I drank the functional programming cool-aid at my first real job. While I do not currently professionally develop with functional programming, I still apply what functional concepts I can -- property testing is a big one.

I'm going to cover three main points:

• What's so special about property testing?
• How can I avoid over-complicating my tests when I can't predetermine expected results?
• When shouldn't I use property testing?

What's so special about property testing?

Of all the tools available in a functional library, Haskell's quickcheck is the one I see most re-purposed in other non-functional languages.

At first glance, property testing looks like a fancy way of saying "generating test data", and in a sense, it is. So why is it "property" testing?

When you test a function with predetermined parameters, what you're really testing is that the function works for those inputs. You could add a lot of test parameters, enough to cover an "acceptable" range, but that's a lot of unnecessary work and nobody is likely to actually do it (though I have seen it).

When you property test, you don't care what the input is - you're not testing that the function returns some value when given some input. You're testing that the function, when given an argument that fits its requirements (lets say an "int"), will do something and return the appropriate response to whatever input it was given.

Let's look at a very simple example, an adder:

def adder(i1, i2):
  return i1 + i2

Simple, it takes two ints and returns the sum. That's the property - this function "returns the sum of two ints".

Let's look at a pretty standard test:

class Tests:
  @pytest.mark.parametrize("input1,input2,expect", [(1, 1, 2), (2, 2, 4)])
  def test_adder(self, input1, input2, expect):
    assert adder(input1, input2) == expect

This test passes: 2 passed in 0.02 seconds. We would expect it to - the sum of 1 and 1 is 2, the sum of 2 and 2 is 4. But that's not what this is testing.

Let's add some more "adders":

def adder2(i1: int, i2: int):
  if i1 == 1:
    return 2
  if i1 == 2:
    return 4

def adder3(i1: int, i2: int):
  return i1*2

And let's run the same test on those:

  @pytest.mark.parametrize("input1,input2,expect", [(1, 1, 2), (2, 2, 4)])
  def test_adder1(self, input1, input2, expect):
    assert adder2(input1, input2) == expect

  @pytest.mark.parametrize("input1,input2,expect", [(1, 1, 2), (2, 2, 4)])
  def test_adder2(self, input1, input2, expect):
    assert adder3(input1, input2) == expect

Tests are still passing: 6 passed in 0.02 seconds
Our tests aren't testing the property of this function, only some explicit result for some explicit input.

Now lets take a look at pytest-quickcheck
This library gives us a new way of specifying test arguments: @pytest.mark.randomize. Let's re-write our first test with it.

    @pytest.mark.randomize(i1=int, i2=int)
    def test_adder(self, i1, i2):
        expect = i1 + i2
        assert adder(i1, i2) == expect

Note that I build expect in the test - we can't predetermine the output when we don't know the input.
This test will pass: 9 passed in 0.03 seconds

Now lets add the rest of the tests:

    @pytest.mark.randomize(i1=int, i2=int)
    def test_adder2(self, i1, i2):
        expect = i1 + i2
        assert adder2(i1, i2) == expect

    @pytest.mark.randomize(i1=int, i2=int)
    def test_adder3(self, i1, i2):
        expect = i1 + i2
        assert adder3(i1, i2) == expect

You wouldn't expect these tests to work - adder2 is an if statement and will explode when its first parameter isn't 1 or 2. Adder3 isn't an adder at all - it multiplies.

E       assert -4819122279534621102 == -6480923863972990104
E        +  where -4819122279534621102 = adder3(-2409561139767310551, -4071362724205679553)

tests2.py:33: AssertionError

Our test is actually testing that our adder is adding. This might seem like overkill (especially since the test completely re-implements the function), but as you test more complicated functions it begins to make a lot more sense.

How can I avoid over-complicating my tests when I can't predetermine expected results?

You might consider the "weakness" of property testing to be the fact that you have to write so much logic in your tests - many people turn their noses at the thought! Why should you have to write logic in your tests, especially as they begin to resemble the thing you're testing in the first place?

First, it's actually okay to re-implement your entire function in your test. Especially in a case like adder. The import part is that your test becomes a static part of your project that will do two things: Prove your function works, and prevent you from breaking the function in the future.

A lot of your tests are going to be for more complicated functions - adder is an oversimplified example. Let's look at a function that uses more complicated structures.
This function will take a collection of dicts containing x and y coordinates, and calculate statistics for the quadrants of a graph based on where the collection's entries lay.

def calculate_graph_quadrants(entries: List[Dict[Any, Any]]):
    total = len(entries)
    quadrants = {
        'quad1': { 'count': 0 },
        'quad2': { 'count': 0 },
        'quad3': { 'count': 0 },
        'quad4': { 'count': 0 }
    }

    for entry in entries:
        quadrant = calc_quadrant(entry['x'], entry['y'])
        key = 'quad{}'.format(quadrant)
        quadrants[key]['count'] += 1
    for _, quad_stats in quadrants.items():
        quad_stats['share'] = quad_stats['count'] / total
    return quadrants

def calc_quadrant: 
    # takes an x and y, returns quadrant of graph coordinates land
    ...

