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<div class="section" id="some-more-examples">
<h1>Some more examples<a class="headerlink" href="#some-more-examples" title="Permalink to this headline">¶</a></h1>
<p>This is a collection of examples of how to use Hypothesis in interesting ways.
It’s small for now but will grow over time.</p>
<p>All of these examples are designed to be run under <a class="reference external" href="https://docs.pytest.org/en/latest/">py.test</a> (<a class="reference external" href="https://nose.readthedocs.io/en/latest/">nose</a> should probably
work too).</p>
<div class="section" id="how-not-to-sort-by-a-partial-order">
<h2>How not to sort by a partial order<a class="headerlink" href="#how-not-to-sort-by-a-partial-order" title="Permalink to this headline">¶</a></h2>
<p>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.</p>
<p>Suppose we’ve got the following type:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Node</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">label</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">label</span> <span class="o">=</span> <span class="n">label</span>
<span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s2">"Node(</span><span class="si">%r</span><span class="s2">, </span><span class="si">%r</span><span class="s2">)"</span> <span class="o">%</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">label</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">sorts_before</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">)</span> <span class="o">>=</span> <span class="nb">len</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">return</span> <span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">)]</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span>
</pre></div>
</div>
<p>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 <code class="docutils literal"><span class="pre">[1,</span> <span class="pre">2]</span></code> will sort before a node with value <code class="docutils literal"><span class="pre">[1,</span> <span class="pre">2,</span> <span class="pre">3]</span></code>,
but neither of <code class="docutils literal"><span class="pre">[1,</span> <span class="pre">2]</span></code> nor <code class="docutils literal"><span class="pre">[1,</span> <span class="pre">3]</span></code> will sort before the other.</p>
<p>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 <code class="docutils literal"><span class="pre">x.sorts_before(y)</span></code>
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:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">total_ordering</span>
<span class="nd">@total_ordering</span>
<span class="k">class</span> <span class="nc">TopoKey</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="n">node</span>
<span class="k">def</span> <span class="nf">__lt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="o">.</span><span class="n">sorts_before</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">True</span>
<span class="k">if</span> <span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="o">.</span><span class="n">sorts_before</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="o">.</span><span class="n">label</span> <span class="o"><</span> <span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="o">.</span><span class="n">label</span>
<span class="k">def</span> <span class="nf">sort_nodes</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="n">xs</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="n">TopoKey</span><span class="p">)</span>
</pre></div>
</div>
<p>This takes the order defined by <code class="docutils literal"><span class="pre">sorts_before</span></code> and extends it by breaking ties by
comparing the node labels.</p>
<p>But now we want to test that it works.</p>
<p>First we write a function to verify that our desired outcome holds:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">is_prefix_sorted</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">xs</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">xs</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">sorts_before</span><span class="p">(</span><span class="n">xs</span><span class="p">[</span><span class="n">i</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">return</span> <span class="kc">True</span>
</pre></div>
</div>
<p>This will return false if it ever finds a pair in the wrong order and
return true otherwise.</p>
<p>Given this function, what we want to do with Hypothesis is assert that for all
sequences of nodes, the result of calling <code class="docutils literal"><span class="pre">sort_nodes</span></code> on it is sorted.</p>
<p>First we need to define a strategy for Node:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">hypothesis</span> <span class="k">import</span> <span class="n">settings</span><span class="p">,</span> <span class="n">strategy</span>
<span class="kn">import</span> <span class="nn">hypothesis.strategies</span> <span class="k">as</span> <span class="nn">s</span>
<span class="n">NodeStrategy</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">builds</span><span class="p">(</span>
<span class="n">Node</span><span class="p">,</span>
<span class="n">s</span><span class="o">.</span><span class="n">integers</span><span class="p">(),</span>
<span class="n">s</span><span class="o">.</span><span class="n">lists</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">booleans</span><span class="p">(),</span> <span class="n">average_size</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_size</span><span class="o">=</span><span class="mi">10</span><span class="p">))</span>
