Safe Haskell | Safe |
---|---|

Language | Haskell98 |

Type classes for random generation of values.

- 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]
- 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
`shrink`

to 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`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

as this shrinks `shrink`

x = Nil:`genericShrink`

x`Nil`

to `Nil`

, and shrinking will go into an
infinite loop.

If all this leaves you bewildered, you might try

to begin with,
after deriving `shrink`

= `genericShrink`

`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.

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)`

.

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)

## 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.

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.

## 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

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

Generates an ordered list.

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

Generate an infinite list.