Having done programming in the past, I can appreciate intuitively that the
mathematical properties of Joy and Factor are highly desirable.

I am having trouble defining precisely why, though.

I can imagine trying to convince a programming team and their managers to
implement their next project in Factor.

"Ok, gentlemen ...  For the next project we are going to use a language,
that is based on another purely-functional-language, but with more features.
Both languages have a syntax similar to arithmetic in
Reverse-Polish-Notation."

"You can think of the language as the following ... "
[
There are three useful styles:

   1. Imperative: programs are commands to modify the stack.
      - e.g. "5" means: push the number 5 !
      - e.g. "+" means: add the top two numbers !
   2. Semantic: programs denote unary functions from stacks to stacks.
      - e.g. "5" denotes the functions which yields a new stack with the
      number 5 on top.
      - e.g. "+" denotes the function which yields a new stack with the top
      two numbers replaced by their sum.
   3. Syntactic: programs are mere text to be evaluated by rewriting.
      - e.g. "5" can be only be part of an expression to be rewritten
      - e.g. "+" is used in rewriting, so "5 3 +" is rewritten "8"

] -- http://www.latrobe.edu.au/phimvt/joy/faq.html

"So, programmers, managers, what do you think?"

I can imagine that some teams would answer, "That is radical".

The resistance to anything resembling formal mathematics has a precedent.

http://www.cs.utexas.edu/~EWD/transcriptions/EWD10xx/EWD1036.html

I am trying to imagine how to convince a programming team that Factor is an
exceptional choice for a language.

I have convinced myself, but I am having trouble pinpointing how I would
convince others.

Any suggestions?

Cheers,
Leonard
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