# Some more examples¶

This is a collection of examples of how to use Hypothesis in interesting ways. It’s small for now but will grow over time.

All of these examples are designed to be run under pytest, and nose should work too.

## How not to sort by a partial order¶

The following is an example that’s been extracted and simplified from a real bug that occurred in an earlier version of Hypothesis. The real bug was a lot harder to find.

Suppose we’ve got the following type:

```
class Node:
def __init__(self, label, value):
self.label = label
self.value = tuple(value)
def __repr__(self):
return f"Node({self.label!r}, {self.value!r})"
def sorts_before(self, other):
if len(self.value) >= len(other.value):
return False
return other.value[: len(self.value)] == self.value
```

Each node is a label and a sequence of some data, and we have the relationship
sorts_before meaning the data of the left is an initial segment of the right.
So e.g. a node with value `[1, 2]`

will sort before a node with value `[1, 2, 3]`

,
but neither of `[1, 2]`

nor `[1, 3]`

will sort before the other.

We have a list of nodes, and we want to topologically sort them with respect to
this ordering. That is, we want to arrange the list so that if `x.sorts_before(y)`

then x appears earlier in the list than y. We naively think that the easiest way
to do this is to extend the partial order defined here to a total order by
breaking ties arbitrarily and then using a normal sorting algorithm. So we
define the following code:

```
from functools import total_ordering
@total_ordering
class TopoKey:
def __init__(self, node):
self.value = node
def __lt__(self, other):
if self.value.sorts_before(other.value):
return True
if other.value.sorts_before(self.value):
return False
return self.value.label < other.value.label
def sort_nodes(xs):
xs.sort(key=TopoKey)
```

This takes the order defined by `sorts_before`

and extends it by breaking ties by
comparing the node labels.

But now we want to test that it works.

First we write a function to verify that our desired outcome holds:

```
def is_prefix_sorted(xs):
for i in range(len(xs)):
for j in range(i + 1, len(xs)):
if xs[j].sorts_before(xs[i]):
return False
return True
```

This will return false if it ever finds a pair in the wrong order and return true otherwise.

Given this function, what we want to do with Hypothesis is assert that for all
sequences of nodes, the result of calling `sort_nodes`

on it is sorted.

First we need to define a strategy for Node:

```
import hypothesis.strategies as st
NodeStrategy = st.builds(Node, st.integers(), st.lists(st.booleans(), max_size=10))
```

We want to generate *short* lists of values so that there’s a decent chance of
one being a prefix of the other (this is also why the choice of bool as the
elements). We then define a strategy which builds a node out of an integer and
one of those short lists of booleans.

We can now write a test:

```
from hypothesis import given
@given(st.lists(NodeStrategy))
def test_sorting_nodes_is_prefix_sorted(xs):
sort_nodes(xs)
assert is_prefix_sorted(xs)
```

this immediately fails with the following example:

```
[Node(0, (False, True)), Node(0, (True,)), Node(0, (False,))]
```

The reason for this is that because False is not a prefix of (True, True) nor vice versa, sorting things the first two nodes are equal because they have equal labels. This makes the whole order non-transitive and produces basically nonsense results.

But this is pretty unsatisfying. It only works because they have the same label. Perhaps we actually wanted our labels to be unique. Let’s change the test to do that.

```
def deduplicate_nodes_by_label(nodes):
table = {node.label: node for node in nodes}
return list(table.values())
```

We define a function to deduplicate nodes by labels, and can now map that over a strategy for lists of nodes to give us a strategy for lists of nodes with unique labels:

```
@given(st.lists(NodeStrategy).map(deduplicate_nodes_by_label))
def test_sorting_nodes_is_prefix_sorted(xs):
sort_nodes(xs)
assert is_prefix_sorted(xs)
```

Hypothesis quickly gives us an example of this *still* being wrong:

```
[Node(0, (False,)), Node(-1, (True,)), Node(-2, (False, False))]
```

Now this is a more interesting example. None of the nodes will sort equal. What is happening here is that the first node is strictly less than the last node because (False,) is a prefix of (False, False). This is in turn strictly less than the middle node because neither is a prefix of the other and -2 < -1. The middle node is then less than the first node because -1 < 0.

