Type classes for random generation of values.
- class Arbitrary a where
- class CoArbitrary a where
- arbitrarySizedIntegral :: 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, Typeable a, RecursivelyShrink (Rep a), Subterms (Rep a)) => a -> [a]
- subterms :: (Generic a, Typeable a, Subterms (Rep a)) => a -> [a]
- recursivelyShrink :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a]
- 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
Random generation and shrinking of values.
A generator for values of the given type.
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:
- Shrink a term to any of its immediate subterms.
- Recursively apply
shrinkto all immediate subterms.
- 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
rin 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.
genericShrink tries shrinking a term to all of its
subterms and, failing that, recursively shrinks the subterms.
Using it, we can define
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.
If all this leaves you bewildered, you might try
to begin with,
Typeable for your type. However, if your data type has any
special invariants, you will need to check that
genericShrink can't break those invariants.
Used for random generation of functions.
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:
Helper functions for implementing arbitrary
Generates an integral number. The number can be positive or negative and its maximum absolute value depends on the size parameter.
Generates an integral number. The number is chosen uniformly from
the entire range of the type. You may want to use
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.
Generates a fractional number. The number can be positive or negative and its maximum absolute value depends on the size parameter.
Generates an element of a bounded type. The element is chosen from the entire range of the type.
Generates an element of a bounded enumeration.
Helper functions for implementing shrink
Shrink a term to any of its immediate subterms, and also recursively shrink all subterms.
All immediate subterms of a term.
Recursively shrink all immediate subterms.
Shrink a list of values given a shrinking function for individual values.
Shrink a fraction, but only shrink to integral values.
Helper functions for implementing coarbitrary
coarbitrary implementation for integral numbers.
coarbitrary implementation for real numbers.