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    quickcheck

    Automatic testing of MoonBit programs

    property-based-testing
    quickcheck
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    #MoonBit QuickCheck

    #Introduction

    The idea of QuickCheck was originally introduced in John's paper QuickCheck: a lightweight tool for random testing of Haskell programs and its Haskell derivation QuickCheck, which aimed at simplifying the writing of tests by generating them. The core is to automatically generate tests based on a the signature of the specification / theorem (i.e. properties which functions should satisfy) and QuickCheck then tests that the properties hold. The idea spread to other languages and is now implemented in MoonBit. Because of the differences in type systems between Haskell and MoonBit, the original idea morphed into something different. There are several differences to this approach:

    • We have discarded many ideas in Haskell QuickCheck that have been proven inappropriate by time.
    • Some features requires a very fancy type system were removed (Or not considered currently). For instance, the generation of functions requires GADT but MoonBit does not.
    • MoonBit QuickCheck brings many modern academic ideas into industrial practice (listed below).

    #Table of Contents

    #Quick Start

    #Installation

    Firstly, you need to install the MoonBit QuickCheck library. You can do this by executing the following command:

    moon add moonbitlang/quickcheck
moon install

    To use the library, you need to import it in your moon.pkg.json file, and for convenience we give an alias qc to the library:

    {
  "import": [{ "path": "moonbitlang/quickcheck", "alias": "qc" }]
}

    #First Look

    Let's start with something very simple. Suppose that we just wrote a function reverse which takes an array as argument and returns its reverse. We want to test its functionality by writing unit tests:

    test "reverse" {
      inspect!(reverse(([] : Array[Int])), content="[]")
      inspect!(reverse([1, 2, 3]), content="[3, 2, 1]")
    }

    Is this enough to prove that this function is correct? No, the bugs may lies in the remaining untested code. But if we want more rigorous verification, we may need to write more test cases. For the complicated program, there would never be time to. How can we reduce the cost of testing? The key to doing so must be to generalize the test functions, so that each function covers not only one test case, but many. This is where QuickCheck comes in. We can write a property that reverse should hold for any array, and QuickCheck will generate a large number of random array and check that the property holds for all of them.

    But what property should we write? We may notice that the reverse of the reverse of an array is the original array. So we can write a property (you can roughly think of it as a function (T) -> Bool) that reverse should hold for any array:

    fn prop_reverse_identity(arr : Array[Int]) -> Bool {
      reverse(reverse(arr)) == arr
    }

    We may consider the code logically as:

    Looks good, now we can use QuickCheck to test this property, this is easily archived by the quick_check_fn function:

    test {
      @qc.quick_check_fn!(prop_reverse_identity)
      // equivalent to quick_check!(Arrow(prop_reverse_identity))
    }

    The quick_check_fn function takes a f: (T) -> Bool, where T satisfies some constraints (We will discuss this later), the function first generates a bunch of random values with type T and then calling the property function f with these values. The results are then collected and will be reported later. In this example, the input value T = Array[Int] and the boolean value true implies that the property holds for some particular values, and the false implies that the property does not hold for some values. When finding a counterexample, the QuickCheck will try to simplify it and then print it to the console. If all the tests passed, the following sentence will be printed to the console:

    +++ [100/0/100] Ok, passed!

    The three number in the brackets are the number of passed, discarded and total tests (the default value of total tests is 100).

    #Failure Diagnosis

    Now let's see another example: suppose we want to write a function remove(arr : Array[Int], x : Int) -> Array[Int] that takes an array and an element and returns a new array with all occurrences of x removed. The intuitive implementation is to search for x in the array and remove it if found:

    fn remove(arr : Array[Int], x : Int) -> Array[Int] {
      match arr.search(x) {
        Some(i) => arr.remove(i) |> ignore
        None => ()
      }
      arr
    }

    Now let's use QuickCheck to test this function. The first thing we need to do is to write a property. We may consider the following properties:

    • If an element was removed from the array, the length of the array should be less than or equal to the original array

    • If an element was removed from the array, the element should not exist in the array anymore

    Now we translate the first property into a MoonBit function (Note that the property function should have exactly one argument, but we can use tuple to pass multiple arguments):

    fn prop_length_is_not_greater(iarr : (Int, Array[Int])) -> Bool {
      let (x, arr) = iarr
      let len = arr.length()
      remove(arr, x).length() <= len
    }

    Run QuickCheck, all tests passed. However, this property is not considered a good property because it is can be fulfilled easily and hence the test is not very meaningful. Most Bugs may still exist in the function.

    test {
      @qc.quick_check_fn!(prop_length_is_not_greater)
    }

    // +++ [100/0/100] Ok, passed!

