Test.QuickCheck.Arbitrary

QuickCheck-2.8.1: 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
  - arbitrary :: Gen a
  - shrink :: a -> [a]
- class CoArbitrary a where
  - coarbitrary :: a -> Gen b -> Gen b
- 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, Arbitrary a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a]
- subterms :: (Generic a, Arbitrary 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

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 Natural |
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 Natural |
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.