[Haskell-cafe] Encoding superclass relationships as a constraint?

Li-yao Xia lysxia at gmail.com
Wed Jun 7 10:36:12 UTC 2017

This ticket about "Quantified contexts" (forall a. ctx a => Show a) 
seems to be what you're looking for.


On 06/07/2017 03:38 AM, Alexis King wrote:
> Using ExistentialQuantification, it’s possible to create a rather
> generic type that packages some arbitrary dictionary up at runtime:
>      data Some ctx = forall a. ctx a => Some a
> This is nice, but it’s not very interesting. It would be nice if we
> could define a Show instance for our type, and a naïve implementation
> is trivial:
>      instance Show (Some Show) where
>        show (Some x) = show x
> However, this isn’t very useful in practice, since it means we can only
> show values of precisely the type (Some Show), which are better
> represented as values of type String. However, we might reasonably have
> some class with Show as a superclass:
>      class Show a => Foo a
>      instance Foo ()
> ...and we might want to show values of type (Some Foo). However, this
> won’t work with the naïve implementation, since Foo is not the same as
> Show.
> Clearly, what we want is some instance like this:
>      instance (ctx ≈> Show) => Show (Some ctx)
> ...where (a ≈> b) can be read “a implies b”. Unfortunately, as far as I
> can tell, this isn’t actually possible in any general way.
> The closest thing I was able to come up with was a less general solution
> using Edward Kmett’s constraints package. It’s possible to write (≈>)
> with some manual boilerplate:
>      import Data.Constraint
>      import Data.Constraint.Forall
>      class Class (ctx a) (ctx' a) => Class1' ctx ctx' a
>      instance Class (ctx a) (ctx' a) => Class1' ctx ctx' a
>      type Class1 ctx ctx' = Forall (Class1' ctx ctx')
>      type a ≈> b = Class1 b a
> ...and then it’s possible to write that Show instance:
>      instance (ctx ≈> Show) => Show (Some ctx) where
>        show (Some (x :: a)) = case inst @(Class1' Show ctx) @a of
>          Sub Dict -> case (cls :: ctx a :- Show a) of
>            Sub Dict -> show x
> However, this means users have to manually implement Class instances for
> their classes. Using the above example of Foo, a user would have to
> write the following instance:
>      instance Class (Show a) (Foo a) where cls = Sub Dict
> With that instance, we can properly show values of type (Some Foo):
>      ghci> Some () :: Some Foo
>      ()
> But this instance is both trivial and annoying, since it means the
> machinery leaks out of the implementation code and into the code that
> uses it. I’m wondering if there’s any way to do this more generally, and
> if not, if there’s any reason it could not or should not be supported
> by GHC itself.
> Alexis
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