Dear Group, I want to define two classes called Group and Ring. The Group class is for Abelian Groups (G,+), i.e. groups with a binary commutative operator ``+'' and an identity element normally denoted by ``0''. The Ring class is meant for cummutative rings (R,+,*) with binary operators ``+'' and ``*'', where ``+'' is commutative and has identity element ``0'', and ``*'' is commutative with identity ``1''. I want to use classes because I want to define rings in terms of existing rings later. A neat way to define the Group and Ring classes seems to have the Ring class being a subclass of the Group class (each Ring should inherit the properties for addition from some Group). Let R be a Ring defined as such. Now it seems to me I have to do something along the following lines: > instance Num R where > (+) r1 r2 = .. -- because r1 + r2 reads a lot better than ``plus r1 r2'' > (*) r1 r2 = .. -- ,, * ,, times ,, > fromEnum i = .. -- so one can say sexy things like 1::R and the like > instance Group R where -- I only want to use (+) :: R -> R -> R but where I can use (*) :: R -> R -> R, which (to me) does not seem to be appropriate. Is there a proper (and simple) way of defining my Group and Ring which still allows me to overload (+) and (*)? Regards, Marc
