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Test.QuickCheck

The QuickCheck manual gives detailed information about using QuickCheck effectively. You can also try https://begriffs.com/posts/2017-01-14-design-use-quickcheck.html, a tutorial written by a user of QuickCheck.

To start using QuickCheck, write down your property as a function returning Bool. For example, to check that reversing a list twice gives back the same list you can write:

import Test.QuickCheck

prop_reverse :: [Int] -> Bool
prop_reverse xs = reverse (reverse xs) == xs

You can then use QuickCheck to test prop_reverse on 100 random lists:

To run more tests you can use the withNumTests combinator:

To use QuickCheck on your own data types you will need to write Arbitrary instances for those types. See the QuickCheck manual for details about how to do that.

When testing fails quickCheck will try to give you a minimal counterexample to your property: @ import Test.QuickCheck

prop_reverse_bad :: [Int] -> Bool prop_reverse_bad xs = reverse xs == xs

However, beware because not all properties that ought to fail will fail when you expect them to:

>>> quickCheck $ \ x y -> x == y
+++ Ok, passed 100 tests.

That's because GHCi will default any type variables in your property to (), so in the example above quickCheck was really testing that () is equal to itself. To avoid this behaviour it is best practise to monomorphise your polymorphic properties when testing:

>>> quickCheck $ \ x y -> (x :: Int) == y
*** Failed! Falsified (after 4 tests and 3 shrinks):
0
1

Running tests

quickCheck :: Testable prop => prop -> IO ()

Tests a property and prints the results to stdout.

By default up to 100 tests are performed, which may not be enough to find all bugs. To run more tests, use withNumTests.

If you want to get the counterexample as a Haskell value, rather than just printing it, try the quickcheck-with-counterexamples package.

data Args

Args specifies arguments to the QuickCheck driver

Args :: Maybe (QCGen, Int) -> Int -> Int -> Int -> Bool -> Int -> Args

replay :: Args -> Maybe (QCGen, Int)

Should we replay a previous test? Note: saving a seed from one version of QuickCheck and replaying it in another is not supported. If you want to store a test case permanently you should save the test case itself.

maxSuccess :: Args -> Int

Maximum number of successful tests before succeeding. Testing stops at the first failure. If all tests are passing and you want to run more tests, increase this number.

maxDiscardRatio :: Args -> Int

Maximum number of discarded tests per successful test before giving up

maxSize :: Args -> Int

Size to use for the biggest test cases

chatty :: Args -> Bool

Whether to print anything

maxShrinks :: Args -> Int

Maximum number of shrinks to do before giving up. Setting this to zero turns shrinking off.

data Result

Result represents the test result

Success :: Int -> Int -> (Map [String] Int) -> (Map String Int) -> (Map String (Map String Int)) -> String -> Result

numTests :: Result -> Int

Number of tests performed

labels :: Result -> (Map [String] Int)

The number of test cases having each combination of labels (see label)

classes :: Result -> (Map String Int)

The number of test cases having each class (see classify)

tables :: Result -> (Map String (Map String Int))

Data collected by tabulate

output :: Result -> String

Printed output

GaveUp :: Int -> Int -> (Map [String] Int) -> (Map String Int) -> (Map String (Map String Int)) -> String -> Result

labels :: Result -> (Map [String] Int)

classes :: Result -> (Map String Int)

tables :: Result -> (Map String (Map String Int))

Failure :: Int -> Int -> Int -> Int -> Int -> QCGen -> Int -> String -> Maybe AnException -> String -> [String] -> [String] -> Set String -> [Witness] -> Result

numShrinks :: Result -> Int

Number of successful shrinking steps performed

numShrinkTries :: Result -> Int

Number of unsuccessful shrinking steps performed

numShrinkFinal :: Result -> Int

Number of unsuccessful shrinking steps performed since last successful shrink

usedSeed :: Result -> QCGen

What seed was used

usedSize :: Result -> Int

What was the test size

reason :: Result -> String

Why did the property fail

theException :: Result -> Maybe AnException

The exception the property threw, if any

failingTestCase :: Result -> [String]

The test case which provoked the failure

failingLabels :: Result -> [String]

The test case's labels (see label)

failingClasses :: Result -> Set String

The test case's classes (see classify)

witnesses :: Result -> [Witness]

The existentially quantified witnesses provided by witness

NoExpectedFailure :: Int -> Int -> (Map [String] Int) -> (Map String Int) -> (Map String (Map String Int)) -> String -> Result

labels :: Result -> (Map [String] Int)

classes :: Result -> (Map String Int)

tables :: Result -> (Map String (Map String Int))

data TestProgress

TestProgress, contains information that might be interesting to external libraries, e.g. Tasty. From this it is possible to install your own callbacks that reports e.g. progress.

