# 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 py.test (nose should probably 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(object):
def __init__(self, label, value):
self.label = label
self.value = tuple(value)
def __repr__(self):
return "Node(%r, %r)" % (self.label, self.value)
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(object):
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:

```
from hypothesis import settings, strategy
import hypothesis.strategies as s
NodeStrategy = s.builds(
Node,
s.integers(),
s.lists(s.booleans(), average_size=5, 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(s.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. Lets change the test to do that.

```
def deduplicate_nodes_by_label(nodes):
table = {}
for node in nodes:
table[node.label] = node
return list(table.values())
NodeSet = s.lists(Node).map(deduplicate_nodes_by_label)
```

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

```
@given(NodeSet)
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 hrange(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 hypothesis-datetime extra package works.

```
>>> from datetime import timedelta
>>> from hypothesis.extra.pytz import timezones
>>> # The datetimes strategy is naive by default, so tell it to use timezones
>>> aware_datetimes = datetimes(timezones=timezones())
>>> @given(aware_datetimes, timezones(), 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, 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, 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, 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
>>> # And we can check that our tests pass
>>> test_convert_via_intermediary()
>>> test_convert_to_and_fro()
>>> test_adding_an_hour_commutes()
>>> test_adding_a_day_commutes()
```

## 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! This is slightly surprising because it’s not really obvious how we would generate an election given the types that Hypothesis knows about.

The trick here turns out to be twofold:

- We can generate a type that is
*much larger*than an election, extract an election out of that, and rely on minimization to throw away all the extraneous detail. - We can use assume and rely on Hypothesis’s adaptive exploration to focus on the examples that turn out to generate interesting elections

Without further ado, here is the code:

```
from hypothesis import given, assume
from hypothesis.strategies import integers, lists
from collections import Counter
def candidates(votes):
return {candidate for vote in votes for candidate in vote}
def build_election(votes):
"""
Given a list of lists we extract an election out of this. We do this
in two phases:
1. First of all we work out the full set of candidates present in all
votes and throw away any votes that do not have that whole set.
2. We then take each vote and make it unique, keeping only the first
instance of any candidate.
This gives us a list of total orderings of some set. It will usually
be a lot smaller than the starting list, but that's OK.
"""
all_candidates = candidates(votes)
votes = list(filter(lambda v: set(v) == all_candidates, votes))
if not votes:
return []
rebuilt_votes = []
for vote in votes:
rv = []
for v in vote:
if v not in rv:
rv.append(v)
assert len(rv) == len(all_candidates)
rebuilt_votes.append(rv)
return rebuilt_votes
@given(lists(lists(integers(min_value=1, max_value=5))))
def test_elections_are_transitive(election):
election = build_election(election)
# Small elections are unlikely to be interesting
assume(len(election) >= 3)
all_candidates = candidates(election)
# Elections with fewer than three candidates certainly can't exhibit
# intransitivity
assume(len(all_candidates) >= 3)
# Now we check if the election is transitive
# 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 = {}
all_candidates = candidates(election)
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:

```
[[3, 1, 4], [4, 3, 1], [1, 4, 3]]
```

Which does indeed do the job: The majority (votes 0 and 1) prefer 3 to 1, the majority (votes 0 and 2) prefer 1 to 4 and the majority (votes 1 and 2) prefer 4 to 3. This is in fact basically the canonical example of the voting paradox, modulo variations on the names of candidates.

## 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 random 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 random 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.

```
import unittest
from hypothesis import given, assume, settings, strategies as st
from collections import namedtuple
import requests
import os
import random
import time
import math
# These tests will be quite slow because we have to talk to an external
# service. Also we'll put in a sleep between calls so as to not hammer it.
# As a result we reduce the number of test cases and turn off the timeout.
settings.default.max_examples = 100
settings.default.timeout = -1
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 eachother. 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)
# Lets 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()
```