with no such shape gets example tests; saying so is a valid outcome.

Check first whether the shape is missing or merely buried. A calculation wrapped in I/O,

a string built by concatenation, an in-place mutation — each has a property and no seam

to assert it through. See [references/refactoring.md](references/refactoring.md) before

concluding there is nothing to assert.

Property catalog

| Property | Formula | Where it applies |

|---|---|---|

| Roundtrip | decode(encode(x)) == x | Serialization, conversion pairs |

| Inverse | f(g(x)) == x | encrypt/decrypt, compress/decompress |

| Oracle | new(x) == reference(x) | Optimization, refactoring, reimplementation |

| Idempotence | f(f(x)) == f(x) | Normalization, formatting, sorting |

| Invariant | Holds before and after | Any transformation, contract state |

| Easy to verify | is_sorted(sort(x)) | Complex algorithms with cheap checkers |

| Commutativity | f(a, b) == f(b, a) | Binary and set operations |

| Associativity | f(f(a,b), c) == f(a, f(b,c)) | Combining operations |

| Identity | f(x, e) == x | Operations with a neutral element |

Strength ordering, weakest to strongest:

no crash → type preservation → invariant → idempotence → roundtrip / oracle.

Assert the strongest property the code supports. "No crash" alone rarely justifies the

dependency — if that is all you can find, either a small rearrangement exposes something

stronger, or the honest report is that this code is a poor PBT candidate. Rule out the

first before settling for the second.

The two ways a property test asserts nothing

• Tautology. assert add(a, b) == a + b restates the implementation; no bug they

share can fail it. Pick a property that constrains the function without recomputing

it. Note the exception: f(x) == f(x) is a genuine determinism property when f

is not obviously pure — serializers over dicts or sets, hashing, anything reading

the clock.

• Vacuity. assume() that filters out nearly every input passes without

exercising anything, and self-contradictory assume() passes having run zero cases.

Push constraints into the strategy so the generator produces valid inputs directly.

Where to look next

Load the one that matches the task in front of you:

| Task | File |

|---|---|

| Writing new tests, designing strategies | [references/generating.md](references/generating.md) |

| The code has no property to assert yet | [references/refactoring.md](references/refactoring.md) |

| Reviewing existing property tests | [references/reviewing.md](references/reviewing.md) |

| A property test just failed | [references/interpreting-failures.md](references/interpreting-failures.md) |

| Library choice, Echidna and Medusa | [references/libraries.md](references/libraries.md) |

Introducing PBT to a project that lacks it

If the project already uses a PBT library, just write the tests in it. If it does not,

adding one is a dependency decision that belongs to the user — offer it once with the

specific property you would write, and take the answer either way.