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The next 700 relational program logics

Authors:

Kenji Maillard,

Cătălin Hriţcu,

Exequiel Rivas,

Antoine Van MuylderAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 4, Pages 1 - 33

https://doi.org/10.1145/3371072

Published: 20 December 2019 Publication History

Abstract

We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an algebraic presentation of relational specifications as a class of relative monads, and link computations and specifications by introducing relational effect observations, which map pairs of monadic computations to relational specifications in a way that respects the algebraic structure. For an arbitrary relational effect observation, we generically define the core of a sound relational program logic, and explain how to complete it to a full-fledged logic for the monadic effect at hand. We show that this generic framework can be used to define relational program logics for effects as diverse as state, input-output, nondeterminism, and discrete probabilities. We, moreover, show that by instantiating our framework with state and unbounded iteration we can embed a variant of Benton's Relational Hoare Logic, and also sketch how to reconstruct Relational Hoare Type Theory. Finally, we identify and overcome conceptual challenges that prevented previous relational program logics from properly dealing with control effects, and are the first to provide a relational program logic for exceptions.

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Cited By

Dardinier TLi AM�ller P(2024)Hypra: A Deductive Program Verifier for Hyper Hoare LogicProceedings of the ACM on Programming Languages10.1145/36897568:OOPSLA2(1279-1308)Online publication date: 8-Oct-2024
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Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
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Dardinier TM�ller P(2024)Hyper Hoare Logic: (Dis-)Proving Program HyperpropertiesProceedings of the ACM on Programming Languages10.1145/36564378:PLDI(1485-1509)Online publication date: 20-Jun-2024
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Index Terms

The next 700 relational program logics
1. Theory of computation
  1. Logic
    1. Hoare logic
    2. Type theory
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics
      1. Categorical semantics

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Published: 20 December 2019

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https://dl.acm.org/doi/10.1145/3689756
Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
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Banerjee ANagasamudram RNaumann DNikouei M(2023)A Relational Program Logic with Data Abstraction and Dynamic FramingACM Transactions on Programming Languages and Systems10.1145/355149744:4(1-136)Online publication date: 10-Jan-2023
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