On the `context` argument for `expressify`

[fingolfin]

Following up issue #1099, I think it would be good if the context argument to expressify was documented, as in: what is it, and how should expressify methods use it? As far as I can tell, it is ultimately passed down to sprint, so we could just say that.

Moreover, though, I think it is supposed to pass to any recursive expressify invocations. Yet this is not always done, e.g. from the AA sources:

function expressify(a::FracElem; context = nothing)
    n = numerator(a, true)
    d = denominator(a, true)
    if isone(d)
        return expressify(n)
    else
        return Expr(:call, ://, expressify(n), expressify(d))
    end
end

and a bunch similar ones. Am I right in assuming these are not intentional, and we really should be adding a bunch of context=context args?

In that case, perhaps it would be worthwhile to reconsider whether context really should be an optional argument. Perhaps it should be required? Possibly even a positional argument instead of a keyword argument.

[tthsqe12]

This one is for @thofma as my original concept of expressify did not have a context. Some things to consider:

1. Does the ~:terse~:compact=>true go in the context?
2. Can a :latex=>true go in the context? If yes, this would make Expr(:latex_form, a, b) a bit redundant.
3. The :size_limit=>100 belongs in the io context and not the context to expressify.

[thofma]

Yes, it should be used recursively. We bolted it onto the system later and wanted to be backwards compatible. That is why it is a keyword argument with default value.

All properties can go into the context that we want, but then we have to be careful with the MIME types.

It is all a bit brittle and the julia printing "system" does not help much with consistency. For example, do you know which method is used to print the element p::MyType when displaying [p, p, p]? It checks whether

Base.show(io::IO, ::MIME"text/plain", p::MyType)

prints a new line and if not it calls

Base.show(io::IO, p::MyType)

(see https://github.com/JuliaLang/julia/issues/36253). There is no context flag indicating whether printing is invoked inside array printing. For dimension > 1 I think :compact => true is, but not for Vector.