Right. Apologies, but I know the basics.

My argument is that "algebraic types" would be less confusing if you actually did algebra using the types. That is it. That is my full argument.

As it is, you have to go through hoops to show what the algebra of the types is. And how that maps to whatever subtyping rules that the popular language you are using is.

Now, my argument is not that there is not some usefulness to understanding the algebra you can do with types. Quite the contrary. I think that is very useful and people should try to understand it.

But my argument remains that without using the common operations that define algebras, namely + and *, that calling them algebraic types does not provide any help in understanding the types for people. It remains an unfortunate naming based on how people are commonly introduced to the term "algebra."