heterogeneous-comparison

There are times when values need to be tested for equality or compared for ordering, even if they aren't statically known to be of equivalent types. Such a test, if successful, may allow that knowledge to be recovered.

Prior Art

base (on singletons):

• TestCoercion f $\approx$ (HetEq f, Strength f ~ Representational)
• TestEquality f $\approx$ (HetEq f, Strength f ~ Nominal)

some (universally):

• GEq f $\cong$ (HetEq f, Strength f ~ Nominal)
• GCompare f $\cong$ (HetOrd f, Strength f ~ Nominal)

Improvements

HetEq and HetOrd are generalised over the strength of evidence captured. This allows them to admit and combine a much broader range of instances, e.g.

instance Eq a => HetEq (Const a) where
  type Strength (Const a) = Phantom
  ...
instance HetEq IORef where
  type Strength IORef = Representational
  ...
instance HetEq TypeRep where
  type Strength TypeRep = Nominal
  ...

type HetEq' f = (KnownRole (Strength f), HetEq f)

instance (HetEq' f, HetEq' g) => HetEq (Product f g) where
  type Strength (Product f g) = Max (Strength f) (Strength g)
  ...
instance (HetEq' f, HetEq' g) => HetEq (Sum     f g) where
  type Strength (Sum     f g) = Min (Strength f) (Strength g)
  ...

Consequently, Data.Hetero.Some has much broader Eq and Ord instances than Data.Some:

instance HetEq  f => Eq  (Some f)
instance HetOrd f => Ord (Some f)

dependent-map could similarly broaden the range of key types by replacing GCompare k with (HetOrd k, Strength k > Phantom), though the rare operations requiring Has' _ k f constraints might not come out on top.