Decouple names from system construction about modelingtoolkit.jl HOT 4 CLOSED

I can certainly take a look. An option is to explicitly map the initial and final subtypes (e.g. DependentVariable => Variable for the nonlinear system hack) and have some default for the rest.

But I think there is a bigger issue than naming and is the fact that certain DSL will also require to create their own types that eventually lower into a Variable of a given subtype (potentially losing information in the process, which we may not want to). Making Expression an abstract type was a great step forward as I can create my own types that generate correct Operations, when applying the registered functions (and lower them to Variable at the end). But that makes me wonder whether DependentVariable et al. should also be abstract types (or some orthogonal trait system) rather than types.

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But that makes me wonder whether DependentVariable et al. should also be abstract types (or some orthogonal trait system) rather than types.

The issue there is that it will never be inferrable, so we'd want to avoid types as otherwise things could slow to a crawl because every piece of code becomes dynamic. As we have it, most things are non-dynamic except for Expression vectors. This is a lot like Julia's AST which uses symbols for things like functions in order to avoid overtyping. But,

But I think there is a bigger issue than naming and is the fact that certain DSL will also require to create their own types that eventually lower into a Variable of a given subtype (potentially losing information in the process, which we may not want to).

That shouldn't lose any information if we just allow information by composition. If we just allow a boxed composition pointer, then most of the generic routines can safely ignore that without an issue.

An option is to explicitly map the initial and final subtypes (e.g. DependentVariable => Variable for the nonlinear system hack) and have some default for the rest.

I don't think we need to explicitly map since making the names flexible will have other advantages anyways.

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Generic composition is now allowed via the context field.

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(1) is complete.

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