Proposal: Add Applicative (and Monoid) instances in GHC.Generics

[Li-yao Xia]

I propose to implement Applicative (and Monoid) instances in 
GHC.Generics, where possible.

Note that we already have Applicative instances for most of those types, 
with the notable exceptions of sums (:+:) (for good reason), and K1 
(which is basically Const).

This would make it possible to easily derive Applicative and Monoid for 
generic product types. That can be useful to merge large configuration 
records, for example.

For that purpose, the missing Applicative instance for K1 is the actual 
limiting factor, as it is sufficient in order to derive the product 
Monoid and Applicative via Generic and Generic1, respectively. The 
Monoid instances for the GHC.Generics constructors might just be fluff 
on top of this.

Current alternatives include: roll your own, semigroups [1], or some 
generic programming library (e.g., one-liner). This proposal offers a 
more lightweight solution.

To summarize, and to organize bikeshedding, I would split this proposal 
in three parts, in order of perceived usefulness:

1. Add an instance (Monoid c => Applicative (K1 i c))

2. Add helpers

         gmempty :: (Generic a, Applicative (Rep a)) => a
         gmempty = to (pure ())

         gmappend :: (Generic a, Applicative (Rep a)) => a -> a -> a
         gmappend a b = to (from a <*> from b)

         -- also gpure, gap for generic Applicative

3. Add Monoid instances

Regards,
Li-yao


[1] 
https://hackage.haskell.org/package/semigroups-0.18.4/docs/Data-Semigroup-Generic.html