Non-termination is sometimes considered an effect. I have been reading about algebraic effect systems (What is algebraic about algebraic effects and handlers?), and I suspect non-termination (like that arising from a fixed point operator) could fit in the algebraic effect framework.
For instance if effects systems act like continuations, it seems easy to add a handler that supplies "fuel" for possibly non-terminating computations.
Another way to encode a non-termination effect might be though SKI combinators, since they are Turing complete and I think they can be presented as an algebra.
The programing language Koka has a non-termination effect, but it is a built in "primitive" effect. So it's unclear to me if it could be encoded by a user in their standard effect system.
Can non-terminating computation be considered an algebraic effect? If so, are there standard ways to do it? Any references would be great.