Deriving for Classes

DerivingClasses.md

Just like you can derive instances for data types (example is from homoiconic)

data Foo = F Int Bool 
 deriving Show

maybe it makes sense to do it for certain type classes.

If you define

class Num a where
 (+), (-), (*) :: a -> a -> a
 negate, abs, signum :: a -> a
 fromInteger :: Integer -> a
 
class Num a => Fractional a where
 (/) :: a -> a -> a
 recip :: a -> a
 fromRational :: Rational -> a

the following instances could be define automatically

instance FAlgebra Num where
 data Sig Num a
  = Sig_add a a
  | Sig_mul a a
  | Sig_min a a
  | Sig_neg a
  | Sig_abs a
  | Sig_signum a
  | Sig_fromInteger Integer
  deriving Functor
  
 runSig :: Num a => Sig Num a -> a
 runSig (Sig_add a b)  = a + b
 runSig (Sig_mul a b)  = a * b
 runSig (Sig_min a b)  = a - b
 runSig (Sig_neg a)    = negate a
 runSig (Sig_abs a)    = abs a
 runSig (Sig_signum a) = signum a
 runSig (Sig_fromInteger i) = fromInteger

instance FAlgebra Fractional where
 data Sig Fractional a
  = Sig_div a a
  | Sig_recip a
  | Sig_fromRational Rational
  | Sig_Fractional_Num (Sig Num a)
  deriving Functor
  
 runSig :: Fractional a => Sig Fractional a -> a
 runSig (Sig_div a1 a2)        = a1/a2
 runSig (Sig_recip a)          = recip a
 runSig (Sig_fromRational r)   = fromRational r
 runSig (Sig_Fractional_Num s) = runSig s

for a type class

class Functor (Sig alg) => FAlgebra alg where
 data Sig alg a
 runSig :: alg a => Sig alg a -> a

So my questions are

Are there other (Type -> Constraint) -> Constraint type classes that could be derived.

Could this be automated, like default instances using Generic