</pre></div>
</div>
<p>We want to generate <em>short</em> 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.</p>
<p>We can now write a test:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">hypothesis</span> <span class="k">import</span> <span class="n">given</span>
<span class="nd">@given</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">lists</span><span class="p">(</span><span class="n">NodeStrategy</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">test_sorting_nodes_is_prefix_sorted</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="n">sort_nodes</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">is_prefix_sorted</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span>
</pre></div>
</div>
<p>this immediately fails with the following example:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">)),</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="kc">True</span><span class="p">,)),</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="kc">False</span><span class="p">,))]</span>
</pre></div>
</div>
<p>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.</p>
<p>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.</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">deduplicate_nodes_by_label</span><span class="p">(</span><span class="n">nodes</span><span class="p">):</span>
<span class="n">table</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
<span class="n">table</span><span class="p">[</span><span class="n">node</span><span class="o">.</span><span class="n">label</span><span class="p">]</span> <span class="o">=</span> <span class="n">node</span>
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
<span class="n">NodeSet</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">lists</span><span class="p">(</span><span class="n">Node</span><span class="p">)</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="n">deduplicate_nodes_by_label</span><span class="p">)</span>
</pre></div>
</div>
<p>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:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nd">@given</span><span class="p">(</span><span class="n">NodeSet</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">test_sorting_nodes_is_prefix_sorted</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="n">sort_nodes</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">is_prefix_sorted</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span>
</pre></div>
</div>
<p>Hypothesis quickly gives us an example of this <em>still</em> being wrong:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="kc">False</span><span class="p">,)),</span> <span class="n">Node</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="kc">True</span><span class="p">,)),</span> <span class="n">Node</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">))])</span>
</pre></div>
</div>
<p>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.</p>
<p>So, convinced that our implementation is broken, we write a better one:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sort_nodes</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">hrange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">xs</span><span class="p">)):</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">j</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">if</span> <span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">sorts_before</span><span class="p">(</span><span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]):</span>
<span class="k">break</span>
<span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span> <span class="n">xs</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
</pre></div>
</div>
<p>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).</p>
<p>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.</p>
</div>
<div class="section" id="time-zone-arithmetic">
<h2>Time zone arithmetic<a class="headerlink" href="#time-zone-arithmetic" title="Permalink to this headline">¶</a></h2>
<p>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.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">datetime</span> <span class="k">import</span> <span class="n">timedelta</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">hypothesis.extra.pytz</span> <span class="k">import</span> <span class="n">timezones</span>
<span class="gp">>>> </span><span class="c1"># The datetimes strategy is naive by default, so tell it to use timezones</span>
<span class="gp">>>> </span><span class="n">aware_datetimes</span> <span class="o">=</span> <span class="n">datetimes</span><span class="p">(</span><span class="n">timezones</span><span class="o">=</span><span class="n">timezones</span><span class="p">())</span>
<span class="gp">>>> </span><span class="nd">@given</span><span class="p">(</span><span class="n">aware_datetimes</span><span class="p">,</span> <span class="n">timezones</span><span class="p">(),</span> <span class="n">timezones</span><span class="p">())</span>
<span class="gp">... </span><span class="k">def</span> <span class="nf">test_convert_via_intermediary</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="n">tz1</span><span class="p">,</span> <span class="n">tz2</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""Test that converting between timezones is not affected</span>
