I talked to Dimitrios. Fundamentally we think we should be able to handle recursive superclasses, albeit we have a bit more work to do on the type inference engine first.

The situation we think we can handle ok is stuff like Edward wants (I've removed all the methods):

class LeftModule Whole m => Additive m

class Additive m => Abelian m
class (Semiring r, Additive m) => LeftModule r m

class Multiplicative m where (*) :: m -> m -> m
class LeftModule Natural m => Monoidal m

class (Abelian m, Multiplicative m, LeftModule m m) => Semiring m
class (LeftModule Integer m, Monoidal m) => Group m

class Multiplicative m => Unital m

class (Monoidal r, Unital r, Semiring r) => Rig

class (Rig r, Group r) => Ring r

The superclasses are recursive but
a) They constrain only type variables
b) The variables in the superclass context are all
mentioned in the head. In class Q => C a b c
fv(Q) is subset of {a,b,c}

Question to all: is that enough?

This would perfectly address all of the needs that I have had!

-Edward