    The later property is considered better, similarly we implement it in MoonBit:

    fn prop_remove_not_presence(iarr : (Int, Array[Int])) -> Bool {
      let (x, arr) = iarr
      remove(arr, x).contains(x).not()
    }

    test {
      @qc.quick_check_fn!(prop_remove_not_presence)
    }

    The QuickCheck reports a failure with a counterexample in the second line after 8 tests:

    *** [8/0/100] Failed! Falsified.
(0, [0, 0])

    When x = 0 and arr = [0, 0] the property does not hold. The remove function should remove all occurrences of x in the array, but it only removes the first one. QuickCheck finds us a succinct counterexample that directly reveals the core of the problem. How does it do this? In practice QuickCheck generates a lot of complex samples and inputs them into the property function to test them, and if it finds a counterexample it doesn't report it immediately, but shrinks accordingly to try to find a simpler counterexample. In this example, as in many cases, the randomly generated test case contains junk values that have nothing to do with the test failure itself. When the counterexample is found, qc will apply some predefined shrinkers to this counterexample and try to explore downwards for smaller counterexamples.

    #Traits

    We've already discussed generation and shrinking, and this section will discuss how these functions are attached to a type. Remind the quick_check_fn function we used before, it is defined as follows in the MoonBit QuickCheck library:

    ///| path: src/driver.mbt
    pub fn quick_check_fn[A : Arbitrary + Shrink + Show, B : Testable](
      f : (A) -> B
    ) -> Unit!Failure {
      quick_check!(Arrow(f))
    }

    Let's look at the type signature first. The quick_check_fn function takes a function f: (A) -> B as argument, where A should have implemented the Arbitrary, Shrink and Show traits, and B should have implemented the Testable trait. In our examples B is fixed to a Bool, this is because Booleans implement the Testable trait, which can actually be more flexible, we will discuss this later, for now we focus on the constraints of A:

    • Arbitrary is a trait that generates random values of a type.
    • Shrink is a trait that allows a value of particular type to be shrunk to simpler ones.
    • Show is used for printing the counterexample when a test fails.

    The function body It takes a value of type that implemented Testable as argument and runs the test. This is an effectful function that may throw an failure to the MoonBit test driver when a test fails (Or give up). If success, it simply returns Unit with the sentence Ok, passed! printed to the console.

    The body of the function contains a call to quick_check and wraps f in Arrow. According to the definition of quick_check, it requires a value prop of a type P that implements Testable as an argument, and under certain conditions: For any type P implementing Testable, and A implementing Arbitrary, Shrink and Show, the Arrow[A, P] type can be implemented as Testable as well. The reader may wonder why we don't directly implement (A) -> P as Testable but instead use Arrow[A, P] as a wrapper. The reason is simple: The MoonBit type system does not allow us to do so.

    pub fn quick_check[P : Testable](prop : P) -> Unit!Failure

    type Arrow[A, P] (A) -> P

    impl[P : Testable, A : Arbitrary + Shrink + Show] Testable for Arrow[A, P]

    #Testable

    Another advantage of using Arrow is that it constructs a Testable, and QuickCheck provides a number of Testable combinators that can be used to modify a test's properties, such as with_max_success to modify the maximum number of successes:

    test {
      @qc.quick_check!(
        @qc.Arrow(prop_remove_not_presence) |> @qc.with_max_success(1000),
      )
    }

    ///| Output: +++ [1000/0/1000] Ok, passed!

    There are many other combinators that can be used to modify the properties of a test, check the document for src/testable.mbt for more details.

    #Arbitrary

    Arbitrary is a trait indicating that a type has the ability to generate random values for given size and random number generator, which is defined in the MoonBit Core library with compiler level support. It has a method arbitrary that takes a size and a random number generator and then returns a random value of the type.

    pub trait Arbitrary {
      arbitrary(Int, RandomState) -> Self
    }

    The vast majority of types in the core library already implement the Arbitrary trait, and users can also write specific instance for their own defined types or use the compiler's automatic derivation. For example, we can derive the Arbitrary trait for our own Nat type:

    enum Nat {
      Zero
      Succ(Nat)
    } derive(Arbitrary, Show)

    test {
      let nat_gen : @qc.Gen[Nat] = @qc.Gen::spawn()
      let nats = nat_gen.samples(size=4)
      inspect!(
        nats,
        content="[Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Zero)))), Succ(Zero), Succ(Succ(Succ(Zero)))]",
      )
    }

    For any type that implements Arbitrary, you can use the Gen::spawn function to get its generator. Calling the generator's method samples will generate some values of that type. Note that Gen is an internal type of QuickCheck, which will be automatically called by the quick_check function, normally do not require the user to access it, here we use it to show the behavior of Arbitrary.

