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Behavioural Equivalence via Modalities for Algebraic Effects

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Niels VoorneveldAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 42, Issue 1

Article No.: 4, Pages 1 - 45

https://doi.org/10.1145/3363518

Published: 21 November 2019 Publication History

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Abstract

The article investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if they enjoy the same behavioural properties. To formulate this, we define a logic whose formulas specify behavioural properties. A crucial ingredient is a collection of modalities expressing effect-specific aspects of behaviour. We give a general theory of such modalities. If two conditions, openness and decomposability, are satisfied by the modalities, then the logically specified behavioural equivalence coincides with a modality-defined notion of applicative bisimilarity, which can be proven to be a congruence by a generalisation of Howe’s method. We show that the openness and decomposability conditions hold for several examples of algebraic effects: nondeterminism, probabilistic choice, global store, and input/output.

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Cited By

Gavazzo FTreglia RVanoni G(2024)Monadic Intersection Types, RelationallyProgramming Languages and Systems10.1007/978-3-031-57262-3_2(22-51)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57262-3_2
Bereczky PHorp�csi DThompson S(2023)A frame stack semantics for sequential Core ErlangProceedings of the 35th Symposium on Implementation and Application of Functional Languages10.1145/3652561.3652566(1-13)Online publication date: 29-Aug-2023
https://dl.acm.org/doi/10.1145/3652561.3652566
Horp�csi DBereczky PThompson S(2023)Program equivalence in an untyped, call-by-value functional language with uncurried functionsJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100857132(100857)Online publication date: Apr-2023
https://doi.org/10.1016/j.jlamp.2023.100857
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Index Terms

Behavioural Equivalence via Modalities for Algebraic Effects
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics

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Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 42, Issue 1

Special Issue on ESOP 2018

March 2020

215 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/3373084

Editor:
Andrew Myers
Cornell University, USA

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Copyright © 2019 ACM.

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Publication History

Published: 21 November 2019

Accepted: 01 July 2019

Revised: 01 July 2019

Received: 01 May 2018

Published in TOPLAS Volume 42, Issue 1

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Cited By

Gavazzo FTreglia RVanoni G(2024)Monadic Intersection Types, RelationallyProgramming Languages and Systems10.1007/978-3-031-57262-3_2(22-51)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57262-3_2
Bereczky PHorpácsi DThompson S(2023)A frame stack semantics for sequential Core ErlangProceedings of the 35th Symposium on Implementation and Application of Functional Languages10.1145/3652561.3652566(1-13)Online publication date: 29-Aug-2023
https://dl.acm.org/doi/10.1145/3652561.3652566
Horpácsi DBereczky PThompson S(2023)Program equivalence in an untyped, call-by-value functional language with uncurried functionsJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100857132(100857)Online publication date: Apr-2023
https://doi.org/10.1016/j.jlamp.2023.100857
Dal Lago UGavazzo F(2022)A relational theory of effects and coeffectsProceedings of the ACM on Programming Languages10.1145/34986926:POPL(1-28)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498692
Wang LLi Q(2022)Bounded complete domains and their logical formInformation and Computation10.1016/j.ic.2022.104958289(104958)Online publication date: Nov-2022
https://doi.org/10.1016/j.ic.2022.104958
Voorneveld N(2022)Runners for Interleaving Algebraic EffectsTheoretical Aspects of Computing – ICTAC 202210.1007/978-3-031-17715-6_26(407-424)Online publication date: 27-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-17715-6_26
Veltri NVoorneveld N(2022)Streams of Approximations, Equivalence of Recursive Effectful ProgramsMathematics of Program Construction10.1007/978-3-031-16912-0_8(198-221)Online publication date: 26-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-16912-0_8
Veltri NVoorneveld N(2021)Inductive and Coinductive Predicate Liftings for Effectful ProgramsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.351.16351(260-277)Online publication date: 29-Dec-2021
https://doi.org/10.4204/EPTCS.351.16
Voorneveld N(2020)From Equations to Distinctions: Two Interpretations of Effectful ComputationsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.317.1317(1-17)Online publication date: 1-May-2020
https://doi.org/10.4204/EPTCS.317.1
Voorneveld N(2020)Combining Algebraic Effect Descriptions Using the Tensor of Complete LatticesElectronic Notes in Theoretical Computer Science10.1016/j.entcs.2020.09.013352(257-281)Online publication date: Oct-2020
https://doi.org/10.1016/j.entcs.2020.09.013
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