Test.QuickCheck.Arbitrary

QuickCheck-2.8.2: Automatic testing of Haskell programs

Safe Haskell | Safe
Language | Haskell98

Test.QuickCheck.Arbitrary

Contents

- Arbitrary and CoArbitrary classes
  - Helper functions for implementing arbitrary
  - Helper functions for implementing shrink
  - Helper functions for implementing coarbitrary
  - Generators which use arbitrary

Description

Type classes for random generation of values.

Synopsis

- class Arbitrary a where
- class CoArbitrary a where
- arbitrarySizedIntegral :: Integral a => Gen a
- arbitrarySizedNatural :: Integral a => Gen a
- arbitraryBoundedIntegral :: (Bounded a, Integral a) => Gen a
- arbitrarySizedBoundedIntegral :: (Bounded a, Integral a) => Gen a
- arbitrarySizedFractional :: Fractional a => Gen a
- arbitraryBoundedRandom :: (Bounded a, Random a) => Gen a
- arbitraryBoundedEnum :: (Bounded a, Enum a) => Gen a
- genericShrink :: (Generic a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a]
- subterms :: (Generic a, GSubterms (Rep a) a) => a -> [a]
- recursivelyShrink :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a]
- genericCoarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b
- shrinkNothing :: a -> [a]
- shrinkList :: (a -> [a]) -> [a] -> [[a]]
- shrinkIntegral :: Integral a => a -> [a]
- shrinkRealFrac :: RealFrac a => a -> [a]
- shrinkRealFracToInteger :: RealFrac a => a -> [a]
- coarbitraryIntegral :: Integral a => a -> Gen b -> Gen b
- coarbitraryReal :: Real a => a -> Gen b -> Gen b
- coarbitraryShow :: Show a => a -> Gen b -> Gen b
- coarbitraryEnum :: Enum a => a -> Gen b -> Gen b
- (><) :: (Gen a -> Gen a) -> (Gen a -> Gen a) -> Gen a -> Gen a
- vector :: Arbitrary a => Int -> Gen [a]
- orderedList :: (Ord a, Arbitrary a) => Gen [a]
- infiniteList :: Arbitrary a => Gen [a]

# Arbitrary and CoArbitrary classes

class Arbitrary a where #

Random generation and shrinking of values.