    #Shrink

    Shrink is a trait that shrinks a value to a simpler one. It has a method shrink that takes a value and returns a iter of simpler values (lazily).

    pub trait Shrink {
      shrink(Self) -> Iter[Self]
    }

    If QuickCheck finds a set of values that fails a given property, it will try to make that value simpler than the original value by getting the shrinks for the value and trying each one in turn to check that the property is still false. If it is, the smaller value becomes the new counterexample and the shrinking process continues with that value.

    #Advanced Topics

    #QuickCheck Invalid Case

    This section summarizes some common mistakes in using QuickCheck:

    • Testing with external effects: If a property requires an external state, for example, the user's input, the global mutable and etc, you should pass the state as an argument to the property function. Otherwise, the property is not a pure function and the test is not repeatable.
    • Mutable arguments was unexpectedly modified: You should keep the arguments immutable in the property function. If you need to modify the arguments, you should make a copy of them.

    #Generators

    Test data is produced by test data generators. QuickCheck defines default generators for some often used types, but you can use your own, and will need to define your own generators for any new types you introduce (Or for simple types we can use the trivial definition by derive(Arbitrary)).

    Generators have types of the form Gen[T], which is a generator for values of type T. It was defined as a struct, it contains single field named gen, with type (Int, RandomState) -> T (The first parameter is the size of the generated value, and the second is the random number generator), notice that this is similar to the arbitrary method in the Arbitrary trait:

    struct Gen[T] {
      gen : (Int, RandomState) -> T
    }

    QuickCheck defines a series of useful methods for Gen[T], for the most basic ones, we can use Gen::new(f: (Int, RandomState) -> T) to create a generator from a function and run it by invoking the run method:

    let g : Gen[Int] = Gen::new(..) // Suppose we have a generator for Int
    let x : Int = g.run(100, RandomState::new()) // Generate a random Int at size 100

    Gen[T] was implemented as functor, applicative and monad which means you can compose it in many ways.

    fn pure[T](val : T) -> Gen[T]
    fn fmap[T, U](self : Gen[T], f : (T) -> U) -> Gen[U]
    fn ap[T, U](self : Gen[(T) -> U], v : Gen[T]) -> Gen[U]
    fn bind[T, U](self : Gen[T], f : (T) -> Gen[U]) -> Gen[U]

    For instance, you can use the fmap method to transform the generated value:

    let g : Gen[Int] = Gen::new(..)
    let g2 : Gen[Int] = g.fmap(fn(x) { x + 1 })
    let g3 : Gen[String] = g.fmap(fn(x) { x.to_string() })

    Or create a dependent generator:

    let g : Gen[Int] = Gen::new(..)
    let g2 : Gen[Int] = g.bind(fn(x : Int) {
      if x == 0 {
        Gen::pure(100)
      } else {
        Gen::pure(200)
      }
    })

    The following documents explains some useful combinators for Gen[T].

    #Choosing between alternatives

    A generator may take the form one_of which chooses among the generators in the array with equal probability. For example, this generates a random boolean which is true with probability one half:

    let gen_bool : Gen[Bool] = one_of([pure(true), pure(false)])

    If you want to control the distribution of results using frequency instead. We have frequency which chooses a generator from the array randomly, but weighs the probability of choosing each alternative by the factor given. For example, this generates true in the probability of .

    let gen_freq : Gen[Bool] = frequency([(4, pure(true)), (1, pure(false))])

    #Size parameter

    We have pointed that test data generators have an size parameter. QuickCheck begins by generating small test cases, and gradually increases the size as testing progresses. Different test data generators interpret the size parameter in different ways: some ignore it, some interprets it as an upper bound on the size of containers. Most generators defined in Arbitrary trait depends on the size parameter but most separated generator combinators does not.

    You can obtain the value of the size parameter using sized combinator.

    pub fn sized[T](f : (Int) -> Gen[T]) -> Gen[T]

    For example, we can make a trivial generator for a list of integers with a given length:

    let gen : Gen[Int] = sized(fn { size => pure(size) })
    let arr = Array::makei(20, fn { i => gen.sample(size=i) })
    inspect!(arr, content="[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]")

    The purpose of size control is to ensure that test cases are large enough to reveal errors, while remaining small enough to test fast. Sometimes the default size control does not achieve this. So we have provided some tool functions like resize and scale (check the document for details) for this purpose.

