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 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
The code has no property to assert yet	references/refactoring.md
Reviewing existing property tests	references/reviewing.md
A property test just failed	references/interpreting-failures.md
Library choice, Echidna and Medusa	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.