ConstraintKinds and default associated empty constraints

[Edward Kmett]

On Wed, Dec 21, 2011 at 6:45 PM, Bas van Dijk <v.dijk.bas at gmail.com> wrote:

> I'm playing a bit with the new ConstraintKinds feature in GHC
> 7.4.1-rc1. I'm trying to give the Functor class an associated
> constraint so that we can make Set an instance of Functor. The
> following code works but I wonder if the trick with: class Empty a;
> instance Empty a, is the recommended way to do this:
>
> {-# LANGUAGE ConstraintKinds, TypeFamilies, FlexibleInstances #-}
>
> import GHC.Prim (Constraint)
>
> import Prelude hiding (Functor, fmap)
>
> import           Data.Set (Set)
> import qualified Data.Set as S (map, fromList)
>
> class Functor f where
>     type C f :: * -> Constraint
>     type C f = Empty
>
>     fmap :: (C f a, C f b) => (a -> b) -> f a -> f b
>
> class Empty a; instance Empty a
>
> instance Functor Set where
>     type C Set = Ord
>     fmap = S.map
>
> instance Functor [] where
>     fmap = map
>
> testList = fmap (+1) [1,2,3]
> testSet  = fmap (+1) (S.fromList [1,2,3])
>
> Cheers and thanks for a great new feature!
>
> Bas
>
>
This is the same solution I wound up with in

https://github.com/ekmett/constraints

Adding an argument to the family would work but is somewhat unsatisfying as
it mucks with polymorphic recursive use of the dictionary, and with placing
constraints on constraints, so I prefer to keep as few arguments as
possible.

You can go farther with Functor by using polymorphic kinds and indexing the
source and destination Category as well as the class of objects in the
category.

I should probably write up what I've done with this, but doing so lets you
have real product and coproduct Category instances, which were previously
not possible (a fact which in part drove me to write all the semigroupoid
code i have on hackage.

-Edward
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