    #Default Generators

    QuickCheck defines default test data generators and shrinkers for some often used types (By trait Arbitrary and Shrink). You do not need to define or apply these explicitly for every property because QuickCheck can provide a property with appropriate generators and shrinkers for the property's arguments. But if you are required to do so, you can use the forall for explicitly universal quantification.

    quick_check!(forall(spawn(), fn(x : List[Int]) { x.rev().rev() == x }))

    Note that the spawn function is useful for creating Gen[T] from its arbitrary instance, in this example the type checker infers the type of the first argument in forall to be Gen[List[T]] from the type of the property function.

    fn Gen::spawn[T : Arbitrary]() -> Gen[T]

    #Custom Generator

    Recall the remove function we want to test before. The QuickCheck do report an error for us, but the generator is quite random and the tuple element (x, arr): (Int, Array[Int]) is independent. In most cases, the x is not in the array, so the test is not very meaningful (falls to the branch None => ()). Now we use the one_of_array combinator to generate a random element from a generated non-empty array, which makes the test more meaningful.

    test {
      quick_check!(
        forall(
          spawn(),
          fn(a : Array[Int]) {
            forall(one_of_array(a),
              fn(y : Int) { remove(a, y).contains(y).not() })
            |> filter(a.length() != 0)
          },
        ),
      )
    }

    We admit the following facts:

    • The first spawn evaluates to a generator of Array[Int].
    • The forall function can be nested.
    • There is a filter function that filters out the test cases that do not satisfy the condition, non-empty array is required in this case.
    • The one_of_array function selects a random element from a non-empty array.

    *** [4/33/100] Failed! Falsified.
[0, 0]
0

    We find that there are 33 cases that do not satisfy the condition, and the counterexample is [0, 0] and 0, which points out the issue clearly. The one_of_array function selects a random element from the array, so the y is always 0 in this case. The remove function only removes the first one, so the property does not hold.

    #Conditional Properties

    Now let's further verify our hypothesis: The function remove only removes the first one but not all. So if we instead formulate a conditional property which restricts the input array contains no duplicated elements, then our tests should pass. Use the function filter can filter out unwanted test cases:

    test {
      fn no_duplicate(x : Array[Int]) -> Bool {
        @sorted_set.from_iter(x.iter()).size() == x.length().to_int64()
      }

      quick_check!(
        forall(
          spawn(),
          fn(iarr : (Int, Array[Int])) {
            let (x, arr) = iarr
            filter(remove(arr.copy(), x).contains(x).not(), no_duplicate(arr))
          },
        ),
      )
    }

    • Notice that we use arr.copy() to make a copy of the array, because the remove function may modify the argument array.
    • The no_duplicate function checks whether the input array contains no duplicated elements.
    • As discussed above, the filter combinator filters out the test cases that do not satisfy the condition.

    Running this test, we find that all tests passed. Now we have strong evidence that the remove function only removes the first one but not all.

    #Classifying Data

    We may interest in the distribution of the generated data: sometimes the generator may produce trivial data that does not help us to find the bugs. We want to find out what data is generated and how often in order to improve the generator. QuickCheck provides functions like label, collect and classify to achieve this.

    test "classes" {
      quick_check_fn!(
        fn(x : List[Int]) {
          Arrow(prop_rev)
          |> classify(x.length() > 5, "long list")
          |> classify(x.length() <= 5, "short list")
        },
      )
    }

    The classify function takes a boolean and a string, and if the boolean is true, the test case is classified with the string.

    +++ [100/0/100] Ok, passed!
22% : short list
78% : long list

    The label function takes a string and classifies the test case with the string.

    test "label" {
      quick_check_fn!(
        fn(x : List[Int]) {
          Arrow(prop_rev)
          |> label(if x.is_empty() { "trivial" } else { "non-trivial" })
        }
      )
    }

    The result is as follows:

    +++ [100/0/100] Ok, passed!
8% : trivial
92% : non-trivial

    The collect function is a generalization of label. The difference is that the collect takes an argument implementing the Show trait, and the label takes a string directly. The collect function is useful when you want to classify the test case with a complex value.