<span class="gp">... </span><span class="sd"> by a detour via another timezone.</span>
<span class="gp">... </span><span class="sd"> """</span>
<span class="gp">... </span> <span class="k">assert</span> <span class="n">dt</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz1</span><span class="p">)</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz2</span><span class="p">)</span> <span class="o">==</span> <span class="n">dt</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nd">@given</span><span class="p">(</span><span class="n">aware_datetimes</span><span class="p">,</span> <span class="n">timezones</span><span class="p">())</span>
<span class="gp">... </span><span class="k">def</span> <span class="nf">test_convert_to_and_fro</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="n">tz2</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""If we convert to a new timezone and back to the old one</span>
<span class="gp">... </span><span class="sd"> this should leave the result unchanged.</span>
<span class="gp">... </span><span class="sd"> """</span>
<span class="gp">... </span> <span class="n">tz1</span> <span class="o">=</span> <span class="n">dt</span><span class="o">.</span><span class="n">tzinfo</span>
<span class="gp">... </span> <span class="k">assert</span> <span class="n">dt</span> <span class="o">==</span> <span class="n">dt</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz2</span><span class="p">)</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nd">@given</span><span class="p">(</span><span class="n">aware_datetimes</span><span class="p">,</span> <span class="n">timezones</span><span class="p">())</span>
<span class="gp">... </span><span class="k">def</span> <span class="nf">test_adding_an_hour_commutes</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""When converting between timezones it shouldn't matter</span>
<span class="gp">... </span><span class="sd"> if we add an hour here or add an hour there.</span>
<span class="gp">... </span><span class="sd"> """</span>
<span class="gp">... </span> <span class="n">an_hour</span> <span class="o">=</span> <span class="n">timedelta</span><span class="p">(</span><span class="n">hours</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">assert</span> <span class="p">(</span><span class="n">dt</span> <span class="o">+</span> <span class="n">an_hour</span><span class="p">)</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz</span><span class="p">)</span> <span class="o">==</span> <span class="n">dt</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz</span><span class="p">)</span> <span class="o">+</span> <span class="n">an_hour</span>
<span class="gp">>>> </span><span class="nd">@given</span><span class="p">(</span><span class="n">aware_datetimes</span><span class="p">,</span> <span class="n">timezones</span><span class="p">())</span>
<span class="gp">... </span><span class="k">def</span> <span class="nf">test_adding_a_day_commutes</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
<span class="gp">... </span> <span class="sd">"""When converting between timezones it shouldn't matter</span>
<span class="gp">... </span><span class="sd"> if we add a day here or add a day there.</span>
<span class="gp">... </span><span class="sd"> """</span>
<span class="gp">... </span> <span class="n">a_day</span> <span class="o">=</span> <span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">assert</span> <span class="p">(</span><span class="n">dt</span> <span class="o">+</span> <span class="n">a_day</span><span class="p">)</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz</span><span class="p">)</span> <span class="o">==</span> <span class="n">dt</span><span class="o">.</span><span class="n">astimezone</span><span class="p">(</span><span class="n">tz</span><span class="p">)</span> <span class="o">+</span> <span class="n">a_day</span>
<span class="gp">>>> </span><span class="c1"># And we can check that our tests pass</span>
<span class="gp">>>> </span><span class="n">test_convert_via_intermediary</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">test_convert_to_and_fro</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">test_adding_an_hour_commutes</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">test_adding_a_day_commutes</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="condorcet-s-paradox">
<h2>Condorcet’s Paradox<a class="headerlink" href="#condorcet-s-paradox" title="Permalink to this headline">¶</a></h2>
<p>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.</p>
<p>Wouldn’t it be neat if we could use Hypothesis to provide an example of this?</p>
<p>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.</p>
<p>The trick here turns out to be twofold:</p>
<ol class="arabic simple">
<li>We can generate a type that is <em>much larger</em> than an election, extract an election out of that, and rely on minimization to throw away all the extraneous detail.</li>
<li>We can use assume and rely on Hypothesis’s adaptive exploration to focus on the examples that turn out to generate interesting elections</li>
</ol>
<p>Without further ado, here is the code:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">hypothesis</span> <span class="k">import</span> <span class="n">given</span><span class="p">,</span> <span class="n">assume</span>
<span class="kn">from</span> <span class="nn">hypothesis.strategies</span> <span class="k">import</span> <span class="n">integers</span><span class="p">,</span> <span class="n">lists</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="k">import</span> <span class="n">Counter</span>