Minimal complete definition

arbitrary

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 # |
Methods arbitrary :: Gen Bool # shrink :: Bool -> [Bool] #
Arbitrary Char # |
Methods arbitrary :: Gen Char # shrink :: Char -> [Char] #
Arbitrary Double # |
Methods arbitrary :: Gen Double # shrink :: Double -> [Double] #
Arbitrary Float # |
Methods arbitrary :: Gen Float # shrink :: Float -> [Float] #
Arbitrary Int # |
Methods arbitrary :: Gen Int # shrink :: Int -> [Int] #
Arbitrary Int8 # |
Methods arbitrary :: Gen Int8 # shrink :: Int8 -> [Int8] #
Arbitrary Int16 # |
Methods arbitrary :: Gen Int16 # shrink :: Int16 -> [Int16] #
Arbitrary Int32 # |
Methods arbitrary :: Gen Int32 # shrink :: Int32 -> [Int32] #
Arbitrary Int64 # |
Methods arbitrary :: Gen Int64 # shrink :: Int64 -> [Int64] #
Arbitrary Integer # |
Methods arbitrary :: Gen Integer # shrink :: Integer -> [Integer] #
Arbitrary Natural # |
Methods arbitrary :: Gen Natural # shrink :: Natural -> [Natural] #
Arbitrary Ordering # |
Methods arbitrary :: Gen Ordering # shrink :: Ordering -> [Ordering] #
Arbitrary Word # |
Methods arbitrary :: Gen Word # shrink :: Word -> [Word] #
Arbitrary Word8 # |
Methods arbitrary :: Gen Word8 # shrink :: Word8 -> [Word8] #
Arbitrary Word16 # |
Methods arbitrary :: Gen Word16 # shrink :: Word16 -> [Word16] #
Arbitrary Word32 # |
Methods arbitrary :: Gen Word32 # shrink :: Word32 -> [Word32] #
Arbitrary Word64 # |
Methods arbitrary :: Gen Word64 # shrink :: Word64 -> [Word64] #
Arbitrary () # |
Methods arbitrary :: Gen () # shrink :: () -> [()] #
Arbitrary IntSet # |
Methods arbitrary :: Gen IntSet # shrink :: IntSet -> [IntSet] #
Arbitrary OrdC # |
Methods arbitrary :: Gen OrdC # shrink :: OrdC -> [OrdC] #
Arbitrary OrdB # |
Methods arbitrary :: Gen OrdB # shrink :: OrdB -> [OrdB] #
Arbitrary OrdA # |
Methods arbitrary :: Gen OrdA # shrink :: OrdA -> [OrdA] #
Arbitrary C # |
Methods arbitrary :: Gen C # shrink :: C -> [C] #
Arbitrary B # |
Methods arbitrary :: Gen B # shrink :: B -> [B] #
Arbitrary A # |
Methods arbitrary :: Gen A # shrink :: A -> [A] #
Arbitrary a => Arbitrary [a] # |
Methods arbitrary :: Gen [a] # shrink :: [a] -> [[a]] #
Arbitrary a => Arbitrary (Maybe a) # |
Methods arbitrary :: Gen (Maybe a) # shrink :: Maybe a -> [Maybe a] #
Integral a => Arbitrary (Ratio a) # |
Methods arbitrary :: Gen (Ratio a) # shrink :: Ratio a -> [Ratio a] #
(RealFloat a, Arbitrary a) => Arbitrary (Complex a) # |
Methods arbitrary :: Gen (Complex a) # shrink :: Complex a -> [Complex a] #
HasResolution a => Arbitrary (Fixed a) # |
Methods arbitrary :: Gen (Fixed a) # shrink :: Fixed a -> [Fixed a] #
Arbitrary a => Arbitrary (IntMap a) # |
Methods arbitrary :: Gen (IntMap a) # shrink :: IntMap a -> [IntMap a] #
Arbitrary a => Arbitrary (Seq a) # |
Methods arbitrary :: Gen (Seq a) # shrink :: Seq a -> [Seq a] #
(Ord a, Arbitrary a) => Arbitrary (Set a) # |
Methods arbitrary :: Gen (Set a) # shrink :: Set a -> [Set a] #
Arbitrary a => Arbitrary (Smart a) # |
Methods arbitrary :: Gen (Smart a) # shrink :: Smart a -> [Smart a] #
Arbitrary a => Arbitrary (Shrink2 a) # |
Methods arbitrary :: Gen (Shrink2 a) # shrink :: Shrink2 a -> [Shrink2 a] #
Integral a => Arbitrary (Small a) # |
Methods arbitrary :: Gen (Small a) # shrink :: Small a -> [Small a] #
(Integral a, Bounded a) => Arbitrary (Large a) # |
Methods arbitrary :: Gen (Large a) # shrink :: Large a -> [Large a] #
(Num a, Ord a, Arbitrary a) => Arbitrary (NonNegative a) # |
Methods arbitrary :: Gen (NonNegative a) # shrink :: NonNegative a -> [NonNegative a] #
(Num a, Eq a, Arbitrary a) => Arbitrary (NonZero a) # |
Methods arbitrary :: Gen (NonZero a) # shrink :: NonZero a -> [NonZero a] #
(Num a, Ord a, Arbitrary a) => Arbitrary (Positive a) # |
Methods arbitrary :: Gen (Positive a) # shrink :: Positive a -> [Positive a] #
Arbitrary a => Arbitrary (NonEmptyList a) # |
Methods arbitrary :: Gen (NonEmptyList a) # shrink :: NonEmptyList a -> [NonEmptyList a] #
(Ord a, Arbitrary a) => Arbitrary (OrderedList a) # |
Methods arbitrary :: Gen (OrderedList a) # shrink :: OrderedList a -> [OrderedList a] #
Arbitrary a => Arbitrary (Fixed a) # |
Methods arbitrary :: Gen (Fixed a) # shrink :: Fixed a -> [Fixed a] #
Arbitrary a => Arbitrary (Blind a) # |
Methods arbitrary :: Gen (Blind a) # shrink :: Blind a -> [Blind a] #
(CoArbitrary a, Arbitrary b) => Arbitrary (a -> b) # |
Methods arbitrary :: Gen (a -> b) # shrink :: (a -> b) -> [a -> b] #
(Arbitrary a, Arbitrary b) => Arbitrary (Either a b) # |
Methods arbitrary :: Gen (Either a b) # shrink :: Either a b -> [Either a b] #
(Arbitrary a, Arbitrary b) => Arbitrary (a, b) # |
Methods arbitrary :: Gen (a, b) # shrink :: (a, b) -> [(a, b)] #
(Ord k, Arbitrary k, Arbitrary v) => Arbitrary (Map k v) # |
Methods arbitrary :: Gen (Map k v) # shrink :: Map k v -> [Map k v] #
(Arbitrary a, ShrinkState s a) => Arbitrary (Shrinking s a) # |
Methods arbitrary :: Gen (Shrinking s a) # shrink :: Shrinking s a -> [Shrinking s a] #
(Function a, CoArbitrary a, Arbitrary b) => Arbitrary (Fun a b) # |
Methods arbitrary :: Gen (Fun a b) # shrink :: Fun a b -> [Fun a b] #
(Function a, CoArbitrary a, Arbitrary b) => Arbitrary ((:->) a b) # |
Methods arbitrary :: Gen (a :-> b) # shrink :: (a :-> b) -> [a :-> b] #
(Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a, b, c) # |
Methods arbitrary :: Gen (a, b, c) # shrink :: (a, b, c) -> [(a, b, c)] #
(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (a, b, c, d) # |
Methods arbitrary :: Gen (a, b, c, d) # shrink :: (a, b, c, d) -> [(a, b, c, d)] #
(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => Arbitrary (a, b, c, d, e) # |
Methods arbitrary :: Gen (a, b, c, d, e) # shrink :: (a, b, c, d, e) -> [(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)`.

