How to put constraints on type variable of kind `Constraint`?

Question

I\'m playing around with the ConstraintKinds extension of GHC. I have the following data type, which is just a box for things fulfilling some one parameter constrai

Answer 1

You cannot make Some c an instance of Show, except trivially.

You want to show the a inside Some, but that variable is existentially quantified, so we cannot depend on any knowledge of the type of a. In particular, we have no way of knowing that a is an instance of Show.

EDIT: I'll expand on my answer. Even with more machinery, and giving up on a Show instance, I still don't think what you want is possible because of the existential quantification.

First I'll rewrite Some in a more familiar form

data Dict p where
    Dict :: p a => a -> Dict p

The usual way to talk about "constraints implying constraints" is with the concept of constraint entailment.

data p :- q where
    Sub :: p a => Dict q -> p :- q

We can think about a value of type p :- q as a proof that if the constraint forall a. p a holds, then forall a. q a follows.

Now we try to write a sensible show-ish function

showD :: p :- Show -> Dict p -> String
showD (Sub (Dict a)) (Dict b) = show b

At a glance, this might work. We have brought the following constraints into scope (forgive the pseudo-exists syntax)

(0) p :: * -> Constraint
(1) exists a. p a           -- (Dict p)
(2) exists b. p b => Show b -- (p :- Show)

But now things fall apart, GHC rightfully complains:

main.hs:10:33:
    Could not deduce (Show a2) arising from a use of `show' 
    from the context (p a)
      bound by a pattern with constructor
                 Sub :: forall (p :: * -> Constraint) (q :: * -> Constraint) a.
                        (p a) => 
                        Dict q -> p :- q,
               in an equation for `showD' 
      at main.hs:10:8-19                    
    or from (Show a1) 
      bound by a pattern with constructor
                 Dict :: forall (p :: * -> Constraint) a. (p a) => a -> Dict p, 
               in an equation for `showD'
      at main.hs:10:13-18 
    or from (p a2)
      bound by a pattern with constructor
                 Dict :: forall (p :: * -> Constraint) a. (p a) => a -> Dict p,
               in an equation for `showD'
      at main.hs:10:23-28   

because it is impossible to unify the a from (1) with the b from (2).

This is the same essential idea that is used throughout the constraints package mentioned in the comments.