Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2003.03170

Diamonds are not forever: Liveness in reactive programming with guarded recursion

Patrick Bahr·Christian Uldal Graulund·Rasmus Møgelberg
View original source ↗Read source document ↗Export metadata ↓

Abstract

When designing languages for functional reactive programming (FRP) the main challenge is to provide the user with a simple, flexible interface for writing programs on a high level of abstraction while ensuring that all programs can be implemented efficiently in a low-level language. To meet this challenge, a new family of modal FRP languages has been proposed, in which variants of Nakano's guarded fixed point operator are used for writing recursive programs guaranteeing properties such as causality and productivity. As an apparent extension to this it has also been suggested to use Linear Temporal Logic (LTL) as a language for reactive programming through the Curry-Howard isomorphism, allowing properties such as termination, liveness and fairness to be encoded in types. However, these two ideas are in conflict with each other, since the fixed point operator introduces non-termination into the inductive types that are supposed to provide termination guarantees. In this paper we show that by regarding the modal time step operator of LTL a submodality of the one used for guarded recursion (rather than equating them), one can obtain a modal type system capable of expressing liveness properties while retaining the power of the guarded fixed point operator. We introduce the language Lively RaTT, a modal FRP language with a guarded fixed point operator and an `until' type constructor as in LTL, and show how to program with events and fair streams. Using a step-indexed Kripke logical relation we prove operational properties of Lively RaTT including productivity and causality as well as the termination and liveness properties expected of types from LTL. Finally, we prove that the type system of Lively RaTT guarantees the absence of implicit space leaks.

Explore related subjects

cs.PL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Patrick Bahr, Christian Uldal Graulund, Rasmus Møgelberg. 2020-08-20. Diamonds are not forever: Liveness in reactive programming with guarded recursion. https://arxiv.org/abs/2003.03170

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Expressive power of one-shot control operators and coroutines

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.

cs.PL↗
arXiv2026

Equality saturation theory exploration à la carte

Rewrite rules are critical in equality saturation, an increasingly popular technique in optimizing compilers, synthesizers, and verifiers. Unfortunately, developing high-quality rulesets is difficult and error-prone. Recent work to automatically infer rewrite rules does not scale to large terms or grammars. Users struggle to guide inference and incrementally construct rulesets because existing rule inference tools are monolithic and opaque. As a result, most equality saturation users still manually develop and maintain rulesets. This paper proposes Enumo, a new domain-specific language for programmable theory exploration. Enumo provides a small set of core operators that enable users to strategically guide rule inference and incrementally build rulesets. Short Enumo programs easily replicate results from state-of-the-art tools like Ruler, but Enumo programs can also scale to infer deeper rules from larger grammars than prior approaches. Enumo's composable operators even facilitate developing new strategies for ruleset inference. We introduce a new fast-forwarding strategy which does not require evaluating terms in the target language, and thus supports domains that were out of scope for prior work. Enumo is also easy to extend: two new operators suffice to incorporate large language models into rule inference, where they complement guided search. We evaluate Enumo and fast-forwarding across a variety of domains. Compared to state-of-the-art techniques, Enumo can synthesize better rulesets over a diverse set of domains, in some cases matching the effects of manually developed rulesets in systems driven by equality saturation.

cs.PL↗
arXiv2026

Authorization Revocation for Long-Running AI Agents: Root-Scoped Quiescence under Delegation and Asynchronous Execution

Long-running AI agents outlive initiating processes through credentials, delegated tasks, queues, callbacks, reservations, and provider-side operations. Cancellation, process exit, and credential revocation neither close every pre-cut carrier nor distinguish independently authorized shared work. We define root-scoped authorization quiescence: for each manifested sink, a certificate accounts for every cut-relevant acceptance under the retired root-epoch atom that precedes its local fence and excludes protected acceptance under that atom after the fence, while permitting exact rebind to a current, independently sufficient support. The root-scoped quiescence protocol linearizes a root cut, fences old-root expansion and protected sinks, represents alternative and conjunctive authority as antichains of minimal sufficient root sets, and composes provider-frontier certificates into a cutset over registered old-root paths. Exact channel-token accounting reconciles transfers; missing or conflicting evidence remains indeterminate. Under stated assumptions, we prove post-cut issuer non-expansion, support-sound projection, compositional soundness under exact channel conservation, independent-support preservation, merge-order independence, and crash/replay stability. A provider-free late-effect test suite matches 17/17 registered outcomes. Two cancellation-only and one cut-only execution accept the same class of already scheduled late effect; two cut-plus-fence executions, one restart, and one stale-process execution reject it. A separately implemented checker verifies 17/17 traces and rejects 44/44 consistently rehashed semantic regressions. The certificate establishes root-relative authorization quiescence within its bound manifest and configuration, not global idleness, rollback, or business completion.

cs.PL↗