smallcheck-1.0: A property-based testing library

MaintainerRoman Cheplyaka <>
Safe HaskellNone




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 mSource

Set the universal quantification context

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

Set the existential quantification context

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

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 :: (Monad m, Show a, Testable m b) => Series m a -> (a -> b) -> Property mSource

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 mSource

Execute a monadic test

(==>) :: (Testable m c, Testable m a) => c -> a -> Property mSource

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 mSource

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 mSource

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 the test-framework package:

It allows to organize SmallCheck properties into a test suite (possibly together with HUnit or QuickCheck tests), apply timeouts, get nice statistics etc.

To use SmallCheck properties with test-framework, install the test-framework-smallcheck package:

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

type Depth = IntSource

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 ()Source

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 Source

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.


Monad m => Testable m Bool 
(Monad m, ~ (* -> *) m n) => Testable n (Property m) 
(Serial m a, Show a, Testable m b) => Testable m (a -> b) 

data Property m Source

The type of properties over the monad m


(Monad m, ~ (* -> *) m n) => Testable n (Property m) 
Typeable1 m => Typeable (Property m)