Property based tests part 3 - generators with too many output values.


This is part 3 in a four part series:

Part 1 - Introduction to property based testing

Part 2 - More about generators

Part 4 - Production code repeated in tests

I’ve been wanting to try property-based testing in a real-life situation for some time, and decided to try it out with the test suite for our open source library ActiveLogin.Identity.

A short background on ActiveLogin.Identity; it’s a library for parsing and validating Swedish identities, such as a Personal Identity Number, let’s call it a pin. For this blog we can be satisfied with the following simplified model: the format for a pin is YYYYMMDDBBBC, i.e. Year, Month, Day, Birth number and a checksum. The birth number is any number three digit number from 001 to 999, the checksum is calculated using the Luhn algorithm. You can also write a pin using a 10 digit format YYMMDD-BBBC or YYMMDD+BBBC, where a “+” indicates that the person has turned or is turning 100 this year.

In the previous posts we have written property tests for valid and invalid pin numbers. In this post we will look at the create function and have to deal with ranges of inputs that are very large.

The create function

The type signature of the create function is:

SwedishPersonalIdentityNumberValues -> Result<SwedishPersonalIdentityNumber, Error>

where SwedishPersonalIdentityNumberValues is just a record for grouping all the input values together:

type SwedishPersonalIdentityNumberValues =
    { Year : int
      Month : int
      Day : int
      BirthNumber : int
      Checksum : int }

Creating valid pins

The first test I would like to write would be a roundtrip test for valid input, just like what we did in Part 1 of this series. It would test the property:

Valid12DigitString -> SwedishPersonalIdentityNumbeValues -> create -> Valid12DigitString

I.e. starting with a valid 12 digit string and extracting the year, month, day, birthnumber and checksum we can create a pin and if we turn that pin back into a 12-digit string we end up with the same valid 12-digit string we started with.

But I will skip it in this blog post because it would be so similar to what we already have seen in Part 1, instead let’s move on to testing invalid inputs where we will run into problems!

Creating a pin with an invalid year

My first approach was to write the following test:

testProp "invalid year returns InvalidYear Error" <|
    fun (ValidValues validValues, InvalidYear invalidYear) ->
        let input = { validValues with Year = invalidYear }
        let result = SwedishPersonalIdentityNumber.create input
        result =! Error(InvalidYear invalidYear)

We get some valid input values and replace the year with an invalid year. Then we assert that create returns the expected Error. It requires us to write a generator for valid SwedishPersonalIdentityNumberValues and a generator for invalid years. They would look like this:

type ValidValues = ValidValues of SwedishPersonalIdentityNumberValues

// Gen<SwedishPersonalIdentityNumber>
let validPin() = gen { return SwedishPersonalIdentityNumberTestData.getRandom() }

// Arb<ValidValues>
let validValues = 
    gen {
        let! pin = validPin()
        let values = 
            { Year = pin.Year.Value
              Month = pin.Month.Value
              Day = pin.Day.Value
              BirthNumber = pin.BirthNumber.Value
              Checksum = pin.Checksum.Value }
        return values |> ValidValues
    } |> Arb.fromGen

SwedishPersonalIdentityNumberTestData.getRandom() is a function from ActiveLogin.Identity.Swedish.TestData1.

type InvalidYear = InvalidYear of int

// int -> int -> Gen<int>
let outsideRange min max =
    let low = Gen.choose (Int32.MinValue, min - 1)
    let high = Gen.choose (max + 1, Int32.MaxValue)
    Gen.oneof [ low; high ]

let invalidYearGen() =
    (1, 9999)
    ||> outsideRange
    |> InvalidYear
    |> Arb.fromGen

where outsideRange is a helper function that takes a min and a max value and generates an int outside of that range. We then provide our range of valid years, and since we are using the System.DateTime type for parsing the year that will be [1, 9999].

How many valid input values are there?

Now, we can run this test, and it will pass, but let’s think about what FsCheck is doing for us here. Specifically the InvalidYear generator is a problem. By default FsCheck will try to falsify our property by generating 200 input values using our generator. How many different values can be generated by InvalidYear though? Ints outside the range [1, 9999], so that would be Int.MaxValue - Int.MinValue - 9999 = 4,294,957,296. Which is more than 200. Quite a bit more actually. When writing a test like this we are probably more worried about tests close to our limits, e.g. invalid years near 1 or near 9999. For example, if we would introduce an bug in our create function so that 10000 is a valid year this test would most likely not catch it.