TestProgress :: Int -> Int -> Int -> Int -> Int -> Int -> TestProgress

currentPassed :: TestProgress -> Int

Number of tests passed so far

maxTests :: TestProgress -> Int

Number of tests to execute

currentShrinks :: TestProgress -> Int

Number of successful shrinking steps

currentFailedShrinks :: TestProgress -> Int

Number of failed shrinking steps since last successful one

stdArgs :: Args

The default test arguments

quickCheckWith :: Testable prop => Args -> prop -> IO ()

Tests a property, using test arguments, and prints the results to stdout.

quickCheckWithResult :: Testable prop => Args -> prop -> IO Result

Tests a property, using test arguments, produces a test result, and prints the results to stdout.

quickCheckResult :: Testable prop => prop -> IO Result

Tests a property, produces a test result, and prints the results to stdout.

recheck :: Testable prop => Result -> prop -> IO ()

Re-run a property with the seed and size that failed in a run of quickCheckResult.

isSuccess :: Result -> Bool

Check if the test run result was a success

Running tests verbosely

verboseCheck :: Testable prop => prop -> IO ()

Tests a property and prints the results and all test cases generated to stdout. This is just a convenience function that means the same as quickCheck . verbose.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

verboseCheckWith :: Testable prop => Args -> prop -> IO ()

Tests a property, using test arguments, and prints the results and all test cases generated to stdout. This is just a convenience function that combines quickCheckWith and verbose.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

verboseCheckWithResult :: Testable prop => Args -> prop -> IO Result

Tests a property, using test arguments, produces a test result, and prints the results and all test cases generated to stdout. This is just a convenience function that combines quickCheckWithResult and verbose.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

verboseCheckResult :: Testable prop => prop -> IO Result

Tests a property, produces a test result, and prints the results and all test cases generated to stdout. This is just a convenience function that combines quickCheckResult and verbose.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

Testing all properties in a module

These functions test all properties in the current module, using Template Haskell. You need to have a {-# LANGUAGE TemplateHaskell #-} pragma in your module for any of these to work.

quickCheckAll :: Q Exp

Test all properties in the current module. The name of the property must begin with prop_. Polymorphic properties will be defaulted to Integer. Returns True if all tests succeeded, False otherwise.

To use quickCheckAll, add a definition to your module along the lines of

return []
runTests = $quickCheckAll

and then execute runTests.

Note: the bizarre return [] in the example above is needed on GHC 7.8 and later; without it, quickCheckAll will not be able to find any of the properties. For the curious, the return [] is a Template Haskell splice that makes GHC insert the empty list of declarations at that point in the program; GHC typechecks everything before the return [] before it starts on the rest of the module, which means that the later call to quickCheckAll can see everything that was defined before the return []. Yikes!

verboseCheckAll :: Q Exp

Test all properties in the current module. This is just a convenience function that combines quickCheckAll and verbose.

verboseCheckAll has the same issue with scoping as quickCheckAll: see the note there about return [].

forAllProperties :: Q Exp

Test all properties in the current module, using a custom quickCheck function. The same caveats as with quickCheckAll apply.

$forAllProperties has type (Property -> IO Result) -> IO Bool. An example invocation is $forAllProperties quickCheckResult, which does the same thing as $quickCheckAll.

forAllProperties has the same issue with scoping as quickCheckAll: see the note there about return [].

allProperties :: Q Exp

List all properties in the current module.

$allProperties has type [(String, Property)].

allProperties has the same issue with scoping as quickCheckAll: see the note there about return [].

Testing polymorphic properties

polyQuickCheck :: Name -> ExpQ

Test a polymorphic property, defaulting all type variables to Integer.

Invoke as $(polyQuickCheck 'prop), where prop is a property. Note that just evaluating quickCheck prop in GHCi will seem to work, but will silently default all type variables to ()!

$(polyQuickCheck 'prop) means the same as quickCheck $(monomorphic 'prop). If you want to supply custom arguments to polyQuickCheck, you will have to combine quickCheckWith and monomorphic yourself.

If you want to use polyQuickCheck in the same file where you defined the property, the same scoping problems pop up as in quickCheckAll: see the note there about return [].

polyVerboseCheck :: Name -> ExpQ

Test a polymorphic property, defaulting all type variables to Integer. This is just a convenience function that combines verboseCheck and monomorphic.

If you want to use polyVerboseCheck in the same file where you defined the property, the same scoping problems pop up as in quickCheckAll: see the note there about return [].

monomorphic :: Name -> ExpQ

Monomorphise an arbitrary property by defaulting all type variables to Integer.

For example, if f has type Ord a => [a] -> [a] then $(monomorphic 'f) has type [Integer] -> [Integer].

If you want to use monomorphic in the same file where you defined the property, the same scoping problems pop up as in quickCheckAll: see the note there about return [].

The Arbitrary typeclass: generation of random values

class Arbitrary a

Random generation and shrinking of values.

QuickCheck provides Arbitrary instances for most types in base, except those which incur extra dependencies. For a wider range of Arbitrary instances see the quickcheck-instances package.

arbitrary :: Gen a

A generator for values of the given type.

It is worth spending time thinking about what sort of test data you want - good generators are often the difference between finding bugs and not finding them. You can use sample, label and classify to check the quality of your test data.

There is no generic arbitrary implementation included because we don't know how to make a high-quality one. If you want one, consider using the testing-feat or generic-random packages.

The QuickCheck manual goes into detail on how to write good generators. Make sure to look at it, especially if your type is recursive!

shrink :: a -> [a]

Produces a (possibly) empty list of all the possible immediate shrinks of the given value.

The default implementation returns the empty list, so will not try to shrink the value. If your data type has no special invariants, you can enable shrinking by defining shrink = genericShrink, but by customising the behaviour of shrink you can often get simpler counterexamples.

