research-article

LTL types FRP: linear-time temporal logic propositions as types, proofs as functional reactive programs

Author:

Alan JeffreyAuthors Info & Claims

PLPV '12: Proceedings of the sixth workshop on Programming languages meets program verification

Pages 49 - 60

https://doi.org/10.1145/2103776.2103783

Published: 24 January 2012 Publication History

Abstract

Functional Reactive Programming (FRP) is a form of reactive programming whose model is pure functions over signals. FRP is often expressed in terms of arrows with loops, which is the type class for a Freyd category (that is a premonoidal category with a cartesian centre) equipped with a premonoidal trace. This type system suffices to define the dataflow structure of a reactive program, but does not express its temporal properties. In this paper, we show that Linear-time Temporal Logic (LTL) is a natural extension of the type system for FRP, which constrains the temporal behaviour of reactive programs. We show that a constructive LTL can be defined in a dependently typed functional language, and that reactive programs form proofs of constructive LTL properties. In particular, implication in LTL gives rise to stateless functions on streams, and the "constrains" modality gives rise to causal functions. We show that reactive programs form a partially traced monoidal category, and hence can be given as a form of arrows with loops, where the type system enforces that only decoupled functions can be looped.

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Cutler JWatson CNkurumeh EHilliard PGoldstein HStanford CPierce B(2024)Stream TypesProceedings of the ACM on Programming Languages10.1145/36564348:PLDI(1412-1436)Online publication date: 20-Jun-2024
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Klinge TLathrop JOsera PRogers A(2024)Reactamole: functional reactive molecular programmingNatural Computing10.1007/s11047-024-09982-523:3(477-495)Online publication date: 19-Apr-2024
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Index Terms

LTL types FRP: linear-time temporal logic propositions as types, proofs as functional reactive programs
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs
      1. Type structures

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cover image ACM Conferences

PLPV '12: Proceedings of the sixth workshop on Programming languages meets program verification

January 2012

90 pages

ISBN:9781450311250

DOI:10.1145/2103776

Program Chairs:
Koen Claessen
Chalmers University of Technology
,
Nikhil Swamy
Microsoft Research

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 24 January 2012

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POPL '12: The 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 24, 2012

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Cited By

Laddad SCheung AHellerstein JMilano M(2025)Flo: A Semantic Foundation for Progressive Stream ProcessingProceedings of the ACM on Programming Languages10.1145/37048459:POPL(241-270)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704845
Cutler JWatson CNkurumeh EHilliard PGoldstein HStanford CPierce B(2024)Stream TypesProceedings of the ACM on Programming Languages10.1145/36564348:PLDI(1412-1436)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656434
Klinge TLathrop JOsera PRogers A(2024)Reactamole: functional reactive molecular programmingNatural Computing10.1007/s11047-024-09982-523:3(477-495)Online publication date: 19-Apr-2024
https://doi.org/10.1007/s11047-024-09982-5
Baldor KWang XNiu JSerrano M(2023)Thorium: A Language for Bounded Verification of Dynamic Reactive ObjectsProceedings of the 10th ACM SIGPLAN International Workshop on Reactive and Event-Based Languages and Systems10.1145/3623506.3623574(1-13)Online publication date: 19-Oct-2023
https://dl.acm.org/doi/10.1145/3623506.3623574
Bahr PMøgelberg R(2023)Asynchronous Modal FRPProceedings of the ACM on Programming Languages10.1145/36078477:ICFP(476-510)Online publication date: 31-Aug-2023
https://dl.acm.org/doi/10.1145/3607847
Gadducci FLaretto ATrotta D(2023)Specification and Verification of a Linear-Time Temporal Logic for Graph TransformationGraph Transformation10.1007/978-3-031-36709-0_2(22-42)Online publication date: 12-Jul-2023
https://doi.org/10.1007/978-3-031-36709-0_2
O'Connor LWickström OJhala RDillig I(2022)Quickstrom: property-based acceptance testing with LTL specificationsProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523728(1025-1038)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523728
BAHR P(2022)Modal FRP for all: Functional reactive programming without space leaks in HaskellJournal of Functional Programming10.1017/S095679682200013232Online publication date: 26-Dec-2022
https://doi.org/10.1017/S0956796822000132
Spies SKrishnaswami NDreyer D(2021)Transfinite step-indexing for terminationProceedings of the ACM on Programming Languages10.1145/34342945:POPL(1-29)Online publication date: 4-Jan-2021
https://dl.acm.org/doi/10.1145/3434294
Bahr PGraulund CMøgelberg R(2021)Diamonds are not forever: liveness in reactive programming with guarded recursionProceedings of the ACM on Programming Languages10.1145/34342835:POPL(1-28)Online publication date: 4-Jan-2021
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