    #Application

    We have applied MoonBit QuickCheck to test the correctness of the MoonBit core. For now we have found several bugs in the core, including:

    #Roadmap and Future Work

    #Data Generation

    • Currently use the SplitMix algorithms

    #Property Verification

    #Shrinking

    #References

    RandomState

    source

    Shrink

    source
    pub(open) trait Shrink {
      shrink(Self) -> Iter[Self] = _
    }

    impl Shrink for Unit
    impl Shrink for Bool
    impl Shrink for Char
    impl Shrink for Int
    impl Shrink for Int64
    impl Shrink for UInt
    impl Shrink for UInt64
    impl Shrink for Float
    impl Shrink for Double
    impl Shrink for String
    impl Shrink for Option[T]
    impl Shrink for Result[T, E]
    impl Shrink for Bytes
    impl Shrink for Array[X]
    impl Shrink for Iter[X]
    impl Shrink for T[T]
    impl Shrink for Tuple2[A, B]
    impl Shrink for Tuple3[A, B, C]
    impl Shrink for Tuple4[A, B, C, D]
    impl Shrink for Tuple5[A, B, C, D, E]
    impl Shrink for Tuple6[A, B, C, D, E, F]

    Testable

    source
    pub(open) trait Testable {
      property(Self) -> Property
    }

    impl Testable for Unit
    impl Testable for Bool
    impl Testable for Option[P]

    Arrow

    source
    pub(all) type Arrow[A, B] (A) -> B

    impl Testable for Arrow[A, P]

    Arrow::inner

    source
    fn[A, B] Arrow::inner(self : Arrow[A, B]) -> ((A) -> B)
    Convert newtype to its underlying type, automatically derived.

    Axiom

    source
    type Axiom[T]

    Axiom::new

    source
    fn[T] Axiom::new(run_axiom : (T) -> Equivalence[T]) -> Axiom[T]

    Axiom::run

    source
    fn[T] Axiom::run(self : Axiom[T], x : T) -> Equivalence[T]

    Axiom::to_property

    source
    fn[T, U] Axiom::to_property(self : Axiom[T], cong : (T) -> U, eq : (U, U) -> Bool) -> ((T) -> Bool)

    Axiom::to_property_eq

    source
    fn[T, U : Eq] Axiom::to_property_eq(self : Axiom[T], cong : (T) -> U) -> ((T) -> Bool)

    Axiom::to_property_parametric

    source
    fn[T, M, N] Axiom::to_property_parametric(self : Axiom[T], cong : (T, M) -> N, eq : (N, N) -> Bool) -> (((T, M)) -> Bool)

    Axiom::to_property_parametric_eq

    source
    fn[T, M, N : Eq] Axiom::to_property_parametric_eq(self : Axiom[T], cong : (T, M) -> N) -> (((T, M)) -> Bool)

    Callback

    source
    type Callback
    TODO: determine the execution of callback by kind

    Config

    source
    type Config
    Configuration for initializing a test runner.

    Discard

    source
    type Discard

    impl Default for Discard
    impl Testable for Discard

    Equivalence

    source
    pub(all) struct Equivalence[T] {
      lhs : T
      rhs : T
    }

    impl Show for Equivalence[T]

    Equivalence::ap

    source
    fn[T, U] Equivalence::ap(self : Equivalence[(T) -> U], other : Equivalence[T]) -> Equivalence[U]

    Equivalence::bind

    source
    fn[T, U] Equivalence::bind(self : Equivalence[T], f : (T) -> Equivalence[U]) -> Equivalence[U]

    Equivalence::equal_by

    source
    fn[T] Equivalence::equal_by(self : Equivalence[T], eq : (T, T) -> Bool) -> Bool

    Equivalence::fmap

    source
    fn[T, U] Equivalence::fmap(self : Equivalence[T], f : (T) -> U) -> Equivalence[U]

    Equivalence::is_equal

    source
    fn[T : Eq] Equivalence::is_equal(self : Equivalence[T]) -> Bool

    Equivalence::new

    source
    fn[T] Equivalence::new(lhs : T, rhs : T) -> Equivalence[T]

    Expected

    source
    pub(all) enum Expected {
      Fail
      Success
      GaveUp
    }

    Gen

    source
    type Gen[T]
    The Gen type represents a generator of values of type T.
    impl Testable for Gen[P]

    Gen::ap

    source
    fn[T, U] Gen::ap(self : Gen[(T) -> U], v : Gen[T]) -> Gen[U]
    Applicative Functor instance for Gen[T]

    Gen::array_with_size

    source
    fn[T] Gen::array_with_size(self : Gen[T], size : Int) -> Gen[Array[T]]

    Gen::bind

    source
    fn[T, U] Gen::bind(self : Gen[T], f : (T) -> Gen[U]) -> Gen[U]
    Monad instance for Gen[T]

    Gen::feat_random

    source
    fn[T : 
    Enumerable    ] Gen::feat_random(size : Int) -> Gen[T]
    Generate a value from an enumerable instance (up to a size bound) @alert unsafe "Experimental: May cause stack overflow"