This looks a bit harder to test than adder - we have to build this entries: List[Dict[Any, Any]], and somehow determine the expect counts and shares per quadrant. We could generate our data like this:

    @pytest.mark.randomize(xl=list_of(int, items=20),
                           yl=list_of(int, items=20))
    def test_calculate_graph_quadrants(self, xl, xy):
        pass

But I wouldn't recommend it - this would require a complete re-implementation of the function. I'm not even going to write what the test would look like because its not worth the effort.

The key to writing a clean property test for a complicated function is to reduce unknowns from your generated data as much as you can without reducing the strength of your test.

    @pytest.mark.randomize(count=int, min_num=1, max_num=50)
    def test_calculate_graph_quadrants(self, count):
        q1 = [{'x': -1, 'y': 1} for _ in range(count)]
        q2 = [{'x': 1, 'y': 1} for _ in range(count)]
        q3 = [{'x': -1, 'y': -1} for _ in range(count)]
        q4 = [{'x': 1, 'y': -1} for _ in range(count)]
        entries = list(itertools.chain(q1, q2, q3, q4)

We're not testing the ability to determine what quadrants the coordinates fall in to - that's a different function. We can assume that it works as intended and write another test for that function later.
So all we really need to make variable is how many entries for each quadrant we want to pass to the function. You could make each a different length, but there is little value in that - we can keep our test simple by passing the same amount of data for each expected quadrant.

Since we know how many entries will fall in to each quadrant, the expected result is actually easy to calculate:

    @pytest.mark.randomize(count=int, min_num=1, max_num=50)
    def test_calculate_graph_quadrants(self, count):
        q1 = [{'x': -1, 'y': 1} for _ in range(count)]
        q2 = [{'x': 1, 'y': 1} for _ in range(count)]
        q3 = [{'x': -1, 'y': -1} for _ in range(count)]
        q4 = [{'x': 1, 'y': -1} for _ in range(count)]
        entries = list(itertools.chain(q1, q2, q3, q4)
    # repeat the count for each quadrant, so the total is simple
    total = count*4
    # Each quadrant has the same count - the expected share will also be the same.
    expected_share = count / total
    # we could also do expected_share = .25
    expect = { q: {'count': count, 'share': expected_share}
               for q in ['quad1', 'quad2', 'quad3', 'quad4']}
    assert calculate_graph_quadrants(entries) == expect

This test will pass, given that calc_quadrant is accurate. That's not too bad, we don't really have that much logic in the test. By controlling what we do and don't want to be randomized, we can determine what our function is supposed to return fairly easily.

Side note: We are all slaves to the limitations of our tools. If we had a library like Scala's scalacheck, we would be able to write a generator for entries that builds the same thing without writing the logic in our tests.

When Shouldn't I Use Property Testing?

You should always use property testing. But some libraries aren't cut out for generation on a limited spectrum that you might want. The following could all be done with scalacheck's custom generators, but with pytest-quickcheck it simply isn't possible.

Let's demonstrate with a test for calc_quadrant. Here's the function:

def calc_quadrant(x: int, y: int):
    if x < 0:
        if y >= 0:
            return 1
        elif y < 0:
            return 3
    if x >= 0:
        if y < 0:
            return 4
        elif y >= 0:
            return 2

We could say that this function has four tightly-defined properties, extending from the four logical paths of x and y's sign (+/-). We could randomly generate x and y and build assert like this:

@pytest.mark.randomize(x=int, y=int)
def test_calc_quadrant(self, x: int, y: int):
    if x < 0:
        if y >= 0:
            expect = 1
        elif y < 0:
            expect = 3
    if x >= 0:
        if y < 0:
            expect = 4
        elif y >= 0:
            expect = 2
    assert calc_quadrant(x, y) == expect

Look at that, we've just copied the whole function over to the test. I know I said its okay to essentially re-implement your function in your test, but in this case I don't really want to. We can achieve a worthwhile result using parametrize, giving all permutations of x and y's signage.

@pytest.mark.parametrize("x,y,expect", [(-1, 1, 1), (1, 1, 2), (-1, -1, 3), (1, -1, 4)])
def test_calc_quadrant(self, x: int, y: int, expect: int):
    assert calc_quadrant(x, y) == expect

We still want to use property testing here though, to cover that any range of the test's input will produce an output in our finite range (1-4).

@pytest.mark.randomize(x=int, y=int)
def test_calc_quadrant_in_range(self, x: int, y: int):
    expect_range = [1, 2, 3, 4]
    assert calc_quadrant(x, y) in expect_range

This way we can prove that the test will only produce an int corresponding to one of four quadrants. Couple this with the manual quadrant test and we have covered enough of the functionality to make most people happy. Obviously calc_quadrant could match specifically for -1 and 1 for our x and y values and otherwise just return 1, which would satisfy both tests.

Whether or not to implement the former property test (which re-implements the function) is really up to you. I would personally only do that if this were black box testing and I couldn't just look at the code to know that it isn't just matching specific values. Otherwise I would say that manual testing for quadrants and property testing for the result being within range is "close enough".