Better default `sizeof(::AbstractArray)`?

[mbauman]

By default, new AbstractArray subtypes fall back to the fully generic sizeof(::Any) implementation that simply gives the size of their fields. Given that we know more about what an AbstractArray is — and given that we have a default write implementation, it seems like we should be able to do a better job of getting closer to the docstring of sizeof:

Size, in bytes, of the canonical binary representation of the given DataType T, if any. Size, in bytes, of object obj if it is not DataType.

For example:

julia> write(IOBuffer(), rand(5,5))
200

julia> sizeof(rand(5,5))
200

julia> write(IOBuffer(), rand(5,5)')
200

julia> sizeof(rand(5,5)')
8

Even the "compressed" representations by default write their whole contents:

julia> using LinearAlgebra

julia> write(IOBuffer(), Diagonal(rand(5)))
200

julia> sizeof(Diagonal(rand(5)))
8

So it'd seem like a sizeof(A::AbstractArray) = length(A) * sizeof(eltype(A)) definition would be better all around. If your array has a specialized canonical representation, then you define sizeof to match when you implement write.