Create a Test for a SmallCheck Testable property

The "depth" parameter for SmallCheck

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

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

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).

Set the uniqueness quantification context.

Bear in mind that \( \exists! x, y\colon p\, x \, y \) is not the same as \( \exists! x \colon \exists! y \colon p \, x \, y \).

For example, \( \exists! x \colon \exists! y \colon |x| = |y| \) is true (it holds only when \(x=y=0\)), but \( \exists! x, y \colon |x| = |y| \) 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.

Set the existential quantification context.

Set the universal quantification context.

Execute a monadic test.

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.

The type of properties over the monad m.

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.

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.

An explanation for the test outcome.