Test.QuickCheck.Arbitrary

Type classes for random generation of values.

Arbitrary and CoArbitrary classes

class Arbitrary a where

Random generation and shrinking of values.

Minimal complete definition

Nothing

Methods

arbitrary :: Gen a

A generator for values of the given type.

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.

Most implementations of shrink should try at least three things:

1. Shrink a term to any of its immediate subterms.
2. Recursively apply shrink to all immediate subterms.
3. 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 subterms
  [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; note that these only work on GHC 7.2 and above. 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.

Instances

Arbitrary Bool

Arbitrary Char

Arbitrary Double

Arbitrary Float

Arbitrary Int

Arbitrary Int8

Arbitrary Int16

Arbitrary Int32

Arbitrary Int64

Arbitrary Integer

Arbitrary Ordering

Arbitrary Word

Arbitrary Word8

Arbitrary Word16

Arbitrary Word32

Arbitrary Word64

Arbitrary ()

Arbitrary OrdC

Arbitrary OrdB

Arbitrary OrdA

Arbitrary C

Arbitrary B

Arbitrary A

Arbitrary a => Arbitrary [a]

(Integral a, Arbitrary a) => Arbitrary (Ratio a)

HasResolution a => Arbitrary (Fixed a)

(RealFloat a, Arbitrary a) => Arbitrary (Complex a)

Arbitrary a => Arbitrary (Maybe a)

Arbitrary a => Arbitrary (Smart a)

Arbitrary a => Arbitrary (Shrink2 a)

Integral a => Arbitrary (Small a)

(Integral a, Bounded a) => Arbitrary (Large a)

(Num a, Ord a, Arbitrary a) => Arbitrary (NonNegative a)

(Num a, Ord a, Arbitrary a) => Arbitrary (NonZero a)

(Num a, Ord a, Arbitrary a) => Arbitrary (Positive a)

Arbitrary a => Arbitrary (NonEmptyList a)

(Ord a, Arbitrary a) => Arbitrary (OrderedList a)

Arbitrary a => Arbitrary (Fixed a)

Arbitrary a => Arbitrary (Blind a)

(CoArbitrary a, Arbitrary b) => Arbitrary (a -> b)

(Arbitrary a, Arbitrary b) => Arbitrary (Either a b)

(Arbitrary a, Arbitrary b) => Arbitrary (a, b)

(Arbitrary a, ShrinkState s a) => Arbitrary (Shrinking s a)

(Function a, CoArbitrary a, Arbitrary b) => Arbitrary (Fun a b)

(Function a, CoArbitrary a, Arbitrary b) => Arbitrary ((:->) a b)

(Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a, b, c)

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (a, b, c, d)

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => Arbitrary (a, b, c, d, e)

class CoArbitrary a where

Used for random generation of functions.

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).

Minimal complete definition

Nothing

Methods

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)

Instances

CoArbitrary Bool

CoArbitrary Char

CoArbitrary Double

CoArbitrary Float

CoArbitrary Int

CoArbitrary Int8

CoArbitrary Int16

CoArbitrary Int32

CoArbitrary Int64

CoArbitrary Integer

CoArbitrary Ordering

CoArbitrary Word

CoArbitrary Word8

CoArbitrary Word16

CoArbitrary Word32

CoArbitrary Word64

CoArbitrary ()

CoArbitrary OrdC

CoArbitrary OrdB

CoArbitrary OrdA

CoArbitrary C

CoArbitrary B

CoArbitrary A

CoArbitrary a => CoArbitrary [a]

(Integral a, CoArbitrary a) => CoArbitrary (Ratio a)

HasResolution a => CoArbitrary (Fixed a)

(RealFloat a, CoArbitrary a) => CoArbitrary (Complex a)

CoArbitrary a => CoArbitrary (Maybe a)

(Arbitrary a, CoArbitrary b) => CoArbitrary (a -> b)

(CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b)

(CoArbitrary a, CoArbitrary b) => CoArbitrary (a, b)

(CoArbitrary a, CoArbitrary b, CoArbitrary c) => CoArbitrary (a, b, c)

(CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d) => CoArbitrary (a, b, c, d)

(CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d, CoArbitrary e) => CoArbitrary (a, b, c, d, e)

Helper functions for implementing arbitrary

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.

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.

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.

arbitrarySizedFractional :: Fractional a => Gen a

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

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.

Helper functions for implementing shrink

genericShrink :: (Generic a, Arbitrary 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, Arbitrary 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.

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

Generic CoArbitrary implementation.

shrinkNothing :: a -> [a]

Returns no shrinking alternatives.

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

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

shrinkIntegral :: Integral a => a -> [a]

Shrink an integral number.

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

Shrink a fraction.

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

Shrink a fraction, but only shrink to integral values.

Helper functions for implementing coarbitrary

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

Deprecated: Use ordinary function composition instead

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

Generators which use arbitrary

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

Generates a list of a given length.

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

Generates an ordered list of a given length.

infiniteList :: Arbitrary a => Gen [a]

Generate an infinite list.