[Haskell-cafe] data kinds and exhaustiveness of typeclass instances

[Seph Shewell Brockway]

On Tue, Mar 02, 2021 at 03:00:55PM +0000, Richard Eisenberg wrote:
> > Is there a way to somehow convince GHC of that fact so that g typechecks?
> 
> No.
> 
> First, it would actually be unsound to do so, because of the possibility of exotic types, built with pathological combinations of type and data families: https://gitlab.haskell.org/ghc/ghc/-/issues/14420 <https://gitlab.haskell.org/ghc/ghc/-/issues/14420>
> 
> But, actually, the bigger problem is that we need a class constraint in order to allow a function to compute at runtime. The function f actually takes two arguments at runtime: a representation of the instance which carries f's implementation (this is sometimes called a dictionary), and the normal argument of type a. `g`, on the other hand, has no access to the dictionary needed at runtime, and so it's unclear how it should compute.
> 
> Put another way: a value of type Foo carries no information (beyond the fact that it terminates), because Foo has only one data constructor. So there's no way that g :: Foo a -> Int could be anything but a constant function. You need the class constraint to change this fact.
> 
> Hope this helps!
> Richard

To elaborate a little on Richard’s answer, this is the reason for
GHC.TypeLits’ KnownNat class, so that we have

natVal :: KnownNat n => proxy n -> Integer

You’d have to supplement your program with a class KnownTag, like so:

data Tag = A | B
data Foo (a :: Tag) = Foo

class KnownTag (a :: Tag) where
  tagVal :: proxy a -> Tag

instance KnownTag A where
  tagVal _ = A

instance KnownTag B where
  tagVal _ = B

class C a where
  f :: a -> Int

instance KnownTag a => C (Foo a) where
  f _ = case tagVal (Proxy :: Proxy a) of A -> 1; B -> 2

g :: KnownTag a => Foo a -> Int
g = f

                                             Regards,

                                             Seph

-- 
Seph Shewell Brockway, BSc MSc (Glas.)
Pronouns: she/her