*Result*: Asymptotic speedup via effect handlers.

*We study a fundamental efficiency benefit afforded by delimited control, showing that for certain higher-order functions, a language with advanced control features offers an asymptotic improvement in runtime over a language without them. Specifically, we consider the generic count problem in the context of a pure functional base language ${\lambda_{\textrm{b}}}$ and an extension ${\lambda_{\textrm{h}}}$ with general effect handlers. We prove that ${\lambda_{\textrm{h}}}$ admits an asymptotically more efficient implementation of generic count than any implementation in ${\lambda_{\textrm{b}}}$. We also show that this gap remains even when ${\lambda_{\textrm{b}}}$ is extended to a language ${{{{{{\lambda_{\textrm{a}}}}}}}}$ with affine effect handlers , which is strong enough to encode exceptions, local state, coroutines and single-shot continuations. This locates the efficiency difference in the gap between 'single-shot' and 'multi-shot' versions of delimited control. To our knowledge, these results are the first of their kind for control operators. [ABSTRACT FROM AUTHOR]

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