    Gen::fmap

    source
    fn[T, U] Gen::fmap(self : Gen[T], f : (T) -> U) -> Gen[U]
    Functor instance for Gen[T] (fmap)

    Gen::join

    source
    fn[T] Gen::join(self : Gen[Gen[T]]) -> Gen[T]

    Gen::new

    source
    Create a new generator from a function

    Gen::resize

    source
    fn[T] Gen::resize(self : Gen[T], size : Int) -> Gen[T]
    Resize a generator to a specific value

    Gen::run

    source
    fn[T] Gen::run(self : Gen[T], i : Int, rs : 
    RandomState    ) -> T
    Run a generator with a size and random state

    Gen::sample

    source
    fn[T] Gen::sample(self : Gen[T], size~ : Int = .., seed~ : UInt64 = ..) -> T
    Generate a value from a generator

    Gen::samples

    source
    fn[T] Gen::samples(self : Gen[T], size~ : Int = .., seed~ : UInt64 = ..) -> Array[T]
    Generate an array of samples from a generator

    Gen::scale

    source
    fn[T] Gen::scale(self : Gen[T], f : (Int) -> Int) -> Gen[T]
    Adjust the size parameter of a generator

    Gen::spawn

    source
    Spawn a new generator from an arbitrary instance

    Gen::such_that

    source
    fn[T] Gen::such_that(self : Gen[T], pred : (T) -> Bool) -> Gen[T]
    Generate a value that satisfies a predicate

    Gen::such_that_maybe

    source
    fn[T] Gen::such_that_maybe(self : Gen[T], pred : (T) -> Bool) -> Gen[T?]
    Attempt to generate a value that satisfies a predicate If failures reach the maximum size, return None

    Outcome

    source
    pub(all) enum Outcome[T] {
      Success
      GaveUp
      Fail(T)
    }

    impl Show for Outcome[T]

    Printer

    source
    type Printer

    Printer::format

    source
    fn Printer::format(self : Printer, str : String) -> String

    Printer::from_buffer

    source
    fn Printer::from_buffer(buf : 
    T    ) -> Printer

    Printer::ident

    source
    fn Printer::ident(self : Printer, size~ : Int = ..) -> Unit

    Printer::unident

    source
    fn Printer::unident(self : Printer) -> Unit

    Printer::write_string

    source
    fn Printer::write_string(self : Printer, str : String) -> Unit

    Property

    source
    type Property

    Replay

    source
    pub(all) struct Replay {
      rand_state : 
    RandomState
      size : Int
    }

    SingleResult

    source
    type SingleResult

    State

    source
    type State
    Internal State of Compiler

    State::complete_test

    source
    fn State::complete_test(self : State, _prop : Property) -> TestSuccess raise TestError

    State::find_failure

    source

    State::give_up

    source
    fn State::give_up(self : State, _prop : Property) -> TestSuccess raise TestError

    State::local_min

    source
    fn State::local_min(self : State, res : SingleResult, ts : Iter[
    Rose    [SingleResult]]) -> (Int, Int, Int, SingleResult)

    State::run_single_test

    source
    fn State::run_single_test(self : State, prop : Property) -> Result[TestSuccess, State] raise TestError
    Run a single test and return the Ok(result) if ended successfully, or Err(state) if it should continue.

    State::run_test

    source
    fn State::run_test(self : State, prop : Property) -> TestSuccess raise TestError

    TestError

    source
    type TestError

    TestSuccess

    source
    type TestSuccess

    alphabet

    source
    fn alphabet() -> Gen[Char]
    Generates alphabet

    associative

    source
    fn[A : Eq] associative(f : (A, A) -> A) -> (((A, A, A)) -> Bool)
    Associative binary operation.

    callback

    source
    fn[P : Testable] callback(p : P, cb : Callback) -> Property

    char_range

    source
    fn char_range(lo : Char, hi : Char) -> Gen[Char]
    Generate char within given range [lo, hi]

    classify

    source
    fn[P : Testable] classify(p : P, cond : Bool, s : String) -> Property
    Classifies a test case based on a condition

    collect

    source
    fn[P : Testable, T : Show] collect(p : P, t : T) -> Property
    Attaches a label (Show) to a test case

    commutative

    source
    fn[A, B : Eq] commutative(f : (A, A) -> B) -> (((A, A)) -> Bool)
    Commutative binary operation.

