Abstract 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.

@article{paperbot2693,
  title = {Asymptotic speedup via effect handlers},
  author = {DANIEL HILLERSTRÖM and SAM LINDLEY and JOHN LONGLEY},
  journal = {Journal of Functional Programming},
  volume = {34},
  year = {2024},
  doi = {10.1017/s0956796824000030}
}