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/...