Arrow Classes

[Wolfgang Jeltsch]

On Thursday, 2003-07-10, 15:33, Ross Paterson wrote:
> [...]

> There are more instances and methods for people to define, even if some of
> them imply others.
>
> As it happens, I would like yet another intermediate class:
>
> 	class BiFunctor a where
> 		bimap :: (b' -> b) -> (c -> c') -> a b c -> a b' c'
>
> (and I have a client for the class: a useful subset of the arrow notation
> needs only this, in fact only the contravariant part.)
>
> Clearly any arrow is also an instance of this class:
>
> 	bimap b c f = arr b >>> f >>> arr c
>
> but you still have to define bimap even if the type is also an arrow.
>
> Subclasses in Haskell cover a range of relationships, including this sense
> where things in the subclass automatically belong to the superclass. Other
> examples include Eq => Ord and Functor vs Monad.  In such cases it would be
> handy if the subclass could define defaults for the superclass methods (e.g.
> Ord defining (==)), so that the superclass instance could be optional.

Exactly. Maybe, the problem is not the existence of many classes but the lack 
of such an "defaults for superclass methods" feature.

Wolfgang