A Python function has a non-trivial input domain (numeric ranges, string formats, list shapes) and example-based tests miss edge cases.
A bug fix needs a property test to prevent regression of a class of inputs (not just the one that caused the bug).
Refactoring code where the new implementation should be observably equivalent to the old (use Hypothesis to verify property: new(x) == old(x) for all x).
Testing parsers / serializers / encoders where round-trip properties hold (decode(encode(x)) == x).

If only one or two specific examples need verification, parametrize or fixtures suffice - Hypothesis is overkill.

Step 1 - Install

pip install hypothesis

Pin a version in requirements-dev.txt / pyproject.toml. Hypothesis is well-maintained but adds 1-2 seconds to test runtime per generated case; default 100 examples per @given.

Step 2 - Basic property test

Per [hyp-quickstart][hq]:

from hypothesis import given, strategies as st

@given(st.integers(0, 100))
def test_example(n):
    assert n < 50

The decorator runs the test 100 times with random n in [0, 100]. On failure, Hypothesis reports the falsifying example (the smallest n that violates the assertion) - typically 50 here.

Step 3 - Strategies

Per [hyp-quickstart][hq], a strategy names the shape of the input. The common ones:

st.integers(0, 100)                   # bounded ints
st.floats(allow_nan=False)            # floats, optionally excluding NaN/Inf
st.text(min_size=1)                   # strings
st.lists(st.integers(), max_size=10)  # collections
st.from_regex(r"[a-z]+@[a-z]+\.com", fullmatch=True)  # format-validated
st.sampled_from(Status)               # enum-like

Full catalog (binary, dictionaries, tuples, builds, composite): references/hypothesis-reference.md.

Step 4 - Composite strategies (dependent fields)

Per [hyp-quickstart][hq], @st.composite lets later values depend on earlier ones via draw():

from hypothesis import strategies as st

@st.composite
def valid_dates(draw):
    year = draw(st.integers(1900, 2100))
    month = draw(st.integers(1, 12))
    if month in (1, 3, 5, 7, 8, 10, 12):
        day = draw(st.integers(1, 31))
    elif month in (4, 6, 9, 11):
        day = draw(st.integers(1, 30))
    else:
        # Feb: account for leap years
        max_day = 29 if (year % 4 == 0 and year % 100 != 0) or year % 400 == 0 else 28
        day = draw(st.integers(1, max_day))
    return date(year, month, day)

@given(valid_dates())
def test_date_round_trip(d):
    assert date.fromisoformat(d.isoformat()) == d

The draw() call requests a value from a strategy; the composite returns the constructed value.

Step 5 - Filtering and assumptions

Two ways to constrain inputs:

# Filter at strategy level (preferred - Hypothesis can sample efficiently)
@given(st.integers(0, 100).filter(lambda x: x % 2 == 0))
def test_even_squares(n):
    assert (n * n) % 2 == 0

# Filter at test level (fallback when filtering depends on multi-input)
from hypothesis import assume

@given(st.integers(), st.integers())
def test_division(a, b):
    assume(b != 0)   # discard cases where b == 0
    result = a // b
    assert result * b + (a - result * b) == a

Per [hyp-quickstart][hq], use .filter() at the strategy level when possible (Hypothesis can sample efficiently). Use assume() inside the test when the precondition involves multiple inputs.

Heavy filtering is a smell - if 90% of generated cases are discarded, redesign the strategy.

Step 6 - Settings and reproducibility

from hypothesis import given, settings, strategies as st

@settings(max_examples=500, deadline=2000)   # 500 cases, 2s deadline per case
@given(st.integers())
def test_expensive(n):
    expensive_function(n)

For CI, set derandomize=True to make failures reproducible across runs (vs random seed = same property test passes locally, fails on CI mysteriously). Full settings table (max_examples, deadline, phases, verbosity): references/hypothesis-reference.md.

Step 7 - Round-trip and metamorphic properties

Two of the most useful property patterns:

Round-trip

import json

@given(st.dictionaries(st.text(), st.integers()))
def test_json_round_trip(d):
    assert json.loads(json.dumps(d)) == d

If decode(encode(x)) == x for all valid x, the encode/decode pair is correct.

Metamorphic (relating two computations on related inputs)

@given(st.lists(st.integers()))
def test_sort_idempotent(xs):
    assert sorted(sorted(xs)) == sorted(xs)

@given(st.lists(st.integers()), st.integers())
def test_sort_commutes_with_offset(xs, offset):
    sorted_xs = sorted(xs)
    sorted_offset = sorted(x + offset for x in xs)
    assert all(s + offset == o for s, o in zip(sorted_xs, sorted_offset))

Metamorphic tests are powerful when the function's "correct output" is hard to specify but its relationship to other inputs is easy.

Step 8 - pytest integration

Per [hyp-quickstart][hq]: "Hypothesis works seamlessly with pytest fixtures and parametrize decorators."

@pytest.fixture
def db_conn():
    # ... setup ...
    yield conn
    # ... teardown ...

@given(st.integers(0, 1000))
def test_with_fixture(db_conn, n):
    db_conn.insert(id=n)
    assert db_conn.find(id=n) == n

Hypothesis re-runs the test body with new n each time; the fixture is set up once per test (per pytest's normal scope rules, unless it's function-scoped - then once per generated case).

Step 9 - CI integration

- run: pytest --hypothesis-seed=42  # deterministic seed for reproducibility

# OR via @settings(derandomize=True)

When a property test fails, the failure includes the falsifying example - copy that into a regression test:

@given(...)
@example(n=42)   # the falsifying example from the prior run
def test_my_property(n):
    ...

@example cases run before generated ones; locks the regression in permanently.

References

references/hypothesis-reference.md - full strategies catalog, @settings table, anti-patterns, limitations.
[hyp-quickstart][hq] - Hypothesis quickstart: @given, strategies, shrinking, composite, assume(), settings.
fast-check-testing, proptest-testing, jqwik-testing, quickcheck-testing - per-language siblings with similar shape.
schemathesis-fuzzing - applies PBT to API schemas (different layer; same conceptual framework).

hypothesis-testing

hypothesis-testing

Overview

When to use