Hi Olaf,
You might like quickcheck-higherorder, "A QuickCheck extension for properties of higher-order values."
https://hackage.haskell.org/package/quickcheck-higherorder
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
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.)
Thanks
Olaf
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