Effect handlers form a powerful construct that can express complex programming abstractions. They are a generalization of exception handlers, but allow resumption of the continuation from where the effect was raised. Allowing continuations to be resumed at most once (one-shot) or an arbitrary number of times (multi-shot) has far-reaching consequences. In addition to performance considerations, multi-shot effects break key rules of reasoning and thus render certain standard transformation/optimizations unsound, especially in languages with mutable references (such as OCaml 5). It is therefore desirable to statically track whether continuations are used in a one-shot or multi-shot discipline, so that a compiler could use this information to efficiently implement effect handlers and to determine what optimizations it may perform.

We address this problem by developing a type and effect system–called Affect–which uses affine types to track the usage of continuations. A challenge is to soundly deal with advanced programming features—such as references that store continuations and nested continuations—which are crucial to support challenging examples from the effects literature (such as control inversion and cooperative concurrency). Another challenge is to support generic type signatures of polymorphic effectful functions. We address these challenges by using and extending Rust’s Cell type and Wadler’s use types. To prove soundness of Affect we model types and judgements semantically via a logical relation in the Iris separation logic framework in Coq.