Most implementations of shrink should try at least three things:

  1. Shrink a term to any of its immediate subterms. You can use subterms to do this.

  1. Recursively apply shrink to all immediate subterms. You can use recursivelyShrink to do this.

  1. Type-specific shrinkings such as replacing a constructor by a simpler constructor.

For example, suppose we have the following implementation of binary trees:

data Tree a = Nil | Branch a (Tree a) (Tree a)

We can then define shrink as follows:

shrink Nil = []
shrink (Branch x l r) =
  -- shrink Branch to Nil
  [Nil] ++
  -- shrink to non-Nil subterms
  [t | t@Branch{} <- [l, r]] ++
  -- recursively shrink subterms
  [Branch x' l' r' | (x', l', r') <- shrink (x, l, r)]

There are a couple of subtleties here:

  • QuickCheck tries the shrinking candidates in the order they appear in the list, so we put more aggressive shrinking steps (such as replacing the whole tree by Nil) before smaller ones (such as recursively shrinking the subtrees).

  • It is tempting to write the last line as [Branch x' l' r' | x' <- shrink x, l' <- shrink l, r' <- shrink r] but this is the wrong thing! It will force QuickCheck to shrink x, l and r in tandem, and shrinking will stop once one of the three is fully shrunk.

There is a fair bit of boilerplate in the code above. We can avoid it with the help of some generic functions. The function genericShrink tries shrinking a term to all of its subterms and, failing that, recursively shrinks the subterms. Using it, we can define shrink as:

shrink x = shrinkToNil x ++ genericShrink x
  where
    shrinkToNil Nil = []
    shrinkToNil (Branch _ l r) = [Nil]

genericShrink is a combination of subterms, which shrinks a term to any of its subterms, and recursivelyShrink, which shrinks all subterms of a term. These may be useful if you need a bit more control over shrinking than genericShrink gives you.

A final gotcha: we cannot define shrink as simply shrink x = Nil:genericShrink x as this shrinks Nil to Nil, and shrinking will go into an infinite loop.

If all this leaves you bewildered, you might try shrink = genericShrink to begin with, after deriving Generic for your type. However, if your data type has any special invariants, you will need to check that genericShrink can't break those invariants.

Helper functions for implementing shrink

genericShrink :: (Generic a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a]

Shrink a term to any of its immediate subterms, and also recursively shrink all subterms.

subterms :: (Generic a, GSubterms (Rep a) a) => a -> [a]

All immediate subterms of a term.

recursivelyShrink :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a]

Recursively shrink all immediate subterms.

shrinkList :: (a -> [a]) -> [a] -> [[a]]

Shrink a list of values given a shrinking function for individual values.

shrinkMap :: Arbitrary a => (a -> b) -> (b -> a) -> b -> [b]

Map a shrink function to another domain. This is handy if your data type has special invariants, but is almost isomorphic to some other type.

shrinkOrderedList :: (Ord a, Arbitrary a) => [a] -> [[a]]
shrinkOrderedList = shrinkMap sort id

shrinkSet :: (Ord a, Arbitrary a) => Set a -> [Set a]
shrinkSet = shrinkMap fromList toList

shrinkMapBy :: (a -> b) -> (b -> a) -> (a -> [a]) -> b -> [b]

Non-overloaded version of `shrinkMap`.

shrinkRealFrac :: RealFrac a => a -> [a]

Shrink a fraction, preferring numbers with smaller numerators or denominators. See also shrinkDecimal.

shrinkBoundedEnum :: (Bounded a, Enum a, Eq a) => a -> [a]

Shrink an element of a bounded enumeration.

Example

data MyEnum = E0 | E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9
   deriving (Bounded, Enum, Eq, Ord, Show)

shrinkDecimal :: RealFrac a => a -> [a]

Shrink a real number, preferring numbers with shorter decimal representations. See also shrinkRealFrac.

Lifting of Arbitrary to unary and binary type constructors

arbitrary1 :: (Arbitrary1 f, Arbitrary a) => Gen (f a)

shrink1 :: (Arbitrary1 f, Arbitrary a) => f a -> [f a]

class Arbitrary2 f

Lifting of the Arbitrary class to binary type constructors.

liftShrink2 :: (a -> [a]) -> (b -> [b]) -> f a b -> [f a b]

arbitrary2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => Gen (f a b)

shrink2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => f a b -> [f a b]

The Gen monad: combinators for building random generators

Generator combinators

choose :: Random a => (a, a) -> Gen a

Generates a random element in the given inclusive range. For integral and enumerated types, the specialised variants of choose below run much quicker.

chooseInt :: (Int, Int) -> Gen Int

A fast implementation of choose for Int.

chooseInteger :: (Integer, Integer) -> Gen Integer

A fast implementation of choose for Integer.

chooseBoundedIntegral :: (Bounded a, Integral a) => (a, a) -> Gen a

A fast implementation of choose for bounded integral types.

chooseEnum :: Enum a => (a, a) -> Gen a

A fast implementation of choose for enumerated types.

chooseAny :: Random a => Gen a

Generates a random element over the natural range of a.

oneof :: HasCallStack => [Gen a] -> Gen a

Randomly uses one of the given generators. The input list must be non-empty.

frequency :: HasCallStack => [(Int, Gen a)] -> Gen a

Chooses one of the given generators, with a weighted random distribution. The input list must be non-empty.

elements :: HasCallStack => [a] -> Gen a

Generates one of the given values. The input list must be non-empty.

growingElements :: HasCallStack => [a] -> Gen a

Takes a list of elements of increasing size, and chooses among an initial segment of the list. The size of this initial segment increases with the size parameter. The input list must be non-empty.

sized :: (Int -> Gen a) -> Gen a

Used to construct generators that depend on the size parameter.