    counterexample

    source
    fn[P : Testable] counterexample(p : P, s : String) -> Property
    Adds a string to the counterexample if the property fails

    distributive_left

    source
    fn[A : Eq] distributive_left(f : (A, A) -> A, g : (A, A) -> A) -> (((A, A, A)) -> Bool)
    Distributive binary operation over left

    distributive_right

    source
    fn[A : Eq] distributive_right(f : (A, A) -> A, g : (A, A) -> A) -> (((A, A, A)) -> Bool)
    Distributive binary operation over right

    expect_fail

    source
    fn[P : Testable] expect_fail(p : P) -> Property

    expect_gave_up

    source
    fn[P : Testable] expect_gave_up(p : P) -> Property

    ext_equal

    source
    fn[A, B : Eq] ext_equal(f : (A) -> B, g : (A) -> B) -> ((A) -> Bool)
    Extensional equality for function.

    failed

    source
    fn failed() -> SingleResult

    filter

    source
    fn[P : Testable] filter(p : P, cond : Bool) -> Property
    Filters a property based on a condition

    flatten_array

    source
    fn[T] flatten_array(arr : Array[Gen[T]]) -> Gen[Array[T]]
    Generate an array of elements from individual generators

    flatten_list

    source
    fn[T] flatten_list(lst : 
    T    [Gen[T]]) -> Gen[
    T    [T]]
    Generate a list of elements from individual generators

    flatten_option

    source
    fn[T] flatten_option(opt : Gen[T]?) -> Gen[T?]
    Generate an option from an optional generator

    flatten_result

    source
    fn[T, E] flatten_result(res : Result[Gen[T], E]) -> Gen[Result[T, E]]
    Generate a result of a generator or return the pure error

    forall

    source
    fn[T : Testable, A : Show] forall(gen : Gen[A], f : (A) -> T) -> Property
    Run with an explicit generator

    forall_shrink

    source
    fn[T : Testable, A : Show] forall_shrink(gen : Gen[A], shrinker : (A) -> Iter[A], f : (A) -> T) -> Property

    frequency

    source
    fn[T] frequency(arr : Array[(Int, Gen[T])]) -> Gen[T]
    Chooses one of the given generators, with a weighted random distribution. @alert unsafe "Panics if the array is empty or total weight is less than one"

    frequency_list

    source
    fn[T] frequency_list(lst : 
    T    [(Int, T)]) -> Gen[T]
    Chooses one of the given generators, with a weighted random distribution. @alert unsafe "Panics if the list is empty or total weight is less than one"

    idempotent

    source
    fn[A : Eq] idempotent(f : (A) -> A) -> ((A) -> Bool)
    Idempotent function.

    if_fail

    source
    fn[P : Testable] if_fail(p : P, f : () -> Unit) -> Property
    Adds a callback that will be called if the property fails

    int_bound

    source
    fn int_bound(bound : Int) -> Gen[Int]
    Generates int within given bound [0, bound)

    int_range

    source
    fn int_range(lo : Int, hi : Int) -> Gen[Int]
    Generates int within given range [lo, hi)

    integer_bound

    source
    Generates integer within given bound [0, bound)

    inverse

    source
    fn[A : Eq, B] inverse(f : (A) -> B, g : (B) -> A) -> ((A) -> Bool)
    Inverse function.

    involutory

    source
    fn[A : Eq] involutory(f : (A) -> A) -> ((A) -> Bool)
    Involutory function.

    label

    source
    fn[P : Testable] label(p : P, s : String) -> Property
    Attaches a label to a test case

    liftA2

    source
    fn[A, B, C] liftA2(f : (A, B) -> C, v : Gen[A], w : Gen[B]) -> Gen[C]
    Lift a binary function to generators

    liftA3

    source
    fn[A, B, C, D] liftA3(f : (A, B, C) -> D, v : Gen[A], w : Gen[B], x : Gen[C]) -> Gen[D]
    Lift a ternary function to generators

    liftA4

    source
    fn[A, B, C, D, E] liftA4(f : (A, B, C, D) -> E, v : Gen[A], w : Gen[B], x : Gen[C], y : Gen[D]) -> Gen[E]
    Lift a quaternary function to generators

    liftA5

    source
    fn[A, B, C, D, E, F] liftA5(f : (A, B, C, D, E) -> F, v : Gen[A], w : Gen[B], x : Gen[C], y : Gen[D], z : Gen[E]) -> Gen[F]
    Lift a quinary function to generators

    liftA6

    source
    fn[A, B, C, D, E, F, G] liftA6(ff : (A, B, C, D, E, F) -> G, v : Gen[A], w : Gen[B], x : Gen[C], y : Gen[D], z : Gen[E], u : Gen[F]) -> Gen[G]
    Lift a senary function to generators

    list_with_size

    source
    fn[T] list_with_size(size : Int, gen : Gen[T]) -> Gen[
    T    [T]]

    local_min_found

    source
    fn local_min_found(st : State, res : SingleResult) -> (Int, Int, Int, SingleResult)

    map_size

    source
    fn[P : Testable] map_size(p : P, f : (Int) -> Int) -> Property

    map_total_result

    source
    fn[P : Testable] map_total_result(prop : P, f : (SingleResult) -> SingleResult) -> Property

    mono_decrease

    source
    fn[A : Compare + Eq, B : Compare + Eq] mono_decrease(f : (A) -> B) -> (((A, A)) -> Bool)
    Monotonic decreasing function.

