[Haskell-cafe] instance Monad m => Functor m

[Hans Aberg]

On 9 Apr 2008, at 15:23, Henning Thielemann wrote:
>> I don't know if it is possible to extend the syntax this way, but  
>> it would be closer to math usage. And one would avoid duplicate  
>> definitions just to indicate different operator names, like:
>> class AdditiveMonoid a where
>>   o :: a
>>   (+) :: a -> a -> a
>> as it could be create using
>> class Monoid (a; o, (+))
>
> I also recognized that problem in the past, but didn't know how to  
> solve it. In Haskell 98, methods are resolved using the types of  
> the operands. How would the compiler find out which implementation  
> of (+) to choose for an expression like x+y using your approach?

Different names result in different operator hierarchies. So a class  
like
   class Monoid (a; unit, mult) where
     unit :: a
     mult :: a -> a -> a
must have an instantiation that specifies the names of the operators.  
In particular, one will need a
   class (Monoid (a; 0; (+)), ...) => Num a ...
if (+) should be used as Monoid.(+) together with Num.(+).

Or give an example you think may cause problems, and I will give it a  
try.

   Hans