For example, listOf, which uses the size parameter as an upper bound on length of lists it generates, can be defined like this:

listOf :: Gen a -> Gen [a]
listOf gen = sized $ \n ->
  do k <- choose (0,n)
     vectorOf k gen

You can also do this using getSize.

getSize :: Gen Int

Returns the size parameter. Used to construct generators that depend on the size parameter.

For example, listOf, which uses the size parameter as an upper bound on length of lists it generates, can be defined like this:

listOf :: Gen a -> Gen [a]
listOf gen = do
  n <- getSize
  k <- choose (0,n)
  vectorOf k gen

You can also do this using sized.

resize :: HasCallStack => Int -> Gen a -> Gen a

Overrides the size parameter. Returns a generator which uses the given size instead of the runtime-size parameter.

scale :: (Int -> Int) -> Gen a -> Gen a

Adjust the size parameter, by transforming it with the given function.

suchThat :: Gen a -> (a -> Bool) -> Gen a

Generates a value that satisfies a predicate.

suchThatMap :: Gen a -> (a -> Maybe b) -> Gen b

Generates a value for which the given function returns a Just, and then applies the function.

suchThatMaybe :: Gen a -> (a -> Bool) -> Gen (Maybe a)

Tries to generate a value that satisfies a predicate. If it fails to do so after enough attempts, returns Nothing.

applyArbitrary2 :: (Arbitrary a, Arbitrary b) => (a -> b -> r) -> Gen r

Apply a binary function to random arguments.

applyArbitrary3 :: (Arbitrary a, Arbitrary b, Arbitrary c) => (a -> b -> c -> r) -> Gen r

Apply a ternary function to random arguments.

applyArbitrary4 :: (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => (a -> b -> c -> d -> r) -> Gen r

Apply a function of arity 4 to random arguments.

Generators for lists

listOf :: Gen a -> Gen [a]

Generates a list of random length. The maximum length depends on the size parameter.

listOf1 :: Gen a -> Gen [a]

Generates a non-empty list of random length. The maximum length depends on the size parameter.

vectorOf :: Int -> Gen a -> Gen [a]

Generates a list of the given length.

vector :: Arbitrary a => Int -> Gen [a]

Generates a list of a given length.

infiniteList :: Arbitrary a => Gen [a]

Generates an infinite list.

shuffle :: [a] -> Gen [a]

Generates a random permutation of the given list.

sublistOf :: [a] -> Gen [a]

Generates a random subsequence of the given list.

orderedList :: (Ord a, Arbitrary a) => Gen [a]

Generates an ordered list.

Generators for particular types

arbitrarySizedIntegral :: Integral a => Gen a

Generates an integral number. The number can be positive or negative and its maximum absolute value depends on the size parameter.

arbitrarySizedNatural :: Integral a => Gen a

Generates a natural number. The number's maximum value depends on the size parameter.

arbitrarySizedFractional :: Fractional a => Gen a

Uniformly generates a fractional number. The number can be positive or negative and its maximum absolute value depends on the size parameter.

arbitrarySizedBoundedIntegral :: (Bounded a, Integral a) => Gen a

Generates an integral number from a bounded domain. The number is chosen from the entire range of the type, but small numbers are generated more often than big numbers. Inspired by demands from Phil Wadler.

arbitraryBoundedIntegral :: (Bounded a, Integral a) => Gen a

Generates an integral number. The number is chosen uniformly from the entire range of the type. You may want to use arbitrarySizedBoundedIntegral instead.

arbitraryBoundedRandom :: (Bounded a, Random a) => Gen a

Generates an element of a bounded type. The element is chosen from the entire range of the type.

arbitraryBoundedEnum :: (Bounded a, Enum a) => Gen a

Generates an element of a bounded enumeration.

Running generators

generate :: Gen a -> IO a

Run a generator. The size passed to the generator is always 30; if you want another size then you should explicitly use resize.

Debugging generators

sample :: Show a => Gen a -> IO ()

Generates some example values and prints them to stdout.

sample' :: Gen a -> IO [a]

Generates some example values.

The Function typeclass: generation of random shrinkable, showable functions

Example of use:

To generate random values of type Fun a b, you must have an instance Function a. If your type has a Show instance, you can use functionShow to write the instance; otherwise, use functionMap to give a bijection between your type and a type that is already an instance of Function. See the Function [a] instance for an example of the latter.

For more information, see the paper "Shrinking and showing functions" by Koen Claessen.

data Fun a b

Generation of random shrinkable, showable functions.

To generate random values of type Fun a b, you must have an instance Function a.

See also applyFun, and Fn with GHC >= 7.8.

Fun :: (a :-> b, b, Shrunk) -> (a -> b) -> Fun a b

applyFun :: Fun a b -> (a -> b)

Extracts the value of a function.

Fn is the pattern equivalent of this function.

prop :: Fun String Integer -> Bool
prop f = applyFun f "banana" == applyFun f "monkey"
      || applyFun f "banana" == applyFun f "elephant"

applyFun2 :: Fun (a, b) c -> (a -> b -> c)

Extracts the value of a binary function.

Fn2 is the pattern equivalent of this function.

prop_zipWith :: Fun (Int, Bool) Char -> [Int] -> [Bool] -> Bool
prop_zipWith f xs ys = zipWith (applyFun2 f) xs ys == [ applyFun2 f x y | (x, y) <- zip xs ys]

applyFun3 :: Fun (a, b, c) d -> (a -> b -> c -> d)

Extracts the value of a ternary function. Fn3 is the pattern equivalent of this function.

