Strong Normalisation for Asynchronous Effects

2026-02-05

AI Summary

This study addresses the strong normalization of computational systems featuring asynchronous algebraic effects, aiming to guarantee termination. By modeling asynchronous behavior through a separation of operation invocation and result interruption mechanisms—and crucially excluding general recursion—the work establishes the first strong normalization theory for a calculus with asynchronous algebraic effects. The approach extends Lindley and Stark’s top-top lifting technique to asynchronous and concurrent settings and employs a modular proof strategy. The main contributions are twofold: a proof that the full asynchronous effect calculus is strongly normalizing in the absence of general recursion, and a further demonstration that its sequential fragment retains strong normalization even when augmented with controlled interruption-driven recursion. All results have been formally verified in Agda.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Agreement, Argumentation & Negotiation
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Asynchronous effects of Ahman and Pretnar complement the conventional synchronous treatment of algebraic computational effects with asynchrony based on decoupling the execution of algebraic operation calls into signalling that an operation's implementation needs to be executed, and into interrupting a running computation with the operation's result, to which the computation can react by installing matching interrupt handlers. Beyond providing asynchrony for algebraic effects, the resulting core calculus also naturally models examples such as pre-emptive multi-threading, (cancellable) remote function calls, multi-party applications, and even a parallel variant of runners of algebraic effects. In this paper, we study the normalisation properties of this calculus. We prove that if one removes general recursion from the original calculus, then the remaining calculus is strongly normalising, including both its sequential and parallel parts. However, this only guarantees termination for very simple asynchronous examples. To improve on this result, we also prove that the sequential fragment of the calculus remains strongly normalising when a controlled amount of interrupt-driven recursive behaviour is reintroduced. Our strong normalisation proofs are structured compositionally as a natural extension of Lindley and Stark's $\top\top$-lifting based approach for proving strong normalisation of effectful languages. All our results are also formalised in Agda.

Problem

• strong normalisation
• asynchronous effects
• algebraic effects
• termination
• recursive behaviour

Innovation

• asynchronous effects
• strong normalisation
• algebraic effects
• interrupt handlers
• TT-lifting