I assume that most of us use a technique called example-based testing when writing unit tests. This technique is based on writing tests that verify the behavior of our functions for specific inputs.

It is a natural way because our perception works based on examples.

Example-based testing for an addition function might look like this:

[InlineData(1, 2, 3)]
[InlineData(2, 2, 4)]
[InlineData(3, 2, 5)]
public void Add_ShouldReturnSumOfTwoNumbers(int a, int b, int expected)
    var result = Calculator.Add(a, b);

It’s simple, after all, what can go wrong with the addition function anymore. A couple of examples are enough and we have 100% coverage. Or do we?

But what if we want to implement our own “super fast” addition function based on bitwise operations? For example, something like the following:

public static int Add(int a, int b)
    while (b != 0)
        int carry = a & b;
        a = a ^ b;
        b = carry << 1;
    return a;

How do we verify that this function is working correctly? What if the algorithm is complicated and a few examples are not enough? This is where property-based testing can help us. This is testing based on defined properties, or perhaps better specifications.

If you remember from math, addition has several properties that must be satisfied:

  1. Commutative property: a + b = b + a
  2. Associative property: (a + b) + c = a + (b + c)
  3. Identity: a + 0 = a

We can use these properties to verify the correctness of our addition function. So that we don’t have to do it all manually the FsCheck library can help us. This is a library primarily designed for the F# language, but its API is also usable in C#.

We will install the library via NuGet:

dotnet add package FsCheck.Xunit
// 👆 based on your testing framework

And then we can write tests based on the properties:

[Property] // 👈 attribute for property-based testing
public Property Add_Should_Be_Commutative(int a, int b)
    return (Add(a, b) == Add(b, a))
        .ToProperty(); // 👈 convert boolean to Property

public Property Add_Should_Be_Associative(int a, int b, int c)
    return (Add(Add(a, b), c) == Add(a, Add(b, c))).ToProperty();

public Property Add_Should_Be_Identity(int a)
    return (Add(a, 0) == a).ToProperty();

And that’s it. Now we have tests that verify the correctness of our addition function based on mathematical properties. And all without having to write specific examples.

The FsCheck will generate random inputs for us and verify our function based on the defined properties. It has many generators for different data types and methodologies on how to generate random inputs (what range, …).

If the test reveals an error, it will use the shrinking method to find us the smallest input that causes the error.

For example, something like this:

FsCheck.Xunit.PropertyFailedException : 
Falsifiable, after 3 tests (11 shrinks) (StdGen (422220575,297303727)):
(-137, 122)
(1, 101)

Yes, it’s not every day we write a function for addition, or similar mathematical functions. But property-based testing can also help us test “common” algorithms or functions. For example, when testing parsers, serializers, validators, …

It is useful when:

  • there is an inverse function (serialization / deserialization, write / read, crypt / decrypt, …)
  • we can define the required properties (commutative, associative, distributive, …)
  • we do refactoring (verifying that the new implementation is equivalent to the old one)
  • we do fuzz testing (we want to see where the limits of our algorithm are)

🔗 Sources