I think there's a bit of a leap between "Option types are useful" and "using terminology to describe simple and common patterns of computation", though.
I think it's not too far from practicality to describe the solution in OP as along the lines of "solving fizzbuzz by combining infinite streams". It's a quirky/cute solution.
I think there's a jump from "knowing these functions / structures can be useful" and "let's use terms like 'semigroup resonance' and 'catamorphism'".
The concepts really aren't that easy (though they are indeed simple). While I disliked the names too at the beginning, I realize now that they are necessary, because it's important to be precise with your words and the concepts are so general that there simply isn't a better word for it. You can try to call a functor a container since both `List a` and `Maybe a` are functors and contain an `a`. But what about `Int -> a`? It is also a functor and doesn't "contain" anything. Perhaps "producer" would be a better word? `data Phantom a = Phantom` doesn't "produce" anything and is still a functor. Eventually you may arrive at a name like "mappable" which is convention just like "functor" and arguably worse because "functor" is more precise and was there first.
Names like StateT and Reader can surely be improved but the names taken directly from mathematics are already the best we can do imo.
I don't know. `Int -> a` is definitely a container in my mind. Imagine a list. What does it contain? Well, it contains the contents of the list, of course! What is it? We don't know until we look inside. What does `Int -> a` contain? It contains an `a`. Which `a` does it contain? We don't know until we look inside (by passing it an `Int`). The only real difference is that in a list I put the value in first and look at it later. With a function, I look at the value first and put the value in later ;-) I'm being silly, but I really do find that treating it as a container makes it much, much easier for me to reason about it.
However, I completely agree that the word "functor" is useful for exactly the reason you imply. It's a kind of special container. It doesn't work exactly the way you imagine containers should work initially. So I guess it's 6 of 1 half a dozen of the other. I just wanted to speak out because I know there are others like me that find reasoning about functors as if they are containers very useful.
When I'm explaining these concepts, I find myself apologizing for the names, usually by stealing the quip "the math people got here first". Programmers usually take commonplace words and tack on an extra technical definition: list, string, class, object. Semigroup and catamorphism stand out as non-ideomatic names. If they had been called combiner and fold they might have seen more widespread use.
I think it's not too far from practicality to describe the solution in OP as along the lines of "solving fizzbuzz by combining infinite streams". It's a quirky/cute solution.
I think there's a jump from "knowing these functions / structures can be useful" and "let's use terms like 'semigroup resonance' and 'catamorphism'".