The MultiParamTypeClasses extension seems to be best suited for the task, as a group can act on many sets, and a set can be acted on by different groups:
-- | Represents an action of semigroup @g@ to set @a@.
--
-- Laws: @'Endo' . 'act'@ must be a homomorphism of semigroups.
class Semigroup g => SemigroupAct g a where
act :: g -> (a -> a)
But soon I realized that with MPTC the compiler has problems inferring types and I had to explicitly specify types when using `act` in many places. Because it seems that in most cases a set will have only a single group acting on it, I was thinking about using FDs:
class Semigroup g => SemigroupAct g a | a -> g where
But on the other hand, this can limit the generality of the type class. I cannot decide which one I should choose.
What would you suggest? According to your experience, would you choose plain MPTC or FD?
Best regards,
Petr Pudlak