The J programming language, developed in the early 1990s by Kenneth E. Iverson and Roger Hui,[4][5] is a synthesis of APL (also by Iverson) and the FP and FL function-level languages created by John Backus.[6]
To avoid repeating the APL special-character problem, J uses only the basic ASCII character set, resorting to the use of the dot and colon as inflections[7] to form short words similar to digraphs.
Looks like in case of J a lot of consideration was given to what's relatively easy to do in terms of chosen set of symbols. The question is, if ASCII wouldn't be a requirement, what would be a modern set of primitives, efficient as the tool for thought. APL at the time was trying to extend - and improve - mathematical notation, no less...
I love this question.
Moving from APL to J is really a step backward in terms of notation. With unicode standard flourishing, we might finally see something that can improve upon the mathematical notation we use and make instructing computers easier. I don't think anyone would be able to answer though… Perhaps one could extend APL symbols to cover all of the J primitives?
If yes then Iverson created really well thought out set which stood the test of time and we can hope will continue to efficiently serve as a good notation - and might be may be extended. If not - then we have the question of what would be a good notation.
References to math notation, which developed over decades and centuries, are good - but sometimes look like not perfect. Iverson was trying to make it better - for example, put the notation in one line, get rid of operation priorities. Is that a success from today's point of view?