<span class="k">def</span> <span class="nf">candidates</span><span class="p">(</span><span class="n">votes</span><span class="p">):</span>
<span class="k">return</span> <span class="p">{</span><span class="n">candidate</span> <span class="k">for</span> <span class="n">vote</span> <span class="ow">in</span> <span class="n">votes</span> <span class="k">for</span> <span class="n">candidate</span> <span class="ow">in</span> <span class="n">vote</span><span class="p">}</span>
<span class="k">def</span> <span class="nf">build_election</span><span class="p">(</span><span class="n">votes</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Given a list of lists we extract an election out of this. We do this</span>
<span class="sd"> in two phases:</span>
<span class="sd"> 1. First of all we work out the full set of candidates present in all</span>
<span class="sd"> votes and throw away any votes that do not have that whole set.</span>
<span class="sd"> 2. We then take each vote and make it unique, keeping only the first</span>
<span class="sd"> instance of any candidate.</span>
<span class="sd"> This gives us a list of total orderings of some set. It will usually</span>
<span class="sd"> be a lot smaller than the starting list, but that's OK.</span>
<span class="sd"> """</span>
<span class="n">all_candidates</span> <span class="o">=</span> <span class="n">candidates</span><span class="p">(</span><span class="n">votes</span><span class="p">)</span>
<span class="n">votes</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">v</span><span class="p">:</span> <span class="nb">set</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">==</span> <span class="n">all_candidates</span><span class="p">,</span> <span class="n">votes</span><span class="p">))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">votes</span><span class="p">:</span>
<span class="k">return</span> <span class="p">[]</span>
<span class="n">rebuilt_votes</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">vote</span> <span class="ow">in</span> <span class="n">votes</span><span class="p">:</span>
<span class="n">rv</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">vote</span><span class="p">:</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">rv</span><span class="p">:</span>
<span class="n">rv</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">rv</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">all_candidates</span><span class="p">)</span>
<span class="n">rebuilt_votes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">rv</span><span class="p">)</span>
<span class="k">return</span> <span class="n">rebuilt_votes</span>
<span class="nd">@given</span><span class="p">(</span><span class="n">lists</span><span class="p">(</span><span class="n">lists</span><span class="p">(</span><span class="n">integers</span><span class="p">(</span><span class="n">min_value</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_value</span><span class="o">=</span><span class="mi">5</span><span class="p">))))</span>
<span class="k">def</span> <span class="nf">test_elections_are_transitive</span><span class="p">(</span><span class="n">election</span><span class="p">):</span>
<span class="n">election</span> <span class="o">=</span> <span class="n">build_election</span><span class="p">(</span><span class="n">election</span><span class="p">)</span>
<span class="c1"># Small elections are unlikely to be interesting</span>
<span class="n">assume</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">election</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">3</span><span class="p">)</span>
<span class="n">all_candidates</span> <span class="o">=</span> <span class="n">candidates</span><span class="p">(</span><span class="n">election</span><span class="p">)</span>
<span class="c1"># Elections with fewer than three candidates certainly can't exhibit</span>
<span class="c1"># intransitivity</span>
<span class="n">assume</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">all_candidates</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">3</span><span class="p">)</span>
<span class="c1"># Now we check if the election is transitive</span>
<span class="c1"># First calculate the pairwise counts of how many prefer each candidate</span>
<span class="c1"># to the other</span>
<span class="n">counts</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
<span class="k">for</span> <span class="n">vote</span> <span class="ow">in</span> <span class="n">election</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">vote</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">vote</span><span class="p">)):</span>
<span class="n">counts</span><span class="p">[(</span><span class="n">vote</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">vote</span><span class="p">[</span><span class="n">j</span><span class="p">])]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># Now look at which pairs of candidates one has a majority over the</span>
<span class="c1"># other and store that.</span>
<span class="n">graph</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">all_candidates</span> <span class="o">=</span> <span class="n">candidates</span><span class="p">(</span><span class="n">election</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">all_candidates</span><span class="p">:</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">all_candidates</span><span class="p">:</span>
