On Tue, Dec 13, 2016 at 12:49 AM, Oleg Grenrus
First the bike shedding: I’d prefer /~ and :/~:.
Those are indeed better.
new Typeable [1] would actually provide heterogenous equality:
eqTypeRep' :: forall k1 k2 (a :: k1) (b :: k2). TypeRep a -> TypeRep b -> Maybe (a :~~: b)
And this one is tricky, should it be:
eqTypeRep' :: forall k1 k2 (a :: k1) (b :: k2). TypeRep a -> TypeRep b -> Either (Either (k1 :/~: k2) (a :/~: b)) (a :~~: b)
i.e. how kind inequality would work?
I don't know. It sounds like some details of how kinds are expressed in TypeRep might still be a bit uncertain, but I'm not tuned in. Maybe we should punt and use heterogeneous inequality? That's over my head.
I'm not sure about propagation rules, with inequality you have to be *very* careful!
irreflexivity, x /~ x and symmetry x /~ y <=> y /~ x are clear.
I assume that in your rules, variables are not type families, otherwise
x /~ y => f x /~ f y doesn't hold if `f` isn't injective. (e.g. type family F x where F x = ()) other direction is true though.
I was definitely imagining them as first-class types; your point that f x /~ f y => x /~ y even if f is a type family is an excellent one.
Also:
f x ~ a -> b, is true with f ~ (->) a, x ~ b.
Whoops! Yeah, I momentarily forgot that (->) is a constructor. Just leave out that bogus piece. Thanks, David Feuer