Expressive power of one-shot control operators and coroutines

Abstract

Control operators, such as exceptions and effect handlers, provide a means of representing computational effects in programs abstractly and modularly. While most theoretical studies have focused on multi-shot control operators, one-shot control operators---which restrict the use of captured continuations to at most once---are gaining attention for their balance between expressiveness and efficiency. This study aims to fill the gap. We present a mathematically rigorous comparison of the expressive power among one-shot control operators, including effect handlers, delimited continuations, and even asymmetric coroutines. Following previous studies on multi-shot control operators, we adopt Felleisen's macro-expressiveness as our measure of expressiveness. We verify the folklore that one-shot effect handlers and one-shot delimited-control operators can be macro-expressed by asymmetric coroutines, but not vice versa. We explain why a previous informal argument fails, and how to revise it to make a valid macro-translation.

82 pages, 17 figures. Extended version of a paper presented at APLAS 2025 (LNCS 16201, pp. 88-106, https://doi.org/10.1007/978-981-95-3585-9_5, full version: arXiv:2509.11901)