So, convinced that our implementation is broken, we write a better one:

```
def sort_nodes(xs):
for i in range(1, len(xs)):
j = i - 1
while j >= 0:
if xs[j].sorts_before(xs[j + 1]):
break
xs[j], xs[j + 1] = xs[j + 1], xs[j]
j -= 1
```

This is just insertion sort slightly modified - we swap a node backwards until swapping it further would violate the order constraints. The reason this works is because our order is a partial order already (this wouldn’t produce a valid result for a general topological sorting - you need the transitivity).

We now run our test again and it passes, telling us that this time we’ve successfully managed to sort some nodes without getting it completely wrong. Go us.

## Time zone arithmetic¶

This is an example of some tests for pytz which check that various timezone
conversions behave as you would expect them to. These tests should all pass,
and are mostly a demonstration of some useful sorts of thing to test with
Hypothesis, and how the `datetimes()`

strategy works.

```
from datetime import timedelta
# The datetimes strategy is naive by default, so tell it to use timezones
aware_datetimes = st.datetimes(timezones=st.timezones())
@given(aware_datetimes, st.timezones(), st.timezones())
def test_convert_via_intermediary(dt, tz1, tz2):
"""Test that converting between timezones is not affected
by a detour via another timezone.
"""
assert dt.astimezone(tz1).astimezone(tz2) == dt.astimezone(tz2)
@given(aware_datetimes, st.timezones())
def test_convert_to_and_fro(dt, tz2):
"""If we convert to a new timezone and back to the old one
this should leave the result unchanged.
"""
tz1 = dt.tzinfo
assert dt == dt.astimezone(tz2).astimezone(tz1)
@given(aware_datetimes, st.timezones())
def test_adding_an_hour_commutes(dt, tz):
"""When converting between timezones it shouldn't matter
if we add an hour here or add an hour there.
"""
an_hour = timedelta(hours=1)
assert (dt + an_hour).astimezone(tz) == dt.astimezone(tz) + an_hour
@given(aware_datetimes, st.timezones())
def test_adding_a_day_commutes(dt, tz):
"""When converting between timezones it shouldn't matter
if we add a day here or add a day there.
"""
a_day = timedelta(days=1)
assert (dt + a_day).astimezone(tz) == dt.astimezone(tz) + a_day
```

## Condorcet’s paradox¶

A classic paradox in voting theory, called Condorcet’s paradox, is that majority preferences are not transitive. That is, there is a population and a set of three candidates A, B and C such that the majority of the population prefer A to B, B to C and C to A.

Wouldn’t it be neat if we could use Hypothesis to provide an example of this?

Well as you can probably guess from the presence of this section, we can! The main trick is to decide how we want to represent the result of an election - for this example, we’ll use a list of “votes”, where each vote is a list of candidates in the voters preferred order. Without further ado, here is the code:

```
from collections import Counter
from hypothesis import given
from hypothesis.strategies import lists, permutations
# We need at least three candidates and at least three voters to have a
# paradox; anything less can only lead to victories or at worst ties.
@given(lists(permutations(["A", "B", "C"]), min_size=3))
def test_elections_are_transitive(election):
all_candidates = {"A", "B", "C"}
# First calculate the pairwise counts of how many prefer each candidate
# to the other
counts = Counter()
for vote in election:
for i in range(len(vote)):
for j in range(i + 1, len(vote)):
counts[(vote[i], vote[j])] += 1
# Now look at which pairs of candidates one has a majority over the
# other and store that.
graph = {}
for i in all_candidates:
for j in all_candidates:
if counts[(i, j)] > counts[(j, i)]:
graph.setdefault(i, set()).add(j)
# Now for each triple assert that it is transitive.
for x in all_candidates:
for y in graph.get(x, ()):
for z in graph.get(y, ()):
assert x not in graph.get(z, ())
```