<span class="k">if</span> <span class="n">counts</span><span class="p">[(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)]</span> <span class="o">></span> <span class="n">counts</span><span class="p">[(</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">)]:</span>
<span class="n">graph</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="nb">set</span><span class="p">())</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
<span class="c1"># Now for each triple assert that it is transitive.</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">all_candidates</span><span class="p">:</span>
<span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">()):</span>
<span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="p">()):</span>
<span class="k">assert</span> <span class="n">x</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="p">())</span>
</pre></div>
</div>
<p>The example Hypothesis gives me on my first run (your mileage may of course
vary) is:</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">]]</span>
</pre></div>
</div>
<p>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.</p>
</div>
<div class="section" id="fuzzing-an-http-api">
<h2>Fuzzing an HTTP API<a class="headerlink" href="#fuzzing-an-http-api" title="Permalink to this headline">¶</a></h2>
<p>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.</p>
<p>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).</p>
<p>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.</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">unittest</span>
<span class="kn">from</span> <span class="nn">hypothesis</span> <span class="k">import</span> <span class="n">given</span><span class="p">,</span> <span class="n">assume</span><span class="p">,</span> <span class="n">settings</span><span class="p">,</span> <span class="n">strategies</span> <span class="k">as</span> <span class="n">st</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="k">import</span> <span class="n">namedtuple</span>
<span class="kn">import</span> <span class="nn">requests</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">random</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="c1"># These tests will be quite slow because we have to talk to an external</span>
<span class="c1"># service. Also we'll put in a sleep between calls so as to not hammer it.</span>
<span class="c1"># As a result we reduce the number of test cases and turn off the timeout.</span>
<span class="n">settings</span><span class="o">.</span><span class="n">default</span><span class="o">.</span><span class="n">max_examples</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">settings</span><span class="o">.</span><span class="n">default</span><span class="o">.</span><span class="n">timeout</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="n">Goal</span> <span class="o">=</span> <span class="n">namedtuple</span><span class="p">(</span><span class="s2">"Goal"</span><span class="p">,</span> <span class="p">(</span><span class="s2">"slug"</span><span class="p">,))</span>
<span class="c1"># We just pass in our API credentials via environment variables.</span>
<span class="n">waspfinder_token</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">getenv</span><span class="p">(</span><span class="s1">'WASPFINDER_TOKEN'</span><span class="p">)</span>
<span class="n">waspfinder_user</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">getenv</span><span class="p">(</span><span class="s1">'WASPFINDER_USER'</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">waspfinder_token</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
<span class="k">assert</span> <span class="n">waspfinder_user</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
<span class="n">GoalData</span> <span class="o">=</span> <span class="n">st</span><span class="o">.</span><span class="n">fixed_dictionaries</span><span class="p">({</span>
<span class="s1">'title'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">text</span><span class="p">(),</span>
<span class="s1">'goal_type'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">sampled_from</span><span class="p">([</span>
<span class="s2">"hustler"</span><span class="p">,</span> <span class="s2">"biker"</span><span class="p">,</span> <span class="s2">"gainer"</span><span class="p">,</span> <span class="s2">"fatloser"</span><span class="p">,</span> <span class="s2">"inboxer"</span><span class="p">,</span>
<span class="s2">"drinker"</span><span class="p">,</span> <span class="s2">"custom"</span><span class="p">]),</span>
<span class="s1">'goaldate'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">one_of</span><span class="p">(</span><span class="n">st</span><span class="o">.</span><span class="n">none</span><span class="p">(),</span> <span class="n">st</span><span class="o">.</span><span class="n">floats</span><span class="p">()),</span>
<span class="s1">'goalval'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">one_of</span><span class="p">(</span><span class="n">st</span><span class="o">.</span><span class="n">none</span><span class="p">(),</span> <span class="n">st</span><span class="o">.</span><span class="n">floats</span><span class="p">()),</span>
<span class="s1">'rate'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">one_of</span><span class="p">(</span><span class="n">st</span><span class="o">.</span><span class="n">none</span><span class="p">(),</span> <span class="n">st</span><span class="o">.</span><span class="n">floats</span><span class="p">()),</span>
