It may help to know that "[computational] effect" is supposed to mean these things together:
- a particular class of computation, in a programming context where we want to define the class and/or take advantage of computations being defined in this way
- to this end computations are wrapped in a type constructor (typically with one argument e.g. State<T>, IO<T>, Maybe<T>).
The jargon is of course terrible and unhelpful (but widely used and used somewhat consistently). It is not necessarily about side-effects, it is not necessarily about interacting with environment. Calling it "algebraic effects" makes it a bit mysterious the various supported methods/callbacks are more or less like an "algebra", since they involve the type parameter T. To top it off, this use of "effect" is quite different from, say "type and effect system", and Moggi's 1991 never used "effect" in "Notions of computation and monads."
The jargon is of course terrible and unhelpful (but widely used and used somewhat consistently). It is not necessarily about side-effects, it is not necessarily about interacting with environment. Calling it "algebraic effects" makes it a bit mysterious the various supported methods/callbacks are more or less like an "algebra", since they involve the type parameter T. To top it off, this use of "effect" is quite different from, say "type and effect system", and Moggi's 1991 never used "effect" in "Notions of computation and monads."