Special case derivative of non-holomorphic functions of type ℂ(^n)→ℝ

A common use case for non-holomorphic functions are norms and similar functions, that project a complex vector space onto the reals. These are also probably the most interesting for optimization problems. According to the Cauchy-Riemann equations, any such functions that are non-trivial have to be non-holomorphic, so we currently only have Wirtinger derivatives to describe these correctly.
In these cases, storing the full Wirtinger primal and conjugate is unnecessary, since by looking at the definitions, it is easy to see, that they each must be the complex conjugate of each other, so one would only need to store one of them. If used in arrays for example, this would save half the memory size otherwise required.
My proposal would be to introduce a singleton type, lets call it ConjugateOfWirtingerConjugatefor lack of a better name. This would be passed as primal to Wirtinger or WirtingerRule and signify that the Wirtinger primal is just the conjugate of the Wirtinger conjugate. This would need to be special cased in a couple of cases: For example if chained with a real derivative, ConjugateOfWirtingerConjugate can be preserved, though otherwise, this would need to fall back to a full Wirtinger derivative.
If there's consensus that something like this would be useful, I could prepare a PR. An alternative would be a special AbstractRule for these cases, which might make some things a bit cleaner, but it might be confusing to have two different types for derivatives of non-holomorphic functions. @jrevels seems to be the main instance on everything Wirtinger, what are your thoughts on this?

Start by examining the existing Wirtinger and WirtingerRule definitions and their handling of real-valued, non-holomorphic functions. Determine whether the proposed singleton type or a separate AbstractRule is appropriate, then add the required special cases and tests for conjugate storage, chaining, and fallback to a full Wirtinger derivative.