<span class="s1">'initval'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">floats</span><span class="p">(),</span>
<span class="s1">'panic'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">floats</span><span class="p">(),</span>
<span class="s1">'secret'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">booleans</span><span class="p">(),</span>
<span class="s1">'datapublic'</span><span class="p">:</span> <span class="n">st</span><span class="o">.</span><span class="n">booleans</span><span class="p">(),</span>
<span class="p">})</span>
<span class="n">needs2</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'goaldate'</span><span class="p">,</span> <span class="s1">'goalval'</span><span class="p">,</span> <span class="s1">'rate'</span><span class="p">]</span>
<span class="k">class</span> <span class="nc">WaspfinderTest</span><span class="p">(</span><span class="n">unittest</span><span class="o">.</span><span class="n">TestCase</span><span class="p">):</span>
<span class="nd">@given</span><span class="p">(</span><span class="n">GoalData</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">test_create_goal_dry_run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
<span class="c1"># We want slug to be unique for each run so that multiple test runs</span>
<span class="c1"># don't interfere with each other. If for some reason some slugs trigger</span>
<span class="c1"># an error and others don't we'll get a Flaky error, but that's OK.</span>
<span class="n">slug</span> <span class="o">=</span> <span class="nb">hex</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">getrandbits</span><span class="p">(</span><span class="mi">32</span><span class="p">))[</span><span class="mi">2</span><span class="p">:]</span>
<span class="c1"># Use assume to guide us through validation we know about, otherwise</span>
<span class="c1"># we'll spend a lot of time generating boring examples.</span>
<span class="c1"># Title must not be empty</span>
<span class="n">assume</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">"title"</span><span class="p">])</span>
<span class="c1"># Exactly two of these values should be not None. The other will be</span>
<span class="c1"># inferred by the API.</span>
<span class="n">assume</span><span class="p">(</span><span class="nb">len</span><span class="p">([</span><span class="mi">1</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">needs2</span> <span class="k">if</span> <span class="n">data</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">])</span> <span class="o">==</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">data</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
<span class="n">assume</span><span class="p">(</span><span class="ow">not</span> <span class="n">math</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">v</span><span class="p">))</span>
<span class="n">data</span><span class="p">[</span><span class="s2">"slug"</span><span class="p">]</span> <span class="o">=</span> <span class="n">slug</span>
<span class="c1"># The API nicely supports a dry run option, which means we don't have</span>
<span class="c1"># to worry about the user account being spammed with lots of fake goals</span>
<span class="c1"># Otherwise we would have to make sure we cleaned up after ourselves</span>
<span class="c1"># in this test.</span>
<span class="n">data</span><span class="p">[</span><span class="s2">"dryrun"</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">data</span><span class="p">[</span><span class="s2">"auth_token"</span><span class="p">]</span> <span class="o">=</span> <span class="n">waspfinder_token</span>
<span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">data</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">data</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">=</span> <span class="s2">"null"</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">data</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">requests</span><span class="o">.</span><span class="n">post</span><span class="p">(</span>
<span class="s2">"https://waspfinder.example.com/api/v1/users/"</span>
<span class="s2">"</span><span class="si">%s</span><span class="s2">/goals.json"</span> <span class="o">%</span> <span class="p">(</span><span class="n">waspfinder_user</span><span class="p">,),</span> <span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">)</span>
<span class="c1"># Lets not hammer the API too badly. This will of course make the</span>
<span class="c1"># tests even slower than they otherwise would have been, but that's</span>
<span class="c1"># life.</span>
<span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
<span class="c1"># For the moment all we're testing is that this doesn't generate an</span>
<span class="c1"># internal error. If we didn't use the dry run option we could have</span>
<span class="c1"># then tried doing more with the result, but this is a good start.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">assertNotEqual</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">status_code</span><span class="p">,</span> <span class="mi">500</span><span class="p">)</span>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
<span class="n">unittest</span><span class="o">.</span><span class="n">main</span><span class="p">()</span>
</pre></div>
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