Fn :: (a -> b) -> Fun a b

A modifier for testing functions.

prop :: Fun String Integer -> Bool
prop (Fn f) = f "banana" == f "monkey"
           || f "banana" == f "elephant"

Fn2 :: (a -> b -> c) -> Fun (a, b) c

A modifier for testing binary functions.

prop_zipWith :: Fun (Int, Bool) Char -> [Int] -> [Bool] -> Bool
prop_zipWith (Fn2 f) xs ys = zipWith f xs ys == [ f x y | (x, y) <- zip xs ys]

Fn3 :: (a -> b -> c -> d) -> Fun (a, b, c) d

A modifier for testing ternary functions.

class Function a

The class Function a is used for random generation of showable functions of type a -> b.

There is a default implementation for function, which you can use if your type has structural equality. Otherwise, you can normally use functionMap or functionShow.

functionMap :: Function b => (a -> b) -> (b -> a) -> (a -> c) -> (a :-> c)

The basic building block for Function instances. Provides a Function instance by mapping to and from a type that already has a Function instance.

functionShow :: (Show a, Read a) => (a -> c) -> (a :-> c)

Provides a Function instance for types with Show and Read.

functionIntegral :: Integral a => (a -> b) -> (a :-> b)

Provides a Function instance for types with Integral.

functionRealFrac :: RealFrac a => (a -> b) -> (a :-> b)

Provides a Function instance for types with RealFrac.

functionBoundedEnum :: (Eq a, Bounded a, Enum a) => (a -> b) -> (a :-> b)

Provides a Function instance for types with Bounded and Enum. Use only for small types (i.e. not integers): creates the list [minBound..maxBound]!

functionVoid :: (forall b. void -> b) -> void :-> c

Provides a Function instance for types isomorphic to Void.

An actual Function Void instance is defined in quickcheck-instances.

The CoArbitrary typeclass: generation of functions the old-fashioned way

class CoArbitrary a

Used for random generation of functions. You should consider using Fun instead, which can show the generated functions as strings.

If you are using a recent GHC, there is a default definition of coarbitrary using genericCoarbitrary, so if your type has a Generic instance it's enough to say

instance CoArbitrary MyType

You should only use genericCoarbitrary for data types where equality is structural, i.e. if you can't have two different representations of the same value. An example where it's not safe is sets implemented using binary search trees: the same set can be represented as several different trees. Here you would have to explicitly define coarbitrary s = coarbitrary (toList s).

coarbitrary :: a -> Gen b -> Gen b

Used to generate a function of type a -> b. The first argument is a value, the second a generator. You should use variant to perturb the random generator; the goal is that different values for the first argument will lead to different calls to variant. An example will help:

instance CoArbitrary a => CoArbitrary [a] where
  coarbitrary []     = 'variant' 0
  coarbitrary (x:xs) = 'variant' 1 . coarbitrary (x,xs)

genericCoarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b

Generic CoArbitrary implementation.

variant :: Integral n => n -> Gen a -> Gen a

Modifies a generator using an integer seed.

coarbitraryIntegral :: Integral a => a -> Gen b -> Gen b

A coarbitrary implementation for integral numbers.

coarbitraryReal :: Real a => a -> Gen b -> Gen b

A coarbitrary implementation for real numbers.

coarbitraryShow :: Show a => a -> Gen b -> Gen b

coarbitrary helper for lazy people :-).

coarbitraryEnum :: Enum a => a -> Gen b -> Gen b

A coarbitrary implementation for enums.

(><) :: (Gen a -> Gen a) -> (Gen a -> Gen a) -> (Gen a -> Gen a)

Use ordinary function composition instead

Combine two generator perturbing functions, for example the results of calls to variant or coarbitrary.

Type-level modifiers for changing generator behavior

These types do things such as restricting the kind of test data that can be generated. They can be pattern-matched on in properties as a stylistic alternative to using explicit quantification.

Examples:

-- Functions cannot be shown (but see 'Function')
prop_TakeDropWhile ('Blind' p) (xs :: ['Test.QuickCheck.Poly.A']) =
  takeWhile p xs ++ dropWhile p xs == xs

prop_TakeDrop ('NonNegative' n) (xs :: ['Test.QuickCheck.Poly.A']) =
  take n xs ++ drop n xs == xs

-- cycle does not work for empty lists
prop_Cycle ('NonNegative' n) ('NonEmpty' (xs :: ['Test.QuickCheck.Poly.A'])) =
  take n (cycle xs) == take n (xs ++ cycle xs)

-- Instead of 'forAll' 'orderedList'
prop_Sort ('Ordered' (xs :: ['Test.QuickCheck.Poly.OrdA'])) =
  sort xs == xs

newtype Blind a

Blind x: as x, but x does not have to be in the Show class.

newtype Fixed a

Fixed x: as x, but will not be shrunk.

data InfiniteList a

InfiniteList xs _: guarantees that xs is an infinite list. When a counterexample is found, only prints the prefix of xs that was used by the program.

Here is a contrived example property:

prop_take_10 :: InfiniteList Char -> Bool
prop_take_10 (InfiniteList xs _) =
  or [ x == \'a\' | x <- take 10 xs ]

In the following counterexample, the list must start with "bbbbbbbbbb" but the remaining (infinite) part can contain anything:

newtype SortedList a

Sorted xs: guarantees that xs is sorted.

newtype Large a

Large x: by default, QuickCheck generates Ints drawn from a small range. Large Int gives you values drawn from the entire range instead.

newtype Small a

Small x: generates values of x drawn from a small range. The opposite of Large.

data Smart a

Smart _ x: tries a different order when shrinking.

