Handling Polymorphic Algebraic Effects

Abstract

Algebraic effects and handlers are a powerful abstraction mechanism to represent and implement control effects. In this work, we study their extension with parametric polymorphism that allows abstracting not only expressions but also effects and handlers. Although polymorphism makes it possible to reuse and reason about effect implementations more effectively, it has long been known that a naive combination of polymorphic effects and let-polymorphism breaks type safety. Although type safety can often be gained by restricting let-bound expressions—e.g., by adopting value restriction or weak polymorphism—we propose a complementary approach that restricts handlers instead of let-bound expressions. Our key observation is that, informally speaking, a handler is safe if resumptions from the handler do not interfere with each other. To formalize our idea, we define a call-by-value lambda calculus $$\lambda _\text {eff}^\text {let}$$ that supports let-polymorphism and polymorphic algebraic effects and handlers, design a type system that rejects interfering handlers, and prove type safety of our calculus.