Law-abiding instances for Arbitrary (Equivalence a) and Arbitrary (Comparison a)

[Zemyla]

(Copied from nick8325/quickcheck#280 )

Data.Functor.Contravariant is now in base, and it includes the types

newtype Equivalence a = Equivalence { getEquivalence :: a -> a -> Bool }
newtype Comparison a = Comparison { getComparison :: a -> a -> Ordering }

and those would be really useful to generate for CoArbitrary, for sort predicates and such. However, the standard Arbitrary instance for them would not be useful, because they don't abide by the reflexivity, symmetry/antisymmetry, and transitivity laws at all.

However, I think I found a way. A CoArbitrary type can be sort of "hashed" by using it on a Gen:

cohash :: CoArbitrary a => QCGen -> Int -> a -> Int
cohash g n a = unGen (coarbitrary a $ MkGen $ \g0 n0 -> fst $ randomR (negate n0, n0) g0) g n

Here, the "size" of the generator represents the "fineness" of the hash.

With that, we can generate the instances as follows:

instance CoArbitrary a => Arbitrary (Equivalence a) where
  arbitrary = MkGen $ \g n -> Equivalence $ \a b -> cohash g n a == cohash g n b

instance CoArbitrary a => Arbitrary (Comparison a) where
  arbitrary = MkGen $ \g n -> Comparison $ \a b -> compare (cohash g n a) (cohash g n b)

(Incidentally, the type Predicate also exists, but can be generated with the standard instance for a -> Bool.)