> For one, if algebraic isn't aiming at the ideas in an algebra, then they absolutely should be using a different name.
Algebraic effects are certainly algebraic, they're just not directly related to algebraic data types. Both ideas are using "algebraic" at different levels, and I think trying to understand algebraic effects by referencing algebraic data types will be more confusing than helpful.
> My point is that the "value" is not the written value of a variable in ways that people are used to working with in their program.
I'm saying that (in algebraic effects) the "value" in question is precisely a normal variable that people are used to working with in programming languages. It is not a type-level value, which is the kind of value in question when we're talking about algebraic data types.
For example, if we take Groups (the algebra referenced in the post), we have a binary operation (that we might call +) along with a few other operations. We could write a piece of code like the following:
x = y + z
The "group" in question here could absolutely be an algebraic effect. And the line of code above could be implemented using algebraic effects, and interpreted using an algebraic effect handler. You don't even need types, if you didn't want them.
> For two, though, the whole idea is how to compose the "value" of different effects together?
No, not really.
Yes, algebraic effects compose well. But so do other effects systems and abstractions (applicatives, etc.). The fact that the effects compose is not what makes them algebraic, it's a consequence of it.
I don't think I can give a proper explanation in a comment, but I would point you to the paper I linked in another comment (https://arxiv.org/abs/1807.05923).
Algebraic effects are certainly algebraic, they're just not directly related to algebraic data types. Both ideas are using "algebraic" at different levels, and I think trying to understand algebraic effects by referencing algebraic data types will be more confusing than helpful.
> My point is that the "value" is not the written value of a variable in ways that people are used to working with in their program.
I'm saying that (in algebraic effects) the "value" in question is precisely a normal variable that people are used to working with in programming languages. It is not a type-level value, which is the kind of value in question when we're talking about algebraic data types.
For example, if we take Groups (the algebra referenced in the post), we have a binary operation (that we might call +) along with a few other operations. We could write a piece of code like the following:
The "group" in question here could absolutely be an algebraic effect. And the line of code above could be implemented using algebraic effects, and interpreted using an algebraic effect handler. You don't even need types, if you didn't want them.> For two, though, the whole idea is how to compose the "value" of different effects together?
No, not really.
Yes, algebraic effects compose well. But so do other effects systems and abstractions (applicatives, etc.). The fact that the effects compose is not what makes them algebraic, it's a consequence of it.
I don't think I can give a proper explanation in a comment, but I would point you to the paper I linked in another comment (https://arxiv.org/abs/1807.05923).