Effects for Efficiency: Asymptotic Speedup with First-Class Control

We study the fundamental efficiency of delimited control. Specifically, we show that effect handlers enable an asymptotic improvement in runtime complexity for a certain class of functions. We consider the generic count problem using a pure PCF-like base language $λ_b$ and its extension with effect handlers $λ_h$. We show that $λ_h$ admits an asymptotically more efficient implementation of generic count than any $λ_b$ implementation. We also show that this efficiency gap remains when $λ_b$ is extended with mutable state. To our knowledge this result is the first of its kind for control operators.