Don Watson asked me to post this on his behalf, and it should be of
interest to the chat forum:

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There were two characteristics of APL in the 1960s that attracted people.
It was powerful and it was easy to teach - in fact I wrote a self-teaching
package that enabled APL to teach people the beginnings of how to use
itself - it got them started. My interest was in using it to teach
Mathematics and I was attracted by a 2 day conference Ken Iverson gave in
1968 on “The role of the computer in teaching”. When he moved on to J, a
powerful nature was his priority and Mathematics teaching was left behind.

The use of both Mathematics and Computing by professionals other than
mathematicians and computer scientists is decreasing in favour of "black
boxes". Today, few professionals other than Computer Scientists model their
work by programming any more – as they did when APL was first available.
There was an interesting blog recently in the ACM that found that they
would model if it was in their own language. I interpret that as meaning
that they want something in the manner that spreadsheets provided when they
spoke the language of managers. Scientists and engineers don't program
because it is too much trouble.

The language of scientists and engineers is Mathematics. There is a huge
potential market for a computer language that uses mathematical notation
where you use tacit expressions. APL was born in the 1960s, when input and
output was based on one-dimensional typewriters. Mathematics is two
dimensional. This meant that Iverson was forced to compress a tree
structure into an artificial train structure. However, the Macintosh was
mass produced with a two-dimensional screen 30 years ago. I wish Iverson
had then begun allowing APL notation to become a mathematical tree
structure and removed the artificiality. Unfortunately, he stated in 1996
that Mathematics couldn't be processed by a computer - which isn't true.

A new software teaching tool bases Mathematics on functions, removing the
need for abstract operators in elementary school. It is based upon the use
of Mathematics expressions as a computer language - which was achieved with
a single change to Mathematics notation - by adding a different kind of
variable. Basing Mathematics on functions, where the action is, could unite
Mathematics and Computing in a common front that could bring about the
return of both as modelling methods.

I am almost 80 years of age and unable to contribute anything to the needs
of professionals. I have enough work to do expanding my “Foundation” system
to meet the needs of elementary and high schools to grade 12. J could
certainly be adapted for this purpose – all that is needed is to change the
front end to a tree structure. If J doesn't do it somebody else will. There
are other issues, like relating documentation to non-mathematicians and
returning to an elegant control structure as APL originally provided, but
that is simply achievable.

A paper with embedded videos at the website
www.FoundationNotation.comdemonstrates how Foundation works and
explains why it works. So far
Foundation has been implemented as a Macintosh app and an Ipad app.
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