Expressive Power of One-Shot Control Operators and Coroutines

2025-09-15

AI Summary

This paper rigorously characterizes the expressivity differences among one-shot control operators—including exceptions, effect handlers, delimited continuations, and asymmetric coroutines. Using Felleisen’s macro-expressibility framework, we employ macro translations, operational semantics, and contextual equivalence to formally establish, for the first time, that asymmetric coroutines macro-express a class of one-shot effect handlers and delimited control operators, but the converse does not hold—correcting a key flaw in prior informal arguments. Our work constructs the first complete expressivity hierarchy for one-shot control operators, precisely delineating relative expressive boundaries among them. This hierarchy provides foundational insights for programming language design and effect system theory.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Comparing expressive power of one-shot control operators
• Investigating macro-expressiveness relationships between operators
• Validating folklore claims about asymmetric coroutines' capabilities

Innovation

• One-shot control operators for computational effects
• Macro-expressiveness comparison using Felleisen's framework
• Asymmetric coroutines express handlers but not vice versa