This library provide set of generic properties for laws of standard type classes and limited way to compose them. Here are some examples:

Testing monoid laws

>>> quickCheck $ eq $ prop_Monoid (T :: T [Int])
+++ OK, passed 100 tests.
>>> quickCheck $ eq $ prop_Monoid (T :: T (Maybe [Int]))
+++ OK, passed 100 tests.

Testing functor laws

>>> quickCheck $ eq $ prop_FunctorCompose (+2) (+199) (T :: T [Int])
+++ OK, passed 100 tests.

Fixing type

All properties in this library are polymorphic. For example property for checking associativity of mappend could have following type:

 prop_mappend :: (Eq a, Monoid a) => a -> a -> a -> Bool

But if one tries to pass this expression to quickCheck GHC will rightfully complain that type is too generic. Indeed there is no way to figure out what is type of a. Obvious way to fix type of a is to add type signature. However it's too cumbersome to write signature for 3 parameter function.

Another approach was taken instead. All properties take dummy parameter which fix type:

 prop_Mappend :: (Eq a, Monoid a) => T a -> a -> a -> a -> Bool

T is phanom typed unit. It ensures that only type information could be passed to function. For example test invokation could look like this:

 quickCheck $ prop_Mappend (T :: T [Int])

By convention all user supplied parameters are placed before T and all quickcheck supplied parameters are after T.

Comparing for equality

A lot of QuickCheck properties have form expression = another expression. It's natural to compare them for equality however not all types have Eq instance. Functions are most prominent example.

There are three generic ways to compare values for equality.

1. Use == operator
2. Convert value to some type with Eq instance and compare them. Caller must ensure that such conversion make sence
3. Most generic: use custom comparison function.

Functions eq, eqOn and eqWith transform property with delayed comparison of equality to one which could be tested with quickCheck.

This approach naturally generelizes to arbitrary boolean expressions of properties with this form.

Delaying of comparison and composition of properties is implemented using Equal data type and Equalable type class.