David Barbour
I wonder if I need something like your use of 'representation' types, i.e. to restrict what sort of elements can be stored in a collection. ... I'll admit to some reluctance, however, to clutter up several typeclasses with four more types. What are your thoughts regarding this issue?
Yes, they certainly do clutter things up... but really, the whole representation business is in there mostly to show that the "functor is identity-on-objects" requirement of Freyd categories need not apply to generalized arrows. If you want to reduce the clutter, the simple trick I'm experimenting with now works like this: start with your multi-parameter class class GArrow g (**) u where ... Then, for all but the first type argument, create a type family indexed by the first type argument: type family GArrowTensor g :: * -> * -> * -- (**) type family GArrowUnit g :: * -- u And then use -XFlexibleContexts to declare a wrapper class with only one argument: class (GArrow g (GArrowTensor g) (GArrowUnit g), GArrowCopy g (GArrowTensor g) (GArrowUnit g), GArrowSwap g (GArrowTensor g) (GArrowUnit g), ... ) => GArrowWrappedUp g I'm sure you could do something similar with the type parameters "c" and "r". The only price is that you can then have only one instance in scope at any given point in time. - a