Is your feature request related to a problem? Please describe.

At the moment, Data.Monoid.Linear.Semigroup is defined as

class Prelude.Semigroup a => Semigroup a where
  (<>) :: a %1 -> a %1 -> a

with a Prelude.Semigroup superclass constraint. Theorically, this is correct. Indeed, any linear semigroup can be made into a non-linear semigroup just by upcasting (<>) :: a %1 -> a %1 -> a to (<>) :: a -> a -> a. A NonLinear newtype also exists in Data.Monoid.Linear.Internal.Semigroup to easily derive Prelude.Semigroup from (linear) Semigroup.

However, things get harder when we try to write a (linear) Semigroup instance for Ap f a. In base, we have instance (Prelude.Applicative f, Prelude.Semigroup a) => Prelude.Semigroup (Ap f a). In linear-base, we would like to have instance (Data.Functor.Linear.Applicative f, Data.Monoid.Linear.Semigroup a) => Data.Monoid.Linear.Semigroup (Ap f a).

But such an instance head requires Prelude.Semigroup (Ap f a) (because of the Prelude.Semigroup => Data.Monoid.Linear.Semigroup relationship), which is not deducible because f is a Data.Functor.Linear.Applicative, not a Prelude (non-linear) one.

Unfortunately, we can't add instance (Data.Functor.Linear.Applicative f, Prelude.Semigroup a) => Prelude.Semigroup (Ap f a), because this has the same head as instance (Prelude.Applicative f, Prelude.Semigroup a) => Prelude.Semigroup (Ap f a) already present in base.

Also, Semigroup and Monoid are the only linear classes which have their non-linear counterpart as superclasses, although it would also make sense for Ord or Eq for example.

Describe the solution you'd like

I see three potential solutions:

• Breaking the Prelude.Semigroup => Data.Monoid.Linear.Semigroup and Prelude.Monoid => Data.Monoid.Linear.Monoid relationships, allowing us to add the instance (Data.Functor.Linear.Applicative f, Data.Monoid.Linear.Semigroup a) => Data.Monoid.Linear.Semigroup (Ap f a)
• OR keeping them, but adding the same kind of reliationship for Eq, Ord, and any eligible linear class, and then
  • Not exporting the Ap newtype
  • OR adding a LinAp newtype