[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.

[taeric]

Right, but this is just explaining algebra. Which, I get that. Connect this to effects, for me. (And fair that just because I assert that I get it, I would wager I don't have as strong of a handle as I should have.)

My understanding for effects was more like "writes to stdout" and such. Probably better to have "opens a stream," "writes to an open stream," and "closes a stream." The algebra that I typically see is to show that you can combine some of these in such a way to either highlight a bug, or to help prevent them.

I got this because many effects typically go through hurdles to find a way to let you log to stderr without it polluting your entire effects system.

[oisdk]

For an algebra, you have some operations and some equations. The group algebra has the + operation, and 0 and -, and all the relevant equations.

You can also form an algebra from logging. One operation might be “write to stdout”. And then a law might be `write x; write y = write (x ++ y)` where ++ is string concatenation.

This is the algebra, the algebra isn’t for combining effects at all. (Yes, you can combine algebraic effects, and the fact that they’re algebraic does help, but that’s for technical reasons that aren’t relevant)

The paper I linked in another comment has a good overview of the topic. It’s really not the kind of thing you can understand from reading a few comments, and the paper is well-written and goes over all of the main points from a pretty basic starting point.

[taeric]

I looked over the paper, but I confess I don't understand how it is helping. Would help a ton to have an example effect that didn't dive into distinguishing "Values", "Computations", "Value types," and "Computation types."

In fact, that it distinguishes values, computations, and the types of both seems more inline with my point? That what most "effect systems" are trying to capture are things that are not typically defined in programs?

So, again, give me some examples of effects and how you would model them. That will go a long way to demonstrate what you mean, here. Even better if you can show how this is already modeled in some code. (Note that I'm not trying to ask you to give this in a post. If you have some more things like that paper to look into, I don't mind looking there. I do plan on spending more time with the paper, already.)

[oisdk]

Well, I gave the example of a logging effect above. In the post there’s also an example of a key-value store effect. What’s missing from these examples exactly?

All of these effects have simple operations (get and put for store, the `write` operation for the logging effect, etc.) These are all normal operations in your language: they just return values, like normal, and the laws that govern them are equivalent to the laws of any other algebra.

Elsewhere you mentioned Boolean algebra, and that people shouldn’t confuse that with algebraic effects: Boolean algebra can absolutely be another example of an algebraic effect! The operations are the Boolean operations (call them whatever you like, + or * or whatever), and the laws are the usual laws.

The point of algebraic effects is in noticing that traditional effects (logging, state, exceptions) can be thought of as algebraic the same way as Boolean algebras or monoids.

If you’re looking for an implementation, there are lots of implementations available in Haskell and other languages. However, to understand those you’d really already have to have a good understanding of the topic first, and then you’d also need to be comfortable with Haskell syntax (and probably free monads as well). I think that the paper really gives the best introduction to the topic, unfortunately there’s no way to simplify it much further.

[taeric]

I don't think I mentioned boolean algebra? I responded to someone else mentioning it. My problem there is still that you are going to be taught how to operate over boolean values using an algebraic construction. (Looking, I think that is accurate. Apologies if I am the one that brought it up somewhere, I don't remember that.)

Which, fair that may help some people. I just feel that this is akin to asking for people to understand algebraic effects using basic algebra from middle school. In basic algebra practices, you lean heavily on the basic operations applied to reals and see how to manipulate equations to discover both solutions and other statements about the equations. (Advanced students will eventually extend to imaginary numbers, but I don't think that changes this statement?)

Similarly, with algebraic datatypes, you learn what it means to combine the domains of types together. Since it is an algebra, you learn this in terms of the basic operations. Hence SumTypes and ProductTypes. My assertion there is that this is hard for people because they don't actually do the algebra on the domains. And, by "they" I largely mean the software that they write.

So, with algebraic effects, I would expect that this is about the ways that effects can be combined using basic algebra tools. But what is it that you are combining? In the types, you were combining domains for analysis. In effects, I'd expect that you are combining whatever it is an effect is. You seem to be saying that an effect is a standard value? But, that seems at odds with the definitions that distinguish "pure" functions from those that have "effects" being defined by things that they cause to happen.

It doesn't help that we typically talk about things that we want to preserve some property on. It isn't enough to say "writes to stderr", we want to know that it does so without clobbering someone else currently writing to the same spot. At the least, we probably want to know that it line buffers output in such a way that that is preserved.

So, when asking for an example, I'm hunting for something to meet me somewhere in the middle. Sucks that this commonly comes down to "writes to a logger."

[oisdk]

I'm afraid I don't think I'm making progress here.

My overall point was that I felt your original comment was a little confused about algebraic effects. You seemed to think that the "algebra" in "algebraic effects" didn't refer to algebraic operations on normal values, which is incorrect. The basic middle-school algebra of a ring (+, *, etc., with all of the normal laws) does indeed give rise to an algebraic effect, and code that uses that effect can just be normal code like `x = 2 * y`. The "effect" here is the "ring" effect.

However, I don't think that this discussion is that productive. If you want to understand algebraic effects, unfortunately there is no substitute for just reading through the fundamental literature (like the paper I linked). I would love to be able to give you a short, easy-to-understand example that explains all the ideas in a few lines, but the concept just isn't that simple.

I see this a lot on this forum in particular: people like to develop a vague intuition for something rather than really understanding the concept properly, but almost always their "intuition" is very inaccurate, and they understand the thing less well than they think they do. Then, they try and teach others the concept, and those learners are even more misled.

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I will try and point out some misconceptions in your last comment here, but again I will caution that I don't think you will be able to fully understand the topic just by reading these comments.

> So, with algebraic effects, I would expect that this is about the ways that effects can be combined using basic algebra tools.

I understand, but that is not what algebraic effects is about.

The "algebra" in algebraic effects doesn't refer to an algebra for combining effects, it refers to algebras like monoid etc., and you get an effect for any particular algebra.

> In effects, I'd expect that you are combining whatever it is an effect is.

This is incorrect. First, there are algebras that have no "combining" at all, and second, the algebras involved are just the normal algebras you're already familiar with, like the boolean algebra etc.

> You seem to be saying that an effect is a standard value? But, that seems at odds with the definitions that distinguish "pure" functions from those that have "effects" being defined by things that they cause to happen.

Yes, an effect is a standard value. And yes, we often want to distinguish pure functions from effectful ones. (By the way, this does not mean that effectful functions are somehow not standard values)

However, in an algebraic effect the algebra does not combine effects.

> It isn't enough to say "writes to stderr", we want to know that it does so without clobbering someone else currently writing to the same spot.

I mean, obviously if the write is going to be performed concurrently you'll need more guarantees.

I included one law that might be important, but you could easily add more. That doesn't change the core concept.

> So, when asking for an example, I'm hunting for something to meet me somewhere in the middle. Sucks that this commonly comes down to "writes to a logger."

I'm not sure what you mean by the "middle"—middle between what two extremes? I picked the writing to a logger example because it was simple, and showed a simple law. The key-value store in the post is a little more complex, and involves a few more laws. In the paper there's even more examples: I/O etc. You have a lot of examples available to you!