So what do we do? Well, in this case I would say that this is probably a code smell to be using an Int32 as input for a year. Even thinking about what we are considering valid years, [1, 9999], might be too big a range for our domain. I think the earliest year for which a pin was issued was around 1860. Also it’s quite optimistic (or pessimistic 🙂) to expect this code to be running in 8000 years time. We would probably be fine if we only considered valid years in the range [1860, 2100].

But let’s say we cannot change the business logic at this point, what can we do then? Like I said FsCheck will by default try to falsify a property 200 times. This is configurable, but to cover 4 billion possible input values we would probably have to run the test 8 billion times or more. Which is not feasible of course.

Another option is to rewrite the generator to return more reasonable ranges of inputs, for example [-100, 0] and [10000, 10100] instead of the full span of Int32. That would require us to increase the MaxTest configuration to 20000. On my machine running the test with 200 iterations takes about a second, and with 20,000 iterations about 4 seconds. A big increase it would seem, but in the end, all 46 tests in the ActiveLogin.Identity test suite still only take 5 seconds to run since we run the all in parallell. I can live with 5 seconds for now.

Testing the inverse property

In some cases it might be useful to look at the inverse of a property when we run in to this issue where the range of invalid inputs is too large to test. E.g. if we cannot test that ‘An invalid year should return InvalidYearError’, then maybe we can test that ‘A valid year should not return InvalidYearError’. It will not fulfill exactly the same requirement, but maybe will be good enough, or useful anyway. And as it turns out, in this domain of personal identity numbers this would be a good test. We are probably more worried that a valid year would be interpreted as an invalid year than the other way around. It would be very inconvenient for a user to not be able to enter their valid pin in a form using our library for validation.

A generator for valid years is not so hard to write:

type ValidYear = ValidYear of int

let validYearGen() =
    Gen.choose (1, 9999)
    |> ValidYear
    |> Arb.fromGen

And we would use it like this:

testProp "valid year does not return InvalidYear Error" <|
    fun (ValidValues values, ValidYear validYear) ->
        let input = { values with Year = validYear }
        let result = SwedishPersonalIdentityNumber.create input
        result <>! (Error(InvalidYear validYear))

But we should note that even in this case it will not be enough to run the test 200 times, we must increase the number of times to run the test which is done by setting the MaxTest property of FsCheck2.

The tests for invalid months and days can be done in the same way as for years, so I will leave them out of this blog post. For invalid birth numbers there’s only one invalid case: 000, so I will leave that out as well.

Creating a pin with an invalid checksum

The checksum is a single digit [0,9] and since we have a generator for ValidValues we know which one is valid. We just need to test with all the others. So for this test we actually won’t create a generator for InvalidChecksums, instead we can calculate all invalid checksums from the valid pin like this:

testProp "invalid checksum returns InvalidChecksum Error" <|
    fun (ValidValues valid) ->
        let invalidChecksums =
            [ 0..9 ]
            |> List.except [ valid.Checksum ]

        let withInvalidChecksums =
                (fun checksum -> { valid with Checksum = checksum })

        let invalidChecksumsAndResults =
                (fun values -> 
                    values.Checksum, SwedishPersonalIdentityNumber.create values)

        |> List.iter (fun (invalidChecksum, result) ->
            match result with
            | Error (InvalidChecksum actual) -> invalidChecksum =! actual
            | _ -> failwith "Expected InvalidChecksum Error")

First we get all invalidChecksums by starting with a list of all digits in the range [0,9] and removing the valid checksum. We then create a list of SwedishPersonalIdentityNumberValues records where we replace the checksum with each of the invalid checksums. Then we call create on all those values to get 9 results. We return those results as tuples together with the invalid checksum to be able to assert we get the expected error. The assertion is done by first pattern matching on each result to make sure it is of type InvalidChecksum. Then we check that the invalid checksum in the error is the expected checksum.


In this post we realised we need to be careful when writing generators to be aware of what their possible outputs can be. If it’s too large there is a great chance we will have flaky tests, or never find any bugs simply because the tests will not run enough times. In the next post we will look at how to write tests without repeating our production code in the test logic.

  1. Due to GDPR and such it’s best practice to not use any ‘random’ Personal Identity Number values in your tests since the pins could actully belong to a real person. The Swedish National Tax Board that is in charge of the Personal Identity Numbers actually provide a list of valid numbers to use for testing purposes. The library ActiveLogin.Identity.Swedish.TestData provides easy access to this test data. 

  2. FsCheck configuration