>>>Being able to say 'group' instead of 'set with an associative binary operation with identities' is essential <<<
OK, but the word "group" should be used for no other meaning...
>>>The reality is that you are not the target audience of their communication, and they are okay with that. You should be too.<<<
As you can see pretty much anyone is the audience of some math and its inconsistency and ambiguity. It just varies the level and the amount of it.
>>>The weirdest assertion that you made is that high-level programming languages ought to be as close as possible to human languages. The two categories of languages exist to communicate fundamentally and widely different groups of concepts. Words represent categories of analogous concepts, and the relevant categories in human life are nothing like the relevant categories in programming. In Haskell, 'functor', 'applicative functor', and 'monad' are highly relevant categories. They pop up everywhere and can be leveraged with great benefit.<<<
False. Computers and software are mainly used to emulate some real world stuff (objects, actions etc.) and to help people with real world stuff in a more automated way.
They aren't used too much to prove theorems or some other math stuff. And pretty much no one cares about proving the so called "mathematical correctness" of a program - a concept that doesn't even make sense in most cases.
Old misconception among FP advocates, even Dijkstra himself admitted that he was kinda wrong about how computer would evolve and what they'd used for. But the associated misconceptions live on.
A language close to human language also helps avoiding errors. That's why you won't see functional languages in critical systems, but rather languages like Ada which is probably the closest programming language to human language. The claims of clarity of FP languages are pretty much at odds with the evidence the real world provides.
If you're going to make the claim that functional languages use ambiguous symbols, you're going to need to back that up with some examples. I find it exceedingly hard to believe that there is any ambiguity in the operators of a statically and strongly typed language like Haskell.
Those "professionals who actually know what they are doing" don't seem to exist when it comes to functional languages. The evidence is the very fact there's not a single piece of important commercial software written in such a language.
The question is rather: can such specialists exist? Because I'm afraid they can't exist because the functional approach is fundamentally wrong.
Examples of ambiguity in FP?
What is the following line supposed to mean and what part of it suggest anything about that:
a b c
How is ~ an intuitive replacement for minus? How is (* 5 5) supposed to be as clear as 5 * 5 ?
ps. dynamic typing and type inference are two awfully bad things and either of them can lead to trouble in large programs