There are a bunch of packages exploring ideas around labelled dimensions, although we are still far from the vision of caring as little as we do about registers:

* https://github.com/JuliaArrays/AxisArrays.jl * https://github.com/davidavdav/NamedArrays.jl * https://github.com/invenia/NamedDims.jl * https://github.com/rafaqz/DimensionalData.jl * https://github.com/ITensor/ITensors.jl

While these don't pass dimension labels along in the type, there are also a number of Einsum-like packages which should work on any storage order, and could be taught to interface with such types:

* https://github.com/Jutho/TensorOperations.jl * https://github.com/under-Peter/OMEinsum.jl * https://github.com/mcabbott/TensorCast.jl