I don't have anything substantive to add, just a nitpick: wouldn't unary be a better term than monadic here? In functional programming, monadic function is generally used to mean, well, a monadic function.
APL's usage of monad predates its use in conjunction with modern functional programming languages, by the way. It goes back to the 60s, and there are plenty of books and papers where these terms are used that way.
I can't say I care too much which terms people use, but in context of APL, I prefer the terms that were used by Iverson and have been in print for more than half a century.
It is confusing, nevertheless, and perhaps merits clarification like any uncommon bit of language does. (Also like any uncommon bit of language, it may seem perfectly normal until people outside your usual circle point out they don’t understand you.)
It would be interesting to track down where these terms came from. The typed functional programming usage of the term monad, being identical to the current mathematical usage, apparently comes[1] from Mac Lane’s classic Categories for the working mathematician (1971) and seems to be motivated by the preexisting term monoid (which I dislike, so that’s a bit disappointing). The use of monadic, dyadic, etc. for relations and operations of (what is now usually called) particular arity is, as far as I can tell, mostly obsolete in mathematics post 1960 or so except for the occasional use by logicians (particularly of a philosophical bent). I’ve found it[2] as far back as Russell and Whitehead’s Principia mathematica (1910–13), but don’t know where they got it from. Still, that explains the use in logic (not that it means it’s a good idea: most of notation in Russell and Whitehead[3] is now spectacularly obscure, and parts of it were obscure even at the time).
APL's usage of monad predates its use in conjunction with modern functional programming languages, by the way. It goes back to the 60s, and there are plenty of books and papers where these terms are used that way.
https://en.wikipedia.org/wiki/Monad_(functional_programming)...
I can't say I care too much which terms people use, but in context of APL, I prefer the terms that were used by Iverson and have been in print for more than half a century.