# [Haskell-cafe] Testing polymorphic properties with QuickCheck

Thu Feb 19 04:23:49 UTC 2015

```Hi Stuart,

If you're testing stand-alone functions, defaulting all type variables
to Integer can probably find a counterexample, provided it's not
something that depends on properties of an instance of Integer like:

prop_assoc a b c = (a + b) + c == a + (b + c)
-- fails for Double

But another type might find the counterexample faster. See this paper
(called Testing Polymorphic Properties):

http://publications.lib.chalmers.se/records/fulltext/local_99387.pdf

Unfortunately, I don't know of an implementation of the method they describe.

Regards,

On Wed, Feb 18, 2015 at 3:41 PM, Stuart Hungerford
<stuart.hungerford at gmail.com> wrote:
> Hi,
>
> I'd like to use QuickCheck to test polymorphic properties and I'm
> wondering if there's any community consenus on how to do this while
> avoiding creating large amounts of boilerplate test code.
>
> As an example, suppose I have this simple simplistic Monoid typeclass:
>
> class Monoid a where
>   zero  :: a
>   (|+|) :: a -> a -> a
>
> And suppose I make these types Monoid instances:
>
>
> instance Monoid Integer where
>   zero  = 0
>   (|+|) = (+)
>
> instance Monoid Rational where
>   zero  = 0
>   (|+|) = (+)
>
> instance (Monoid a, Monoid b) => Monoid (a, b) where
>   zero = (zero, zero)
>   (|+|) (x, y) (u, v) = (x |+| u, y |+| v)
>
>
> Using QuickCheck and the Tasty test framework I'd like to test the
> Monoid laws across the relevant types (I'm only showing one part of
> one law here) as QuickCheck properties:
>
>
> prop_left_add_id :: (Eq a, Monoid a) => a -> Bool
> prop_left_add_id x = zero |+| x == x
>
> monoid_suite :: TestTree
> monoid_suite = testGroup "monoid" [
>   testProperty "left additive identity (Integer)"
>     (prop_left_add_id :: Integer -> Bool),
>
>   testProperty "left additive identity (Rational)"
>     (prop_left_add_id :: Rational -> Bool),
>
>   testProperty "left additive identity ((Integer, Integer))"
>     (prop_left_add_id :: (Integer, Integer) -> Bool),
>   -- ...]
>
>
> And this is where I start creating a lot of essentially boilerplate
> code. I'm wondering if there's any consensus on the way to go about
> this kind of testing?
>
> Researching this issue I've found ways of combining various GHC
> extensions and the type system to (I think) write the properties more
> at the type level. There are QuickCheck and Tasty modules that aim to
> find all properties in a module and test them, but polymorphic
> properties are automatically defaulted to Integer arguments. I'm also
> tempted by Template Haskell to write what's essentially code
> generation templates.
>