Effects for Efficiency: Asymptotic Speedup with First-Class Control

Abstract

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 ${\lambda }_b$ and its extension with effect handlers ${\lambda }_h$. We show that ${\lambda }_h$ admits an asymptotically more efficient implementation of generic count than any ${\lambda }_b$ implementation. We also show that this efficiency gap remains when ${\lambda }_b$ is extended with mutable state. To our knowledge this result is the first of its kind for control operators.