This is what an enumeration is, partially because that's precisely what the word "enumeration" means; the ability to assign an ordinal number to each value in the enumeration. To "enumerate" a set is to assign integers to them. In Python, for instance, see the "enumerate" function, which does exactly enumeration on the output of some iterator.
Sum types can be used to represent enumerations, but it's very restrictive subset of sum types. Trying to understand what a "sum type" is through the lens of a single integer would be a very strange way to approach them. Nor are sum types a "superset" of an enumeration; a base sum type is not an enumeration. You need to add more things to it to get an enumeration. In a Venn diagram they're the classic two cicles with some overlap in the middle but with distinct bits on each side.
I do not understand the strangely active desire some people seem to have to erase the distinction between these two things, as if some advantage will result, as if sum types will somehow become more useful than they are or as if they will somehow lose their abilities if we don't also call them enumerations. There is no advantage to smudging these two unique things together. Not saying that you are promoting this per se, the__alchemist, just that I've seen it a lot and I don't get it. It's like someone wanting to claim that database and files are really the same thing; well, sure, there's some overlap, but each does many things the other doesn't and trying to squint until they actually are the same thing is generally the exact wrong direction to go to attain understanding.
To put it another way, when adding an "enumeration" into a network protocol, you allocate some fixed number of bits to hold a given sized integer. When you add "a sum type" into a network protocol, you have a lot more work to do in general.
To put it yet another way, enumerations have meaningful implementations of a ".Next()" that a sum type really doesn't. If you have a sensible implementation of a given method on one type of thing and it's not sensible on some other thing, then clearly they can not be the same thing.
(I say multiple times that a sum types doesn't have such an implementation in this message. By that I mean that while it is trivial to have a "data Color = Red | Green | Blue | RGB Int Int Int" and implement an iterator to walk through all possible values, it is not something that is generally done for all sum types, and if the sum type also includes functions or other complex values it isn't in general possible at all in common programming languages. Again, writing an interator for "all possible functions" is perfectly theoretically possible, but in engineering terms not something anyone would actually do. All enumerations can be iterated.)
