Transform systems robustly by remaking systems

[hersle]

This is an attempt to strengthen the robustness of system transformations (i.e. processes that turn one system into another).

Internally, as pointed out in #1710 and #1752, there is inconsistency between

1. transformations that re-calls the system constructor with the modified fields (dropping unspecified fields, but redoing checks),
2. transformations that uses @set! sys.field = value from Setfield.jl (keeping unspecified fields, but skipping checks).

Field dropping has spawned bugs like #2845 and #2502, which usually gets "duct tape patched" by adding that single field for one particular system type. Transforming systems in a uniform way could prevent such bugs in the future, and maybe simplify some internal machinery. Maybe it would also be more efficient to "batch remake" several modified fields with a single new constructor call, rather than @set! sys.field1 = value1; @set! sys.field2 = value2; ... which I think calls the constructor several times.

Externally, I "envision" that a simple and robust interface could facilitate users making their own custom transformations. Maybe another package using ModelingToolkit would like to build models in a way that requires some simple application-dependent transformation of the system. Every user shouldn't have to reinvent a machinery for doing this themselves.

This is a draft for now. I would really appreciate thoughts and suggestions, or to know if you think this is not a good idea.

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

[hersle]

For now I've tried the remake(sys) functionality out in a few select places. In particular, I "showcase" how it can be used to implement an extend() function that handles all fields of arbitrary system types (hopefully).

I would try to take it further, but first I think it is more important to decide whether this is a good idea at all, and if so to settle the base mechanism 😅

[ChrisRackauckas]

I think this is a great idea. Indeed mutation is not a good idea on systems, and a safe remake would help make things more robust for people to do things.

[isaacsas]

FWIW in Catalyst I came to the conclusion this would be very helpful to have and perhaps reduce errors when transforming systems a little while ago: SciML/Catalyst.jl#935

We would definitely hook into this for ReactionSystems.