    mono_increase

    source
    fn[A : Compare + Eq, B : Compare + Eq] mono_increase(f : (A) -> B) -> (((A, A)) -> Bool)
    Monotonic increasing function.

    nat

    source
    fn nat() -> Gen[Int]

    neg_int

    source
    fn neg_int() -> Gen[Int]
    Generates a negative integer

    numeral

    source
    fn numeral() -> Gen[Char]
    Generates a numeral char

    one_of

    source
    fn[T] one_of(arr : Array[Gen[T]]) -> Gen[T]
    Randomly uses one of the given generators. @alert unsafe "Panics if the array is empty"

    one_of_array

    source
    fn[T] one_of_array(val : Array[T]) -> Gen[T]
    Randomly select one element from an array @alert unsafe "Panics if the array is empty"

    one_of_list

    source
    fn[T] one_of_list(lst : 
    T    [T]) -> Gen[T]
    Randomly uses one of the given generators in list @alert unsafe "Panics if the list is empty"

    pure

    source
    fn[T] pure(val : T) -> Gen[T]
    Functor instance for Gen[T] (pure)

    pure_eq

    source
    fn[T] pure_eq(x : T) -> Equivalence[T]

    quad

    source
    fn[T, U, V, W] quad(gen1 : Gen[T], gen2 : Gen[U], gen3 : Gen[V], gen4 : Gen[W]) -> Gen[(T, U, V, W)]
    Create quad generator from four generators

    quick_check

    source
    fn[P : Testable] quick_check(prop : P, max_shrinks? : Int, max_success? : Int, max_size? : Int, discard_ratio? : Int, expect~ : Expected = .., abort~ : Bool = ..) -> Unit raise Failure

    quick_check_fn

    source
    fn[A : 
    Arbitrary     + Shrink + Show, B : Testable] quick_check_fn(f : (A) -> B, max_shrinks? : Int, max_success? : Int, max_size? : Int, discard_ratio? : Int, expect~ : Expected = .., abort~ : Bool = ..) -> Unit raise Failure

    quick_check_with

    source
    fn[P : Testable] quick_check_with(cfg : Config, prop : P) -> Unit raise Failure

    quick_check_with_result

    source
    fn[P : Testable] quick_check_with_result(cfg : Config, prop : P) -> TestSuccess raise TestError

    rejected

    source
    fn rejected() -> SingleResult

    run_prop

    source

    shrinking

    source
    fn[P : Testable, T] shrinking(shrinker : (T) -> Iter[T], x0 : T, pf : (T) -> P) -> Property

    sized

    source
    fn[T] sized(f : (Int) -> Gen[T]) -> Gen[T]
    Create sized generators

    small_int

    source
    fn small_int() -> Gen[Int]
    Primitive Generators and Combinators

    sorted_list

    source
    fn[T : Compare + Eq] sorted_list(size : Int, gen : Gen[T]) -> Gen[
    T    [T]]

    succeed

    source
    fn succeed() -> SingleResult

    terminate

    source
    fn[P : Testable] terminate(p : P) -> Property
    Modifies a property to make it terminate after the first test

    triple

    source
    fn[T, U, V] triple(gen1 : Gen[T], gen2 : Gen[U], gen3 : Gen[V]) -> Gen[(T, U, V)]
    Create triple generator from three generators

    tuple

    source
    fn[T, U] tuple(gen1 : Gen[T], gen2 : Gen[U]) -> Gen[(T, U)]
    Create tuple generator from two generators

    with_discarded_ratio

    source
    fn[P : Testable] with_discarded_ratio(p : P, n : Int) -> Property

    with_max_shrinks

    source
    fn[P : Testable] with_max_shrinks(p : P, n : Int) -> Property

    with_max_size

    source
    fn[P : Testable] with_max_size(p : P, n : Int) -> Property

    with_max_success

    source
    fn[P : Testable] with_max_success(p : P, n : Int) -> Property

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