Smart :: Int -> a -> Smart a

newtype Shrink2 a

Shrink2 x: allows 2 shrinking steps at the same time when shrinking x

data Shrinking s a

Shrinking _ x: allows for maintaining a state during shrinking.

Property combinators

newtype Property

The type of properties.

class Testable prop

The class of properties, i.e., types which QuickCheck knows how to test. Typically a property will be a function returning Bool or Property.

property :: prop -> Property

Convert the thing to a property.

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> prop) -> Property

Optional; used internally in order to improve shrinking. Tests a property but also quantifies over an extra value (with a custom shrink and show function). The Testable instance for functions defines propertyForAllShrinkShow in a way that improves shrinking.

forAll :: (Show a, Testable prop) => Gen a -> (a -> prop) -> Property

Explicit universal quantification: uses an explicitly given test case generator.

forAllShrink :: (Show a, Testable prop) => Gen a -> (a -> [a]) -> (a -> prop) -> Property

Like forAll, but tries to shrink the argument for failing test cases.

forAllShow :: Testable prop => Gen a -> (a -> String) -> (a -> prop) -> Property

Like forAll, but with an explicitly given show function.

forAllShrinkShow :: Testable prop => Gen a -> (a -> [a]) -> (a -> String) -> (a -> prop) -> Property

Like forAllShrink, but with an explicitly given show function.

forAllBlind :: Testable prop => Gen a -> (a -> prop) -> Property

Like forAll, but without printing the generated value.

forAllShrinkBlind :: Testable prop => Gen a -> (a -> [a]) -> (a -> prop) -> Property

Like forAllShrink, but without printing the generated value.

shrinking :: Testable prop => (a -> [a]) -> a -> (a -> prop) -> Property

Shrinks the argument to a property if it fails. Shrinking is done automatically for most types. This function is only needed when you want to override the default behavior.

(a -> [a])

shrink-like function.

a

The original argument

(==>) :: Testable prop => Bool -> prop -> Property

Implication for properties: The resulting property holds if the first argument is False (in which case the test case is discarded), or if the given property holds. Note that using implication carelessly can severely skew test case distribution: consider using cover to make sure that your test data is still good quality.

data Discard

If a property returns Discard, the current test case is discarded, the same as if a precondition was false.

An example is the definition of ==>:

(==>) :: Testable prop => Bool -> prop -> Property
False ==> _ = property Discard
True  ==> p = property p

discard :: a

A special error value. If a property evaluates discard, it causes QuickCheck to discard the current test case. This can be useful if you want to discard the current test case, but are somewhere you can't use ==>, such as inside a generator.

(===) :: (Eq a, Show a) => a -> a -> Property

(=/=) :: (Eq a, Show a) => a -> a -> Property

total :: NFData a => a -> Property

Checks that a value is total, i.e., doesn't crash when evaluated.

ioProperty :: Testable prop => IO prop -> Property

Do I/O inside a property.

Warning: any random values generated inside of the argument to ioProperty will not currently be shrunk. For best results, generate all random values before calling ioProperty, or use idempotentIOProperty if that is safe.

idempotentIOProperty :: Testable prop => IO prop -> Property

Do I/O inside a property.

Warning: during shrinking, the I/O may not always be re-executed. Instead, the I/O may be executed once and then its result retained. If this is not acceptable, use ioProperty instead.

Controlling property execution

verbose :: Testable prop => prop -> Property

Prints out the generated test case every time the property is tested. Only variables quantified over inside the verbose are printed.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

verboseShrinking :: Testable prop => prop -> Property

Prints out the generated test case every time the property fails, including during shrinking. Only variables quantified over inside the verboseShrinking are printed.

Note: for technical reasons, the test case is printed out after the property is tested. To debug a property that goes into an infinite loop, use within to add a timeout instead.

noShrinking :: Testable prop => prop -> Property

Disables shrinking for a property altogether. Only quantification inside the call to noShrinking is affected.

withNumTests :: Testable prop => Int -> prop -> Property

Configures how many times a property will be tested.

For example,

quickCheck (withNumTests 1000 p)

will test p up to 1000 times.

withMaxSuccess :: Testable prop => Int -> prop -> Property

Use withNumTests instead

Configures how many times a property will be tested.

For example,

quickCheck (withMaxSuccess 1000 p)

will test p up to 1000 times.

within :: Testable prop => Int -> prop -> Property

Considers a property failed if it does not complete within the given number of microseconds.

Note: if the property times out, variables quantified inside the `within` will not be printed. Therefore, you should use `within` only in the body of your property.

Good: prop_foo a b c = within 1000000 ...

Bad: prop_foo = within 1000000 $ \a b c -> ...

Bad: prop_foo a b c = ...; main = quickCheck (within 1000000 prop_foo)

discardAfter :: Testable prop => Int -> prop -> Property

Discards the test case if it does not complete within the given number of microseconds. This can be useful when testing algorithms that have pathological cases where they run extremely slowly.

withDiscardRatio :: Testable prop => Int -> prop -> Property

Configures how many times a property is allowed to be discarded before failing.

For example,

quickCheck (withDiscardRatio 10 p)

will allow p to fail up to 10 times per successful test.

withMaxSize :: Testable prop => Int -> prop -> Property

Configure the maximum size a property will be tested at.

withMaxShrinks :: Testable prop => Int -> prop -> Property

Configure the maximum number of times a property will be shrunk.

