There is a bit of information in this thread:

https://stackoverflow.com/questions/46967744/rank-operator-vs-axis-notation

On Wed, Dec 20, 2017 at 4:37 AM, Erling Hellenäs <[email protected]>
wrote:

> What I found in this paper is that Rank was a concept already in some APL
> dialects. It was not new to J. I did not find any direct comparison between
> the axis notation and the rank notation which could justify the selection
> of the latter for J. /Erling
>
>
>
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