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.
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.