The example Hypothesis gives me on my first run (your mileage may of course vary) is:

```
[["A", "B", "C"], ["B", "C", "A"], ["C", "A", "B"]]
```

Which does indeed do the job: The majority (votes 0 and 1) prefer B to C, the majority (votes 0 and 2) prefer A to B and the majority (votes 1 and 2) prefer C to A. This is in fact basically the canonical example of the voting paradox.

## Fuzzing an HTTP API¶

Hypothesis’s support for testing HTTP services is somewhat nascent. There are plans for some fully featured things around this, but right now they’re probably quite far down the line.

But you can do a lot yourself without any explicit support! Here’s a script I wrote to throw arbitrary data against the API for an entirely fictitious service called Waspfinder (this is only lightly obfuscated and you can easily figure out who I’m actually talking about, but I don’t want you to run this code and hammer their API without their permission).

All this does is use Hypothesis to generate arbitrary JSON data matching the format their API asks for and check for 500 errors. More advanced tests which then use the result and go on to do other things are definitely also possible. The schemathesis package provides an excellent example of this!

```
import math
import os
import random
import time
import unittest
from collections import namedtuple
import requests
from hypothesis import assume, given, strategies as st
Goal = namedtuple("Goal", ("slug",))
# We just pass in our API credentials via environment variables.
waspfinder_token = os.getenv("WASPFINDER_TOKEN")
waspfinder_user = os.getenv("WASPFINDER_USER")
assert waspfinder_token is not None
assert waspfinder_user is not None
GoalData = st.fixed_dictionaries(
{
"title": st.text(),
"goal_type": st.sampled_from(
["hustler", "biker", "gainer", "fatloser", "inboxer", "drinker", "custom"]
),
"goaldate": st.one_of(st.none(), st.floats()),
"goalval": st.one_of(st.none(), st.floats()),
"rate": st.one_of(st.none(), st.floats()),
"initval": st.floats(),
"panic": st.floats(),
"secret": st.booleans(),
"datapublic": st.booleans(),
}
)
needs2 = ["goaldate", "goalval", "rate"]
class WaspfinderTest(unittest.TestCase):
@given(GoalData)
def test_create_goal_dry_run(self, data):
# We want slug to be unique for each run so that multiple test runs
# don't interfere with each other. If for some reason some slugs trigger
# an error and others don't we'll get a Flaky error, but that's OK.
slug = hex(random.getrandbits(32))[2:]
# Use assume to guide us through validation we know about, otherwise
# we'll spend a lot of time generating boring examples.
# Title must not be empty
assume(data["title"])
# Exactly two of these values should be not None. The other will be
# inferred by the API.
assume(len([1 for k in needs2 if data[k] is not None]) == 2)
for v in data.values():
if isinstance(v, float):
assume(not math.isnan(v))
data["slug"] = slug
# The API nicely supports a dry run option, which means we don't have
# to worry about the user account being spammed with lots of fake goals
# Otherwise we would have to make sure we cleaned up after ourselves
# in this test.
data["dryrun"] = True
data["auth_token"] = waspfinder_token
for d, v in data.items():
if v is None:
data[d] = "null"
else:
data[d] = str(v)
result = requests.post(
"https://waspfinder.example.com/api/v1/users/"
"%s/goals.json" % (waspfinder_user,),
data=data,
)
# Let's not hammer the API too badly. This will of course make the
# tests even slower than they otherwise would have been, but that's
# life.
time.sleep(1.0)
# For the moment all we're testing is that this doesn't generate an
# internal error. If we didn't use the dry run option we could have
# then tried doing more with the result, but this is a good start.
self.assertNotEqual(result.status_code, 500)
if __name__ == "__main__":
unittest.main()
```