Simple Generics-based arbitrary generators.

Here is an example. Define your type.

data Tree a = Leaf a | Node (Tree a) (Tree a)
  deriving Generic

Pick an arbitrary implementation.

instance Arbitrary a => Arbitrary (Tree a) where
  arbitrary = genericArbitrary (weights (9 % 8 % ()))

arbitrary :: Gen (Tree a) picks a Leaf with probability 9/17, or a Node with probability 8/17, and recursively fills their fields with arbitrary.

Distribution of constructors

The distribution of constructors can be specified using weights applied to a special list of weights in the same order as the data type definition. This assigns to each constructor a probability proportional to its weight; in other words, p_C = weight_C / sumOfWeights.

The list of weights is built up with the (%) operator as a cons, and using the unit () as the empty list, in the order corresponding to the data type definition. The uniform distribution can be obtained with uniform.

Example

For Tree, genericArbitrary produces code equivalent to the following:

genericArbitrary :: Arbitrary a => Weights (Tree a) -> Gen (Tree a)
genericArbitrary (weighted (x % y % ())) =
  frequency
    [ (x, Leaf <$> arbitrary)
    , (y, Node <$> arbitrary <*> arbitrary)
    ]

Uniform distribution

You can specify the uniform distribution (all weights equal) with uniform. genericArbitraryU is available as a shorthand for genericArbitrary uniform.

Note that for many types, a uniform distribution tends to produce big values. For instance for Tree a, generated values are finite but the average number of Leaf and Node constructors is infinite.

Checked weights

GHC 8.0.1 and above only.

The weights actually have type W "ConstructorName" (just a newtype around Int), so that you can annotate a weight with its corresponding constructor, and it will be checked that you got the order right.

This will type-check.

weighted ((x :: W "Leaf") % (y :: W "Node") % ()) :: Weights (Tree a)
weighted (x % (y :: W "Node") % ()) :: Weights (Tree a)

This will not: the first requires an order of constructors different from the definition of the Tree type; the second doesn't have the right number of weights.

weighted ((x :: W "Node") % y % ()) :: Weights (Tree a)
weighted (x % y % z % ()) :: Weights (Tree a)

Ensuring termination

As was just mentioned, one must be careful with recursive types to avoid producing extremely large values.

The alternative genericArbitrary' implements a simple strategy to keep values at reasonable sizes: the size parameter of Gen is divided among the fields of the chosen constructor. When it reaches zero, the generator selects a finite term whenever it can find any of the given type. This generally ensures that the number of constructors remains close to the initial size parameter passed to Gen.

A natural number n determines the maximum depth of terms that can be used to end recursion. It is encoded using Z :: Z and S :: n -> S n.

genericArbitrary' n (weights (...))

With n = Z, the generator looks for a simple nullary constructor. If none exist at the current type, as is the case for our Tree type, it carries on as in genericArbitrary.

genericArbitrary' Z :: Arbitrary a => Weights (Tree a) -> Gen (Tree a)
genericArbitrary' Z (weights (x % y % ())) =
  frequency
    [ (x, Leaf <$> arbitrary)
    , (y, scale (`div` 2) $ Node <$> arbitrary <*> arbitrary)
    -- 2 because Node is 2-ary.
    ]

Here is another example with nullary constructors:

data Tree' = Leaf1 | Leaf2 | Node3 Tree' Tree' Tree'
  deriving Generic

instance Arbitrary Tree' where
  arbitrary = genericArbitrary' Z (weights (1 % 2 % 3 % ()))

Here, genericArbitrary' Z is equivalent to:

genericArbitrary' Z :: Weights Tree' -> Gen Tree'
genericArbitrary' Z (weights (x % y % z % ())) =
  sized $ n ->
    if n == 0 then
      -- If the size parameter is zero, the non-nullary alternative is discarded.
      frequency $
        [ (x, return Leaf1)
        , (y, return Leaf2)
        ]
    else
      frequency $
        [ (x, return Leaf1)
        , (y, return Leaf2)
        , (z, resize (n `div` 3) node)  -- 3 because Node3 is 3-ary
        ]
  where
    node = Node3 <$> arbitrary <*> arbitrary <*> arbitrary

To increase the chances of termination when no nullary constructor is directly available, such as in Tree, we can pass a larger depth n. The effectiveness of this parameter depends on the concrete type the generator is used for.

For instance, if we want to generate a value of type Tree (), there is a value of depth 1 (represented by S Z) that we can use to end recursion: Leaf ().

genericArbitrary' (S Z) :: Weights (Tree ()) -> Gen (Tree ())
genericArbitrary' (S Z) (weights (x % y % ())) =
  sized $ n ->
    if n == 0 then
      return (Leaf ())
    else
      frequency
        [ (x, Leaf <$> arbitrary)
        , (y, scale (`div` 2) $ Node <$> arbitrary <*> arbitrary)
        ]

Because the argument of Tree must be inspected in order to discover values of type Tree (), we incur some extra constraints if we want polymorphism.

UndecidableInstances is also required.

instance (Arbitrary a, Generic a, ListBaseCases Z (Rep a))
  => Arbitrary (Tree a) where
  arbitrary = genericArbitrary' (S Z) (weights (1 % 2 % ()))

A synonym is provided for brevity.

instance (Arbitrary a, BaseCases' Z a) => Arbitrary (Tree a) where
  arbitrary = genericArbitrary' (S Z) (weights (1 % 2 % ()))