Traits for static arrays and friends

One thing that was realized in the AbstractArray interface is that traits are a convenient and powerful way of expressing ways of interacting with different types of arrays, the prototypical exampling being LinearFast vs LinearSlow. I wanted to discuss some possible traits that would be useful for StaticArrays.jl while keeping in mind that with future language enhancements (e.g. the trait system experiments of Traitor.jl) might make them easier to use and interface into Base in the future.

• Dispatch on size. We could have some kind of Dimensions trait (@timholy suggested SDims to complement Base.Dims). Unlike FixedSizeArrays, the size isn't specified in the abstract StaticVector{T}, while the package is meant to use the size() on types interface, it doesn't make it easy to allow, e.g., any 3-vector. Introducing a trait would at least allow an "official" way of doing that. Speculatively, this could be extended so that SDims <: AbstractDimensions and Base.Array etc have a dimensions trait with run-time size information (but compile-time rank). The dimensions trait could be combined with the "indices" trait being proposed/used in Base for non-1-based indexing.
• Mutable vs. immutable. Or, more specifically, does setindex! work? Most algorithms in Base are defined using similar but that doesn't work for immutables, and it is a pain to define alternatives here that things other than StaticArray can't use at all.
• Perhaps stack-allocated vs heap-allocated? We would put extra effort in for stack-allocated things so that we never make new heap allocations. This is obviously related to Mutable vs Immutable and similar vs similar_type.

Any thoughts appreciated. Is it a good idea to be defining types here, in this package?

Start by reading the issue's discussion of AbstractArray, LinearFast versus LinearSlow, and the linked Traitor.jl experiments. Compare the proposed dimensions, mutability, and allocation traits with the package's current interfaces. Done requires a maintainer-approved trait design and an agreed implementation scope; this issue does not name files or tests.