*QCheck

This section of the textbook is optional.

One of the key pieces of functionality provided by QCheck is the ability to generate pseudorandom values of various types. Here is some of the signature of the module that does that:

module QCheck : sig
  ...
  module Gen : 
    sig
      type 'a t = Random.State.t -> 'a
      val int : int t
      val generate  : ?rand:Random.State.t -> n:int -> 'a t -> 'a list
      val generate1 : ?rand:Random.State.t          -> 'a t -> 'a
      ...
    end
  ...
end

An 'a QCheck.Gen.t is a function that takes in a PRNG state and uses it to produce a pseudorandom value of type 'a. So QCheck.Gen.int produces pseudorandom integers. The function generate1 actually does the generation of one pseudorandom value. It takes an optional argument that is a PRNG state; if that argument is not supplied, it uses the default PRNG state. The function generate produces a list of n pseduorandom values.

QCheck implements many producers of pseudorandom values. Here are a few more of them:

module QCheck : sig
  ...
  module Gen : 
    sig
      val int : int t
      val small_int : int t
      val int_range : int -> int -> int t
      val list : 'a t -> 'a list t
      val list_size : int t -> 'a t -> 'a list t
      val string : ?gen:char t -> string t
      val small_string : ?gen:char t -> string t
      ...
    end
  ...
end

You can read the documentation of those and many others.

Properties and Arbitraries

There are two more ideas we need to understand before we can get to testing with QCheck: properties and arbitraries.

Properties. It's tempting to think that QCheck would enable us to test a function by generating many pseudorandom inputs to the function, running the function on them, then checking that the outputs are correct. But there's immediately a problem: how can QCheck know what the correct output is for each of those inputs? Since they're randomly generated, the test engineer can't hardcode the right outputs, as we've usually been doing with OUnit test suites this semester.

So instead, QCheck allows us to check whether a property of each output holds. A property is a function of type t -> bool, for some type t, that tells use whether the value of type t exhibits some desired characteristic. Here, for example, here are two properties; one that determines whether an integer is even, and another that determines whether a list is sorted in non-decreasing order according to the built-in <= operator:

let is_even n = 
  n mod 2 = 0

let rec is_sorted = function
  | [] -> true
  | [h] -> true
  | h1::(h2::t as t') -> h1 <= h2 && is_sorted t'

Arbitraries. The way we present to QCheck the outputs to be checked is with a value of type 'a QCheck.Arbitrary. This type represents an "arbitrary" value of type 'a—that is, it has been pseudorandomly chosen as a value that we want to check, and more specifically, to check whether it satisfies a property.

We can create arbitraries (as we'll call them) out of generators using the function QCheck.make : 'a QCheck.Gen.t -> 'a QCheck.arbitrary. (Actually that function takes some optional arguments that we elide here.) This isn't actually the normal way to create arbitraries, but it's a simple way that will help us understand them; we'll get to the normal way in a little while. For example, the following expression represents an arbitrary integer:

QCheck.make QCheck.Gen.int

You can read the documentation of QCheck and its arbitraries.

Testing Properties with QCheck

To construct a QCheck test, we create an arbitrary and a property, and pass them to QCheck.Test.make : 'a QCheck.arbitrary -> ('a -> bool) -> QCheck.Test.t. (That function also takes some optional arguments that we elide here.) The test will generate some number of arbitraries (by default, 100) and check whether the property holds of each of them. For example, the following code creates a QCheck test that checks whether an arbitrary integer is even; the probability that this test will pass is only \(2^{-100}\):

let t = QCheck.Test.make (QCheck.make QCheck.Gen.int) is_even

If we want to change the number of arbitraries that are checked, we can pass an optional integer argument ~count to QCheck.Test.make.

We can run that test with QCheck_runner.run_tests : QCheck.Test.t list -> int. (Once more, that function takes some optional arguments that we elide here.) The integer it returns is 0 if all the tests in the list pass, and 1 otherwise. For the test above, running it will output 1 with high probability, because it will generate at least one odd integer. The output would look like the following:

# QCheck_runner.run_tests [t];;
  test `<test>` failed on >= 1 cases: <instance>                                                                                                                 failure (1 tests failed, ran 1 tests)                                           
- : int = 1

Unfortunately, that output isn't very informative; it doesn't tell us what particular values failed to satisfy the property! We'll fix that problem in a little while.

If you want to make an OCaml program that runs QCheck tests and prints the results, there is a function QCheck_runner.run_tests_main that works much like OUnit2.run_test_tt_main: just invoke it as the final expression in a test file. For example:

let tests = (* code that constructs a [QCheck.Test.t list] *)

let _ = QCheck_runner.run_tests_main tests

If that code is in a file test_x.ml, you can compile and run it as follows:

$ ocamlbuild -pkg qcheck test_x.byte
$ ./test_x.byte

QCheck tests can be converted to OUnit tests and included in the usual kind of OUnit test suite we've been writing all along. The function that does this is QCheck_runner.to_ounit2_test : QCheck.Test.t -> OUnit2.test.

Informative Output

We noted above that the output of QCheck so far has told us only whether some arbitraries satisfied a property, but not which arbitraries failed to satisfy it. Let's fix that problem.

The issue is with how we constructed an arbitrary directly out of a generator. An arbitrary is properly more than just a generator. The QCheck library needs to know how to print values of the generator, and a few other things as well. You can see that in the definition of 'a QCheck.arbitrary:

module QCheck :
  ...
  sig 
    type 'a arbitrary = {
      gen : 'a QCheck.Gen.t;
      print : ('a -> string) option;                                                
      small : ('a -> int) option;
      shrink : 'a QCheck.Shrink.t option;
      collect : ('a -> string) option;
    }
    ...
  end

In addition to the generator field gen, there is a field containing an optional function to print values from the generator, and a few other optional fields as well. Luckily, we don't usually have to find a way to complete those fields ourselves; the QCheck module provides many arbitraries that correspond to the generators found in QCheck.Gen:

module QCheck :
  sig
    ...
    val int : int arbitrary
    val small_int : int arbitrary
    val int_range : int -> int -> int arbitrary
    val list : 'a arbitrary -> 'a list arbitrary
    val list_of_size : int Gen.t -> 'a arbitrary -> 'a list arbitrary
    val string : string arbitrary
    val small_string : string arbitrary
    ...
  end

Using those arbitraries, we can get improved error messages:

# let t = QCheck.Test.make QCheck.int is_even;;
# QCheck_runner.run_tests [t];;
  test `<test>` failed on >= 1 cases: 2227842673298200061                                                                                                        
failure (1 tests failed, ran 1 tests)                                                                                                               failure (1 tests failed, ran 1 tests)                                           
- : int = 1

The final piece of less-than-informative output in that message, <test>, is there because we haven't given the test case a name. We can do that by passing the optional argument ~name to QCheck.Test.make.

Testing functions with QCheck

So far we've used QCheck only to test whether a randomly generated value satisfies some property. We haven't tried to use that value as input to a function of interest—the function we really want to test—and see whether the function's output satisfies a property. Let's do that now.

Here is a QCheck test to see whether the output of double is correct:

let double x = 2 * x

let t = QCheck.Test.make QCheck.int
         (fun x ->
            let y = double x
            in y = 2*x)

Note how the property we pass to QCheck.Test.make takes in a value (which will be value generated by QCheck.int), computes a function of that value (double x), then checks whether that computed output satisfies a property of interest (equals 2*x).

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