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)

coarbitrary :: (Generic a, GCoArbitrary (Rep a)) => 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 # |
Methods coarbitrary :: Bool -> Gen b -> Gen b #
CoArbitrary Char # |
Methods coarbitrary :: Char -> Gen b -> Gen b #
CoArbitrary Double # |
Methods coarbitrary :: Double -> Gen b -> Gen b #
CoArbitrary Float # |
Methods coarbitrary :: Float -> Gen b -> Gen b #
CoArbitrary Int # |
Methods coarbitrary :: Int -> Gen b -> Gen b #
CoArbitrary Int8 # |
Methods coarbitrary :: Int8 -> Gen b -> Gen b #
CoArbitrary Int16 # |
Methods coarbitrary :: Int16 -> Gen b -> Gen b #
CoArbitrary Int32 # |
Methods coarbitrary :: Int32 -> Gen b -> Gen b #
CoArbitrary Int64 # |
Methods coarbitrary :: Int64 -> Gen b -> Gen b #
CoArbitrary Integer # |
Methods coarbitrary :: Integer -> Gen b -> Gen b #
CoArbitrary Natural # |
Methods coarbitrary :: Natural -> Gen b -> Gen b #
CoArbitrary Ordering # |
Methods coarbitrary :: Ordering -> Gen b -> Gen b #
CoArbitrary Word # |
Methods coarbitrary :: Word -> Gen b -> Gen b #
CoArbitrary Word8 # |
Methods coarbitrary :: Word8 -> Gen b -> Gen b #
CoArbitrary Word16 # |
Methods coarbitrary :: Word16 -> Gen b -> Gen b #
CoArbitrary Word32 # |
Methods coarbitrary :: Word32 -> Gen b -> Gen b #
CoArbitrary Word64 # |
Methods coarbitrary :: Word64 -> Gen b -> Gen b #
CoArbitrary () # |
Methods coarbitrary :: () -> Gen b -> Gen b #
CoArbitrary IntSet # |
Methods coarbitrary :: IntSet -> Gen b -> Gen b #
CoArbitrary OrdC # |
Methods coarbitrary :: OrdC -> Gen b -> Gen b #
CoArbitrary OrdB # |
Methods coarbitrary :: OrdB -> Gen b -> Gen b #
CoArbitrary OrdA # |
Methods coarbitrary :: OrdA -> Gen b -> Gen b #
CoArbitrary C # |
Methods coarbitrary :: C -> Gen b -> Gen b #
CoArbitrary B # |
Methods coarbitrary :: B -> Gen b -> Gen b #
CoArbitrary A # |
Methods coarbitrary :: A -> Gen b -> Gen b #
CoArbitrary a => CoArbitrary [a] # |
Methods coarbitrary :: [a] -> Gen b -> Gen b #
CoArbitrary a => CoArbitrary (Maybe a) # |
Methods coarbitrary :: Maybe a -> Gen b -> Gen b #
(Integral a, CoArbitrary a) => CoArbitrary (Ratio a) # |
Methods coarbitrary :: Ratio a -> Gen b -> Gen b #
(RealFloat a, CoArbitrary a) => CoArbitrary (Complex a) # |
Methods coarbitrary :: Complex a -> Gen b -> Gen b #
HasResolution a => CoArbitrary (Fixed a) # |
Methods coarbitrary :: Fixed a -> Gen b -> Gen b #
CoArbitrary a => CoArbitrary (IntMap a) # |
Methods coarbitrary :: IntMap a -> Gen b -> Gen b #
CoArbitrary a => CoArbitrary (Seq a) # |
Methods coarbitrary :: Seq a -> Gen b -> Gen b #
CoArbitrary a => CoArbitrary (Set a) # |
Methods coarbitrary :: Set a -> Gen b -> Gen b #
(Arbitrary a, CoArbitrary b) => CoArbitrary (a -> b) # |
Methods coarbitrary :: (a -> b) -> Gen b -> Gen b #
(CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) # |
Methods coarbitrary :: Either a b -> Gen b -> Gen b #
(CoArbitrary a, CoArbitrary b) => CoArbitrary (a, b) # |
Methods coarbitrary :: (a, b) -> Gen b -> Gen b #
(CoArbitrary k, CoArbitrary v) => CoArbitrary (Map k v) # |
Methods coarbitrary :: Map k v -> Gen b -> Gen b #
(CoArbitrary a, CoArbitrary b, CoArbitrary c) => CoArbitrary (a, b, c) # |
Methods coarbitrary :: (a, b, c) -> Gen b -> Gen b #
(CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d) => CoArbitrary (a, b, c, d) # |
Methods coarbitrary :: (a, b, c, d) -> Gen b -> Gen b #
(CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d, CoArbitrary e) => CoArbitrary (a, b, c, d, e) # |
Methods coarbitrary :: (a, b, c, d, e) -> Gen b -> Gen b #

## 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, 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.

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.

infiniteList :: Arbitrary a => Gen [a] #

Generate an infinite list.