Signature restriction for polymorphic algebraic effects

It has been well known that naively combining polymorphic effects and polymorphic type assignment breaks type safety. Existing approaches to this problem are classified into two groups: one for restricting how effects are triggered and the other for restricting how they are implemented. This work explores a new approach to the safety of polymorphic effects in polymorphic type assignment. A novelty of our work lies in finding a restriction on effect interfaces. To formalize our idea, we employ algebraic effects and handlers, where an effect interface is given by a set of operations coupled with type signatures. We propose signature restriction, a new notion to restrict the type signatures of operations, and show that signature restriction is sufficient to ensure type safety of an effectful language equipped with unrestricted polymorphic type assignment. We also develop a type-and-effect system to enable the use of both operations that follow and do not follow signature restriction in a single program.