ConstraintKinds and default associated empty constraints

[Gábor Lehel]

On Mon, Jan 9, 2012 at 4:53 PM, Simon Peyton-Jones
<simonpj at microsoft.com> wrote:
> Three things about this ConstraintKinds thread:
>
> First, about
>  class Functor f where
>    type C f a :: Constraint
>    type C f a = ()
> vs
>  class Functor f where
>    type C f :: * -> Constraint
>    type C f = \_ -> ()
>
> I don't know any way of dealing in a decent way with the latter, because it lacks type level lambdas.  GHC currently allows only the former.  I hope that is enough.  If not, perhaps give an example?
>
>
> Second, it's true that the former would permit you to *index* on 'a' as well as being parametric in 'a' (which is probably more what you intend).  That's a deficiency, but it's largely a notational one.  Maybe there should be some way to specify in a type family definition that some parameters can't be used for indexing.  It's orthogonal to the question of Constraint kinds, or of defaults for associated types.
>
>
> Third, () does indeed stand both for the unit tuple and for the empty constraint, depending on context.  So the code below works fine with HEAD.  I think it's ok with the 7.4 branch too, but it would be safer if someone would check that.  I included a test for the case tha Antoine found an error with, namely
>            Could not deduce (FC [] Int) arising from a use of `fmap'
>
> Simon
>
> ===================================================================
> {-# LANGUAGE ConstraintKinds, TypeFamilies, FlexibleInstances #-}
> module CK where
>
> 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 a :: Constraint
>    type C f a = ()
>
>    fmap :: (C f a, C f b) => (a -> b) -> f a -> f b
>
> instance Functor Set where
>    type C Set a = Ord a
>    fmap = S.map
>
> instance Functor [] where
>    fmap = map
>
> testList = fmap (+1) [1,2,3]
> testSet  = fmap (+1) (S.fromList [1,2,3])
> test2 = fmap (+1) [1::Int]

The problem with this is that you can't write, for example:

type OldFunctor f = (Functor f, forall a. C (f a) ~ ())

(If we had quantified contexts[1], then maybe, but we don't, and it
doesn't seem like it would be even theoretically possible for indexed
constraints without whole program analysis.)

With the other solution, though, you can write:

type OldFunctor f = (Functor f, C f ~ Empty) -- (In the real world I'd
rather call these Functor and Exofunctor...)

Again, I have no problem at all with the Empty class, it's the same
solution I've used. It's even kind polymorphic if you turn that
extension on. The syntax isn't superficially as nice, but it's nice
enough, does the job, and I don't see how you could do better short of
adding type-level lambdas (so you can write type C f = \_ -> ()).

[1] http://hackage.haskell.org/trac/ghc/ticket/2893


>
> | -----Original Message-----
> | From: glasgow-haskell-users-bounces at haskell.org [mailto:glasgow-haskell-
> | users-bounces at haskell.org] On Behalf Of Andres Löh
> | Sent: 09 January 2012 07:28
> | To: Antoine Latter
> | Cc: glasgow-haskell-users at haskell.org
> | Subject: Re: ConstraintKinds and default associated empty constraints
> |
> | Hi.
> |
> | > The definitions are accepted by GHC:
> | >
> | >   class Functor f where
> | >       type FC f a :: Constraint
> | >       type FC f a = ()
> | >
> | >       fmap :: (FC f a, FC f b) => (a -> b) -> f a -> f b
> | >
> | >   instance Functor [] where
> | >       fmap = map
> |
> | Yes. This is what I would have expected to work.
> |
> | > But I don't like the 'a' being an index parameter, and then the
> | > following expression:
> | >
> | >   fmap (+1) [1::Int]
> | >
> | > Gives the error:
> | >
> | >    Could not deduce (FC [] Int) arising from a use of `fmap'
> | >    In the expression: fmap (+ 1) [1 :: Int]
> | >    In an equation for `it': it = fmap (+ 1) [1 :: Int]
> | >
> | >> gives the error:
> | >>
> | >>    Number of parameters must match family declaration; expected 1
> | >>    In the type synonym instance default declaration for `FC'
> | >>    In the class declaration for `Functor'
> |
> | I get the same error, but it looks like a bug to me: If I move the
> | declaration
> |
> | type FC f a = ()
> |
> | to the instance, then the example passes.
> |
> | Cheers,
> |   Andres
> |
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>
>
>
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