[oisdk]

> I'd assume "algebraic effects" are to talk about performing algebra on the effects. That is, you are specifically going to talk about how different things combine effects

This is a misconception. The "algebra" does not refer to an algebra of effects, or combining effects in any way.

It's more like it's the other way around: "algebraic effects" are effects generated from algebras. These algebras are precisely-defined mathematical objects (like groups, monoids, etc.), so you have an "effect" that corresponds to monoids, an "effect" that corresponds to groups, and so on.

> My point is simply that there is no value in the program that says an effect has or has not completed. This is why I compare it to stepping through the program. The "line of code" that is active in executing code is not a first class value in your program.

I know: I'm trying to say that the "algebra" of "algebraic effects" do refer to first-class values. The + and * from other algebraic operations are the algebraic operations you might use for an algebraic effect.

[taeric]

I feel that you just spelled potato and then pronounced it differently. :D

If you have examples you recommend, I'd be game to look over them.

What is a first class "value" that is referenced in algebraic effects?

[oisdk]

I mean, the program snippet that I gave above contains 3 first-class values. If you write `x = y + z + 0`, or any other statement that uses the group algebra (or any other algebra), you can use algebraic effects to describe the semantics. The “first-class values” here are the x, y, and z: there’s nothing fancy going on. You can even use the group laws to show that the statement is equivalent to `x = y + z` (or whatever). It’s just normal, value-level algebra.