For example,

quickCheck (withMaxShrinks 100 p)

will cause p to only attempt 100 shrinks on failure.

once :: Testable prop => prop -> Property

Modifies a property so that it only will be tested once. Opposite of again.

again :: Testable prop => prop -> Property

Modifies a property so that it will be tested repeatedly. Opposite of once.

mapSize :: Testable prop => (Int -> Int) -> prop -> Property

Adjust the test case size for a property, by transforming it with the given function.

Conjunction and disjunction

(.&.) :: (Testable prop1, Testable prop2) => prop1 -> prop2 -> Property

Nondeterministic choice: p1 .&. p2 picks randomly one of p1 and p2 to test. If you test the property 100 times it makes 100 random choices.

(.&&.) :: (Testable prop1, Testable prop2) => prop1 -> prop2 -> Property

Conjunction: p1 .&&. p2 passes if both p1 and p2 pass.

conjoin :: Testable prop => [prop] -> Property

Take the conjunction of several properties.

data Every

Conjunction monoid built with `.&&.`.

Use `property @Every` as an accessor which doesn't leak existential variables.

Note: monoid laws are satisfied up to isSuccess unless one is using `checkCoverage`.

Every :: forall p. Testable p => p -> Every

(.||.) :: (Testable prop1, Testable prop2) => prop1 -> prop2 -> Property

Disjunction: p1 .||. p2 passes unless p1 and p2 simultaneously fail.

disjoin :: Testable prop => [prop] -> Property

Take the disjunction of several properties.

data Some

Disjunction monoid built with `.||.`.

Use `property @Some` as an accessor which doesn't leak existential variables.

Note: monoid laws are satisfied up to isSuccess unless one is using `checkCoverage`.

Some :: forall p. Testable p => p -> Some

What to do on failure

data Witness

Wit :: forall a. (Typeable a, Show a) => a -> Witness

witness :: (Typeable a, Show a, Testable prop) => a -> prop -> Property

Return a value in the witnesses field of the Result returned by quickCheckResult. Witnesses are returned outer-most first.

In ghci, for example:

counterexample :: Testable prop => String -> prop -> Property

Adds the given string to the counterexample if the property fails.

printTestCase :: Testable prop => String -> prop -> Property

Use counterexample instead

Adds the given string to the counterexample if the property fails.

withProgress :: Testable prop => (TestProgress -> IO ()) -> prop -> Property

Performs an IO action every time a property is tested, after every test. The IO action is allowed to depend on TestProgress, which contains information regarding how testing is progressing.

Note: QC invokes callbacks before the internal state has been updated to reflect the most recent test. The means that e.g. currentPassed will, after the first test has been executed, still show 0.

whenFail :: Testable prop => IO () -> prop -> Property

Performs an IO action after the last failure of a property.

whenFail' :: Testable prop => IO () -> prop -> Property

Performs an IO action every time a property fails. Thus, if shrinking is done, this can be used to keep track of the failures along the way.

expectFailure :: Testable prop => prop -> Property

Indicates that a property is supposed to fail. QuickCheck will report an error if it does not fail.

Analysing test case distribution

label :: Testable prop => String -> prop -> Property

Attaches a label to a test case. This is used for reporting test case distribution.

For example:

prop_reverse_reverse :: [Int] -> Property
prop_reverse_reverse xs =
  label ("length of input is " ++ show (length xs)) $
    reverse (reverse xs) === xs

Each use of label in your property results in a separate table of test case distribution in the output. If this is not what you want, use tabulate.

collect :: (Show a, Testable prop) => a -> prop -> Property

Attaches a label to a test case. This is used for reporting test case distribution.

collect x = label (show x)

For example:

prop_reverse_reverse :: [Int] -> Property
prop_reverse_reverse xs =
  collect (length xs) $
    reverse (reverse xs) === xs

Each use of collect in your property results in a separate table of test case distribution in the output. If this is not what you want, use tabulate.

classify :: Testable prop => Bool -> String -> prop -> Property

Reports how many test cases satisfy a given condition.

For example:

prop_sorted_sort :: [Int] -> Property
prop_sorted_sort xs =
  sorted xs ==>
  classify (length xs > 1) "non-trivial" $
  sort xs === xs
Bool

True if the test case should be labelled.

String

Label.

tabulate :: Testable prop => String -> [String] -> prop -> Property

Collects information about test case distribution into a table. The arguments to tabulate are the table's name and a list of values associated with the current test case. After testing, QuickCheck prints the frequency of all collected values. The frequencies are expressed as a percentage of the total number of values collected.

You should prefer tabulate to label when each test case is associated with a varying number of values. Here is a (not terribly useful) example, where the test data is a list of integers and we record all values that occur in the list:

prop_sorted_sort :: [Int] -> Property
prop_sorted_sort xs =
  sorted xs ==>
  tabulate "List elements" (map show xs) $
  sort xs === xs

Here is a more useful example. We are testing a chatroom, where the user can log in, log out, or send a message:

data Command = LogIn | LogOut | SendMessage String deriving (Data, Show)
instance Arbitrary Command where ...

There are some restrictions on command sequences; for example, the user must log in before doing anything else. The function valid :: [Command] -> Bool checks that a command sequence is allowed. Our property then has the form:

prop_chatroom :: [Command] -> Property
prop_chatroom cmds =
  valid cmds ==>
    ...

The use of ==> may skew test case distribution. We use collect to see the length of the command sequences, and tabulate to get the frequencies of the individual commands:

prop_chatroom :: [Command] -> Property
prop_chatroom cmds =
  wellFormed cmds LoggedOut ==>
  'collect' (length cmds) $
  'tabulate' "Commands" (map (show . 'Data.Data.toConstr') cmds) $
    ...

