[Haskell-cafe] Re: Fundeps: I feel dumb

[Creighton Hogg]

On 13 Apr 2006 03:27:03 -0000, oleg at pobox.com <oleg at pobox.com> wrote:
>
> Creighton Hogg wrote:
>
> >     No instance for (MatrixProduct a (Vec b) c)
> >       arising from use of `<*>' at <interactive>:1:3-5
> >     Probable fix: add an instance declaration for (MatrixProduct a
> >     (Vec b) c)
> >     In the definition of `it': it = 10 <*> (vector 10 ([0 .. 9]))
>
> Let us look at the instance
>
>   class MatrixProduct a b c | a b -> c where
>     (<*>) :: a -> b -> c
>   instance (Num a) => MatrixProduct a (Vec a) (Vec a) where
>
> it defines what happens when multiplying a vector of some numeric type
> 'a' by a value _of the same_ type. Let us now look at the error
> message:
> >       (MatrixProduct a (Vec b) c)
>
> That is, when trying to compile your expression
>         10 <*> (vector 10 ([0 .. 9]))
> the typechecker went looking for (MatrixProduct a (Vec b) c)
> where the value and the vector have different numeric types. There is
> no instance for such a general case, hence the error. It is important
> to remember that the typechecker first infers the most general type
> for an expression, and then tries to resolve the constraints. In your
> expression,
>         10 <*> (vector 10 ([0 .. 9]))
> we see constants 10, 10, 0, 9. Each constant has the type Num a => a.
> Within the expression 0 .. 9, both 0 and 9 must be of the same type
> (because [n .. m] is an abbreviation for enumFromThen n m, and
> according
> to the type of the latter
>           enumFromThen :: a -> a -> [a]
> both arguments must be of the same type).
>
> But there is nothing that says that the first occurrence of 10 must be
> of the same numeric type as the occurrence of 9. So, the most general
> type assignment will be (Num a => a) for 10, and (Num b => b) for 9.

Thank you very much for the explanation:  it makes alot of sense.
So, if one does not want to for alot of type declarations into the
code, which would be fairly awkward, is there a way to do this with
fundeps or other type extensions that will be alot prettier or is any
way of defining type classes going to run into the same problems?