The Representation Problem: semantic types, vs computational types

Types get used in many ways, especially in Julia.
We can for this discussion break them down into two kinds.
Either a semantic use:for example the Int 5 in fill(x, 5)
or computational convience use, e.g. the Int 5 in exp2(5),
where it is just much faster to compute exp2 if your input is a Int.

In the semantic use, that Int has no derviative, it differential is DoesNotExist.
Or the singleton differential.

Where as in the computational convience case, the Int has a deriviative it's exp2(5)*log(2).

This also occurs for various kinda of (structured) sparsity.
Where you might do for computational convience f(u::AbstactMatrix) = istriu(u) ? f(UpperTrriangular(u)) : ...
Its important not to allow pertubations on the structual zeros of sparse types, when those have semantic meaning.
But when they don't then you should allow them to be perturbed.

idk if this affects us directly.
It might be something to document.

The issue names no files, tests, or entry points. Start by reviewing the existing ChainRulesCore documentation and conventions for semantic versus computational types, then determine whether the distinction can be documented and what examples would establish the intended derivative behavior.