Hi Richard,

Thanks a lot for your answer.
We had a discussion about some "Tensor" type some time ago:


Today I have a type constructor "Tensor" in which there is a data 
constructor Tensor (among others):

data Tensor :: Nat -> * where
    Tensor :: String -> [IndependentVar] -> Tensor order

The idea is that, for example, I may have a vector function of time and 
position, for example the electric field:

E( r, t )

(E: electric field, r: position vector, t: time)

So, I have a Tensor (E) that depends on two tensors (r and t). I want to put 
r and t in a list, the list of independent variable of which E is a 
function. But we see immediately that r and t have not the same type: the 
first is of type "Tensor One", the second of type "Tensor Zero". Thus we 
cannot put them in a list. This is why I have tried to use an heterogeneous 


Thus in the first place the problem comes from the fact that I have put the 
order of the Tensor in the type rather than in the data constructors. But it 
is useful:

* I can make type synonyms
type Scalar = Tensor Zero
type Vector = Tensor One

* with multi-parameter typeclasses, I can define operations as:

class Division a b c | a b -> c where
     (/) :: a -> b -> c

and then I implement these operations on a subset of types:

instance (PrettyPrint (Tensor a)) => Division (Tensor a) Scalar (Tensor a) 
   ZeroTensor / _ = ZeroTensor
   _ / ZeroTensor = error "Division by zero!"
   t / s = Divide t s

So, the code is clear, and instead of runtime dimension checks, everything 
is detected at compilation. So the choice of putting the order in the type 
seems to be correct.
My only need to use Typeable comes from the heterogeneous list. But how to 
do without?



Richard Eisenberg wrote:

> Thankfully, the problem you have is fixed in HEAD -- the most recent
> version of GHC that we are actively working on. I am able, using the HEAD
> build of GHC, to use a `deriving Typeable` annotation to get a Typeable
> instance for a type that has non-*-kinded parameters. To get the HEAD
> compiler working, see here:
> http://hackage.haskell.org/trac/ghc/wiki/Building
> However, I'm worried that other aspects of your design may be suboptimal.
> The `Box` type you mentioned a few posts ago is called an existential
> type. Existential types have constructors who have type parameters that
> are *not* mentioned in the conclusion. As an example, your `Box`
> constructor involved a type parameter `a`, but the `Box` type itself has
> no parameters. This existential nature of the type is why your comparison
> didn't work.
> A Tensor, however, doesn't seem like it would need to be an existential
> type. The order of the tensor should probably (to my thinking) appear in
> the type, making it not existential anymore.
> In general, I (personally -- others will differ here) don't love using
> Typeable. By using Typeable, you are essentially making a part of your
> program dynamically typed (i.e., checked at runtime). The beauty of
> Haskell (well, one of its beauties) is how it can check your code
> thoroughly at compile time using its rich type language. This prevents the
> possibility of certain bugs at runtime. Using Typeable circumvents some of
> that, so I would recommend thinking carefully about your design to see if
> its use can be avoided.
> Just to diffuse any flames I get for the above paragraph: I fully support
> the role of Typeable within Haskell. Indeed, sometimes it is unavoidable.
> In fact, I have a small update to the Typeable interface on my to-do list
> (adding functionality, not changing existing). I am just arguing that its
> use should be judicious.

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