[Haskell-cafe] Context for type parameters of type constructors

[Dylan Thurston]

On Mon, Mar 29, 2004 at 06:00:57PM +0200, Henning Thielemann wrote:
> Thus I setup a type constructor VectorSpace
> in the following way:
> 
> > module VectorSpace
> >    where
> >
> > class VectorSpace v where
> >    zero  :: v a
> >    add   :: v a -> v a -> v a
> >    scale :: a -> v a -> v a
> 
> I haven't added context requirements like (Num a)
> to the signatures of 'zero', 'add', 'scale'
> because I cannot catch all requirements
> that instances may need.
> 
> The problematic part is the 'scale' operation
> because it needs both a scalar value and a vector.
> Without the 'scale' operation
> 'v' could be simply a type (*)
> rather than a type constructor (* -> *).

Right.

I recommend you use multi-parameter type classes, with a type of the
scalars and the type of the vectors.  For the method you're using, you
need to add a 'Num a' context.  You say that you 'cannot catch all
requirements that instances may need', but certainly any instance will
need that context.

If you use multi-parameter type classes, then in your instance
declaration you can specify exactly what requirements you need.  For
instance:

> class VectorSpace v a where
>   zero :: v
>   add :: v -> v -> v
>   scale :: a -> v -> v

> instance VectorSpace IntArray Int where ...

> instance (Num a) => VectorSpace (GenericArray a) a where ...

Peace,
	Dylan
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