Structured Handling of Scoped Effects.

Algebraic effects offer a versatile framework that covers a wide variety of effects. However, an important family of operations— those that delimit a scope, and usually modelled as handlers—are not algebraic, thus preventing them from being used freely in conjunction with algebraic operations. Although proposals for scoped operations ex- ist, they are either ad-hoc and unprincipled, or too inconvenient for practical programming. This paper provides the best of both worlds: a theoretically-founded model of scoped effects that is convenient for im- plementation and reasoning. Our new model is based on an adjunction between a locally finitely presentable category and a category of functo- rial algebras. Using comparison functors between adjunctions, we show that our new model, the earlier indexed model, and a third approach that simulates scoped operations in terms of algebraic ones have equal expressivity for handling scoped operations. We consider our new model to be the sweet spot between ease of implementation and structuredness. Additionally, our approach automatically induces fusion laws of handlers of scoped effects, which are useful for reasoning and optimisation