Quick summary: Gilad Bracha introduces a new programming language called ShapeRank. It seems to be based on APL but introduces the concept of streams which are [vectors | tensors | arrays] of unbounded length.
Personally I think array programming languages are the future and one of the most popular programming languages in science and engineering is Matlab, and it is to some extent an array based programming language [1].
I am surprised that the author (and reviewers of the paper) has missed to perform proper literature review, for example it missed other recent and promising works on functional array programming languages namely Single Assignment C (SAC) and Futhark [2],[3].
ShapeRank also seems to take vector algebra "tensor" concept to the extreme and to be honest it's better to based on "versor" since geometric algebra is probably the future of computer algebra [4].
Last but not least and probably the most controversial is that why create another standalone array language from scratch? It will be better to make a seamless DSL based on general purpose language like D language and you do not have to re-invent most of the libraries (and C library support in D is second to none). Arguably the most successful recent effort on array based scientific programming language is Julia and it is still very much dependent on some Fortran based libraries for speed. While with D you can go "turtle all the way down" and still meet the speed requirements that are needed in scientific computing [5].
[1]https://en.m.wikipedia.org/wiki/Array_programming
[2]http://www.sac-home.org/doku.php
[4]https://en.m.wikipedia.org/wiki/Comparison_of_vector_algebra...
[5]http://blog.mir.dlang.io/glas/benchmark/openblas/2016/09/23/...
I'd love to drop Python and go all in with a true array language (i.e. not Matlab), but you only really have 4 options:
Dyalog APL, J, Kdb+, Shakti.
All of those are closed source and expensive (Dyalog is fairly affordable, but still a paid product) with the exception of J. J is a cool language, but isn't quite my cup of tea.
So if one of the new projects ever picked up steam and got a decent sized community with hooks into all the same numeric libraries as Numpy, and some decent charting libraries...then we would have something nice.