Checking test case distribution

cover :: Testable prop => Double -> Bool -> String -> prop -> Property

Checks that at least the given proportion of successful test cases belong to the given class. Discarded tests (i.e. ones with a false precondition) do not affect coverage.

Note: If the coverage check fails, QuickCheck prints out a warning, but the property does not fail. To make the property fail, use checkCoverage.

For example:

prop_sorted_sort :: [Int] -> Property
prop_sorted_sort xs =
  sorted xs ==>
  cover 50 (length xs > 1) "non-trivial" $
  sort xs === xs
Double

The required percentage (0-100) of test cases.

Bool

True if the test case belongs to the class.

String

Label for the test case class.

coverTable :: Testable prop => String -> [(String, Double)] -> prop -> Property

Checks that the values in a given table appear a certain proportion of the time. A call to coverTable table [(x1, p1), ..., (xn, pn)] asserts that of the values in table, x1 should appear at least p1 percent of the time that table appears, x2 at least p2 percent of the time that table appears, and so on.

Note: If the coverage check fails, QuickCheck prints out a warning, but the property does not fail. To make the property fail, use checkCoverage.

Continuing the example from the tabulate combinator...

data Command = LogIn | LogOut | SendMessage String deriving (Data, Show)
prop_chatroom :: [Command] -> Property
prop_chatroom cmds =
  wellFormed cmds LoggedOut ==>
  'tabulate' "Commands" (map (show . 'Data.Data.toConstr') cmds) $
    ...

...we can add a coverage requirement as follows, which checks that LogIn, LogOut and SendMessage each occur at least 25% of the time:

prop_chatroom :: [Command] -> Property
prop_chatroom cmds =
  wellFormed cmds LoggedOut ==>
  coverTable "Commands" [("LogIn", 25), ("LogOut", 25), ("SendMessage", 25)] $
  'tabulate' "Commands" (map (show . 'Data.Data.toConstr') cmds) $
    ... property goes here ...

checkCoverage :: Testable prop => prop -> Property

Check that all coverage requirements defined by cover and coverTable are met, using a statistically sound test, and fail if they are not met.

Ordinarily, a failed coverage check does not cause the property to fail. This is because the coverage requirement is not tested in a statistically sound way. If you use cover to express that a certain value must appear 20% of the time, QuickCheck will warn you if the value only appears in 19 out of 100 test cases - but since the coverage varies randomly, you may have just been unlucky, and there may not be any real problem with your test generation.

When you use checkCoverage, QuickCheck uses a statistical test to account for the role of luck in coverage failures. It will run as many tests as needed until it is sure about whether the coverage requirements are met. If a coverage requirement is not met, the property fails.

Example:

quickCheck (checkCoverage prop_foo)

checkCoverageWith :: Testable prop => Confidence -> prop -> Property

Check coverage requirements using a custom confidence level. See stdConfidence.

An example of making the statistical test less stringent in order to improve performance:

quickCheck (checkCoverageWith stdConfidence{certainty = 10^6} prop_foo)

data Confidence

The statistical parameters used by checkCoverage.

Confidence :: Integer -> Double -> Confidence

certainty :: Confidence -> Integer

How certain checkCoverage must be before the property fails. If the coverage requirement is met, and the certainty parameter is n, then you should get a false positive at most one in n runs of QuickCheck. The default value is 10^9.

Lower values will speed up checkCoverage at the cost of false positives.

If you are using checkCoverage as part of a test suite, you should be careful not to set certainty too low. If you want, say, a 1% chance of a false positive during a project's lifetime, then certainty should be set to at least 100 * m * n, where m@ is the number of uses of cover in the test suite, and n is the number of times you expect the test suite to be run during the project's lifetime. The default value is chosen to be big enough for most projects.

tolerance :: Confidence -> Double

For statistical reasons, checkCoverage will not reject coverage levels that are only slightly below the required levels. If the required level is p then an actual level of tolerance * p will be accepted. The default value is 0.9.

Lower values will speed up checkCoverage at the cost of not detecting minor coverage violations.

stdConfidence :: Confidence

The standard parameters used by checkCoverage: certainty = 10^9, tolerance = 0.9. See Confidence for the meaning of the parameters.

Generating example test cases

labelledExamples :: Testable prop => prop -> IO ()

Given a property, which must use label, collect, classify or cover to associate labels with test cases, find an example test case for each possible label. The example test cases are minimised using shrinking.

For example, suppose we test delete x xs and record the number of times that x occurs in xs:

prop_delete :: Int -> [Int] -> Property
prop_delete x xs =
  classify (count x xs == 0) "count x xs == 0" $
  classify (count x xs == 1) "count x xs == 1" $
  classify (count x xs >= 2) "count x xs >= 2" $
  counterexample (show (delete x xs)) $
  count x (delete x xs) == max 0 (count x xs-1)
  where count x xs = length (filter (== x) xs)

labelledExamples generates three example test cases, one for each label:

labelledExamplesWith :: Testable prop => Args -> prop -> IO ()

A variant of labelledExamples that takes test arguments.

labelledExamplesWithResult :: Testable prop => Args -> prop -> IO Result

A variant of labelledExamples that takes test arguments and returns a result.

labelledExamplesResult :: Testable prop => prop -> IO Result

A variant of labelledExamples that returns a result.

Build record and source files

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