smallcheck-1.1.2: A property-based testing library

Copyright(c) Colin Runciman et al.
MaintainerRoman Cheplyaka <>
Safe HaskellSafe




This module exports the main pieces of SmallCheck functionality.

To generate test cases for your own types, refer to Test.SmallCheck.Series.

For pointers to other sources of information about SmallCheck, please refer to the README at


Constructing tests

The simplest kind of test is a function (possibly of many arguments) returning Bool. The function arguments are interpreted as being universally, existentially or uniquely quantified, depending on the quantification context.

The default quantification context is universal (forAll).

forAll, exists and existsUnique functions set the quantification context for function arguments. Depending on the quantification context, the test \x y -> p x y may be equivalent to:

The quantification context affects all the variables immediately following the quantification operator, also extending past over, changeDepth and changeDepth1 functions.

However, it doesn't extend past other functions, like monadic, and doesn't affect the operands of ==>. Such functions start a fresh default quantification context.


  • \x y -> p x y means ∀ x, y. p x y
  • exists $ \x y -> p x y means ∃ x, y: p x y
  • exists $ \x -> forAll $ \y -> p x y means ∃ x: ∀ y. p x y
  • existsUnique $ \x y -> p x y means ∃! (x, y): p x y
  • existsUnique $ \x -> over s $ \y -> p x y means ∃! (x, y): y ∈ s && p x y
  • existsUnique $ \x -> monadic $ \y -> p x y means ∃! x: ∀ y. [p x y]
  • existsUnique $ \x -> existsUnique $ \y -> p x y means ∃! x: ∃! y: p x y
  • exists $ \x -> (\y -> p y) ==> (\z -> q z) means ∃ x: (∀ y. p y) => (∀ z. p z)

forAll :: Testable m a => a -> Property m #

Set the universal quantification context

exists :: Testable m a => a -> Property m #

Set the existential quantification context

existsUnique :: Testable m a => a -> Property m #

Set the uniqueness quantification context.

Bear in mind that ∃! (x, y): p x y is not the same as ∃! x: ∃! y: p x y.

For example, ∃! x: ∃! y: |x| = |y| is true (it holds only when x=0), but ∃! (x,y): |x| = |y| is false (there are many such pairs).

As is customary in mathematics, existsUnique $ \x y -> p x y is equivalent to existsUnique $ \(x,y) -> p x y and not to existsUnique $ \x -> existsUnique $ \y -> p x y (the latter, of course, may be explicitly written when desired).

That is, all the variables affected by the same uniqueness context are quantified simultaneously as a tuple.

over :: (Show a, Testable m b) => Series m a -> (a -> b) -> Property m #

over s $ \x -> p x makes x range over the Series s (by default, all variables range over the series for their types).

Note that, unlike the quantification operators, this affects only the variable following the operator and not subsequent variables.

over does not affect the quantification context.

monadic :: Testable m a => m a -> Property m #

Execute a monadic test

(==>) :: (Testable m c, Testable m a) => c -> a -> Property m infixr 0 #

The ==> operator can be used to express a restricting condition under which a property should hold. It corresponds to implication in the classical logic.

Note that ==> resets the quantification context for its operands to the default (universal).

changeDepth :: Testable m a => (Depth -> Depth) -> a -> Property m #

Run property with a modified depth. Affects all quantified variables in the property.

changeDepth1 :: (Show a, Serial m a, Testable m b) => (Depth -> Depth) -> (a -> b) -> Property m #

Quantify the function's argument over its series, but adjust the depth. This doesn't affect any subsequent variables.

Running tests

smallCheck is a simple way to run a test.

As an alternative, consider using a testing framework.

The packages and provide integration with Tasty and HSpec, two popular testing frameworks.

They allow to organize SmallCheck properties into a test suite (possibly together with HUnit or QuickCheck tests) and provide other useful features.

For more ways to run the tests, see Test.SmallCheck.Drivers.

type Depth = Int #

Maximum depth of generated test values.

For data values, it is the depth of nested constructor applications.

For functional values, it is both the depth of nested case analysis and the depth of results.

smallCheck :: Testable IO a => Depth -> a -> IO () #

A simple driver that runs the test in the IO monad and prints the results.

Main types and classes

class Monad m => Testable m a where #

Class of tests that can be run in a monad. For pure tests, it is recommended to keep their types polymorphic in m rather than specialising it to Identity.

Minimal complete definition



test :: a -> Property m #


Monad m => Testable m Bool # 


test :: Bool -> Property m #

(Monad m, (~) (* -> *) m n) => Testable n (Property m) # 


test :: Property m -> Property n #

(Serial m a, Show a, Testable m b) => Testable m (a -> b) # 


test :: (a -> b) -> Property m #

Monad m => Testable m (Either Reason Reason) #

Works like the Bool instance, but includes an explanation of the result.

Left and Right correspond to test failure and success respectively.

data Property m #

The type of properties over the monad m


(Monad m, (~) (* -> *) m n) => Testable n (Property m) # 


test :: Property m -> Property n #

type Reason = String #

An explanation for the test outcome