Earlier quoted context omitted.
Wow, that's a very detailed look. Thanks! Feel free to email me; my address is in my profile. The terminology is definitely a work in progress. It's mostly for my attempts to teach programming using Mu. I noticed that mathematical words intimidated some students. I tried to write up my rationale here: http://akkartik.name/post/mu . But I've certainly started mixing up the terms with my student, so it might not last.
> Functions, arguments, classes, methods, objects, threads, locks, all these are reassuring everyday words, and yet their meaning in programming (and math) bears no relation to their everyday meaning. (from http://akkartik.name/post/mu ) I can see how the use of the term "arguments" could be confusing ("parameters" or "inputs" would make more sense), and "threads" is a rather tenuous metaphor for how scheduling works…
Functions are what something is for, as opposed to form. It isn't natural to think about their inputs and outputs.
It's quite possible my solutions are too blunt and problematic, but these seem like real problems.