Test.AC.Class.Monad

Properties for testing that instances of the Monad class perform correctly.

This testing requires an Eq instance, which not all Monads actually have. It also requires a Show instance, which is also uncommon. The Label1 wrapper may be useful in dealing with the Show requirement.

Tests are supplied both in regular "unlabelled" form, and also in a special "labelled" form, where function objects have Labels attached to them. Because of this, the function used for each test can be recorded in the test log, which can be quite helpful.

Unlabelled tests

p_return_bind :: (Monad m, Eq (m y), Show x, Show (m x), Show (m y)) => x -> (x -> m y) -> Test

Check that return x >>= f == f x.

p_bind_return :: (Monad m, Eq (m x), Show (m x)) => m x -> Test

Check that mx >>= return == mx.

p_bind_associative :: (Monad m, Eq (m z), Show (m x), Show (m y), Show (m z)) => m x -> (x -> m y) -> (y -> m z) -> Test

Check that >>= is associative.

Approximately, mx >>= (f >>= g) == (mx >>= f) >>= g, but that doesn't type-check. To be exact, mx >>= (\ x -> f x >>= g) == (mx >>= f) >>= g.

p_Monad :: (Monad m, Eq (m x), Show x, Show (m x)) => [x] -> [x -> m x] -> [m x] -> Test

Given a list of distinct inputs, run all applicable Monad tests on all combinations of inputs. (If the inputs are not distinct, some redundant tests will be performed.)

The argument types have been constrainted a bit to keep the function's type signature reasonably simple.

p_Functor_Monad :: (Functor m, Monad m, Eq (m y), Show (m x), Show (m y)) => m x -> (x -> y) -> Test

Check that fmap f mx == mx >>= return . f.

Labelled tests

p_return_bind_L :: (Monad m, Eq (m y), Show x, Show (m x), Show (m y)) => x -> Label (x -> m y) -> Test

Check that return x >>= f == f x.

p_bind_associative_L :: (Monad m, Eq (m z), Show (m x), Show (m y), Show (m z)) => m x -> Label (x -> m y) -> Label (y -> m z) -> Test

Check that >>= is associative.

Approximately, mx >>= (f >>= g) == (mx >>= f) >>= g, but that doesn't type-check. To be exact, mx >>= (\ x -> f x >>= g) == (mx >>= f) >>= g.

p_Monad_L :: (Monad m, Eq (m x), Show x, Show (m x)) => [x] -> [Label (x -> m x)] -> [m x] -> Test

Given a list of distinct inputs, run all applicable Monad tests on all combinations of inputs. (If the inputs are not distinct, some redundant tests will be performed.)

The argument types have been constrainted a bit to keep the function's type signature reasonably simple.

p_Functor_Monad_L :: (Functor m, Monad m, Eq (m y), Show (m x), Show (m y)) => m x -> Label (x -> y) -> Test

Check that fmap f mx == mx >>= return . f.