More concise printing of detector type?

[gdalle]

I'm wondering if we can make the printing of TracerSparsityDetector() shorter. At the moment it looks like

julia> TracerSparsityDetector()
TracerSparsityDetector{SparseConnectivityTracer.GradientTracer{SparseConnectivityTracer.IndexSetGradientPattern{Int64, BitSet}}, SparseConnectivityTracer.HessianTracer{SparseConnectivityTracer.DictHessianPattern{Int64, BitSet, Dict{Int64, BitSet}, SparseConnectivityTracer.NotShared}}}()

But we don't have to specify all type parameters if they correspond to the default settings. You can draw inspiration from the new printing I coded for ADTypes, which only tries to reproduce the constructor. See example here: https://github.com/SciML/ADTypes.jl/blob/f206682addbc27b450f51d51e9a4082fb9b7cdb4/src/dense.jl#L190-L196

[adrhill]

Yes, that would be an improvement.

[adrhill]

How about this?

julia> for detector in (:TracerSparsityDetector, :TracerLocalSparsityDetector)
           @eval function Base.show(io::IO, d::$detector{GradientTracer{PG}, HessianTracer{PH}}; indent=0) where {PG,PH}
               println(io, $detector, "{")
               println(io, "  ", "GradientTracer pattern: ", PG)
               println(io, "  ", "HessianTracer pattern:  ", PH)
               print(io, "}")
               return nothing
           end
       end

julia> TracerSparsityDetector()
TracerSparsityDetector{
  GradientTracer pattern: SparseConnectivityTracer.IndexSetGradientPattern{Int64, BitSet}
  HessianTracer pattern:  SparseConnectivityTracer.DictHessianPattern{Int64, BitSet, Dict{Int64, BitSet}, SparseConnectivityTracer.NotShared}
}

Or should we just print TracerSparsityDetector() instead of leaking all our internals?

[gdalle]

Ideally, Base.show(io, object) is supposed to give you a string that you can parse back into the object itself. Of course not everyone knows or cares. In any case, I don't think most users will ever go beyond TracerSparsityDetector(), and those users don't need to know the type parameters. So for them, I would simplify printing of at least the default detector, and maybe leave complex printing if one of the settings differs from the default?