My understanding is that monads can only be composed in specific orders or not at all without monad transformers. The "algebraic" part of algebraic effects is

My understanding is that monads can only be composed in specific orders or not at all without monad transformers. The "algebraic" part of algebraic effects is that the effects also come with implicit compositional rules that say how you can put them together. You can design a family effects with rules like commutativity and associativity, so that you can be sure of how to compose them.