[Haskell-cafe] property testing, point-free style

Li-yao Xia lysxia at gmail.com
Wed May 31 13:06:26 UTC 2023

Hi Olaf,

You might like quickcheck-higherorder, "A QuickCheck extension for 
properties of higher-order values."


One of the key bits is a class for testable equality, which may have an 
instance for (a -> b), unlike Eq:

|class TestEq a where (=?) :: a -> a -> Property |||

The package has more bells and whistles to further streamline writing 
properties that quantify over functions.

If you only ever compare unary first-order functions, you really only 
need the single instance TestEq (a -> b), which you can extract as a 
self-contained operator:

(=?) :: (Coarbitrary a, Show a, Arbitrary b, Eq b, Show b) => (a -> b) 
-> (a -> b) -> Property
(=?) f g = property $ \x -> f x === g x



On 2023-05-31 12:25 PM, Olaf Klinke wrote:

Dear Cafe,

The expression

\x -> f x == g x

is a testable property, as long as values for x can be randomly
generated. For clarity I'd prefer a point-free style, e.g.

f ≡ g

Are there extensions to QuickCheck that let me write this? The
QuickCheck package itself does not seem to contain such an operator. My
current work-around is a
     newtype ExtensionalEquality a b
that holds two functions of type (a -> b) and a Testable instance for
it. But I've got a hunch that I re-invented some wheel here. (My
ExtensionalEquality is isomorphic to
     Refl (a -> b) (a -> b)
but Refl ist conceptually about type equality, not term equality.)


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