Trait-based dispatch

[YingboMa]

Using the standard Julia type hierarchy limits people to do <: Number when defining a type, but this is not generally doable for generic codes. I wonder if we can use isreal, iscomplex, isscalar, ismatrix, etc to do the dispatch.

[YingboMa]

One common example is a wrapper type that tries to simulate Var{T} <: T. It's impossible to use ChainRules.jl on that with the current approach.

[oxinabox]

I see what you are saying.
With noting to be clear:
If the primal function uses trait dispatch, then the rule must also.
And if the primal function doesn't, then you need 1 rule method per primal method.
That's actually almost always true, needing one rule method per primal method.

Though a question is: why do you need rules for Var{T} that acts like T?
In most code I have seen/written such objects delegate a call of foo(x::Var{T}) to a call of foo(::T).
Either on a field or on a value it computes. Potentially, with some pre or post processing.
Thus, if you have a rule for foo(::T), then your AD should easily and efficiently (maybe constant folded even) take care of making sure foo(::Var{T}) works.

[YingboMa]

For symbolic manipulations, we need to have Var{T} that doesn't call into foo(::T) directly, since Var{T} doesn't know the actual value, but at the same time, Var{T} needs to behave like T to trace through the program.

[lamorton]

Here's a potential use-case. ODESolutions allow indexing using a symbolic variable name. Internally, solution_interface.jl specializes getindex to either look up or compute the result as necessary.

Whether a variable is considered symbolic is defined by the function issymbollike, not by a particular type. It would be nice to dispatch on this, because at present I'm getting method ambiguities.