WIP: Add default IsScalar trait

[pabloferz]

While struggling with #16986, I figured that an IsScalar trait (as opposed to HasLength by default) would help to handle the different scenarios that broadcast might encounter.

[mauro3]

This could be useful outside Base too. For instance in ODE.jl, we try to do computations component-wise when the state is a Vector-like thing and not if it is scalar-like. Whilst dispatching on AbstractVector vs Any should catch most use cases, there are probably some which are not covered. See https://github.com/JuliaLang/ODE.jl/blob/a0ef97d6249e62a089370787850ae697e3d94962/src/runge_kutta.jl#L173

[nalimilan]

Wouldn't it be better to have an IsCollection trait instead (which would be the inverse of IsScalar)? It would also be easier to define, as you know when something is a collection, while scalars are defined as anything which isn't a collection (including any custom type by default).

[pabloferz]

I wrote IsScalar in part because HasLength() as default seems incorrect #15977. Also because I was thinking in how to make broadcast, collect andproduct work with scalars while still disallowing iteration for numbers in the future.

I wouldn't mind having a an IsCollection trait. The problem for me is: what the default definition for iteratorsize(::Type) should be? or should we have iteratorsize throw an error for scalars an have only traits for collections? (that would make it difficult to work with scalars in functions that should handle iteration over combinations of those with arrays).

[nalimilan]

I wouldn't mind having a an IsCollection trait. The problem for me is: what the default definition for iteratorsize(::Type) should be? or should we have iteratorsize throw an error for scalars an have only traits for collections? (that would make it difficult to work with scalars in functions that should handle iteration over combinations of those with arrays).

Let's raise an error for now, since length doesn't work by default for scalars. Then we can revise this when deciding what to do of iteration on numbers.

[JeffBezanson]

I don't think it makes sense to say that an iterator is a scalar. "Scalar" has proven very difficult to pin down, the standard example being Strings, which are iterable but also often occur as array elements. The best approach is to use something like broadcast(s->"pfx"*s, strings) instead of expecting broadcast(*, "pfx", strings) to work.

[stevengj]

My feeling (see ##16966) is that broadcast should default to treating things as scalars, unless broadcast_shape has been defined for them. map should should default to treating things as iterables. Then there is a well-defined role for each function.

(In particular, I think broadcast should treat strings as "scalars".)

In consequence, I don't think broadcast or map should need one to define an IsScalar trait.

[pabloferz]

Closing this, given that the strategy followed in #16986 does not need of this trait. If there is interest in the future for something like it I can reopen it and work on it.