Quantitative Behavioural Reasoning for Higher-order Effectful Programs

Gavazzo, Francesco

doi:10.1145/3209108.3209149

Cited by 26 publications

(41 citation statements)

References 40 publications

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“…Relators. Gavazzo [2018] recently proposed a type system for differential privacy that is parameterized by a signature of algebraic effects. The type system is given a relational interpretation in terms of relators, which lift relations on values to relations on monadic computations:…”

Section: Related Workmentioning

confidence: 99%

“…The type systems for information flow control generally trade off precision for good automation [Sabelfeld and Myers 2003]. Various specialized type systems and static analysis tools have also been proposed for checking differential privacy [Barthe et al 2015;Gaboardi et al 2013;Gavazzo 2018;Winograd-Cort et al 2017;Zhang and Kifer 2017] or doing relational cost analysis [Çiçek et al 2017].…”

Section: Related Workmentioning

confidence: 99%

“…Many semantic techniques have been proposed for reasoning about relational properties such as observational equivalence, including techniques based on binary logical relations [Ahmed et al 2009;Benton et al 2009Benton et al , 2013Benton et al , 2014Dreyer et al 2010Dreyer et al , 2011Dreyer et al , 2012Mitchell 1986], bisimulations [Dal Lago et al 2017;Koutavas and Wand 2006;Sangiorgi et al 2011;Sumii 2009] and combinations thereof [Hur et al 2012[Hur et al , 2014. While these powerful techniques are often not directly automated, they can still be used for verification [Timany and Birkedal 2019] and for providing semantic correctness proofs for relational program logics [Dreyer et al 2010[Dreyer et al , 2011 and other verification tools [Benton et al 2016;Gavazzo 2018].…”

Section: Related Workmentioning

confidence: 99%

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The next 700 relational program logics

Maillard

Hriţcu

Rivas

et al. 2019

Proc. ACM Program. Lang.

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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 characterization for 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 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 effects such as exceptions, and are the first to provide a proper semantic foundation and a relational program logic for exceptions.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

The next 700 relational program logics

Maillard

Hriţcu

Rivas

et al. 2019

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

show abstract

“…The challenge that accompanies the use of such approximate program transformations [66] is to come up with methods to measure and bound the error they produce. This has motivated much literature on program metrics [6], [65], [8], [31], [9], [25], [19], [26], [35], that is, on semantics in which types are endowed with a notion of distance. This approach has found widespread applications, for example in differential privacy [7], [5], [12] and reinforcement learning [33].…”

Section: Introductionmentioning

confidence: 99%

On Generalized Metric Spaces for the Simply Typed Lambda-Calculus

Pistone

2021

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way. However, the application of generalized metrics to higher-order languages like the simply typed lambda calculus has so far proved unsatisfactory. In this paper we investigate a new approach to the construction of cartesian closed categories of generalized metric spaces. Our starting point is a quantitative semantics based on a generalization of usual logical relations. Within this setting, we show that several families of generalized metrics provide ways to extend the Euclidean metric to all higher-order types.

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“…In particular, while two-valued notions of process equivalence just flag small deviations between systems as inequivalence, behavioural metrics can provide more fine-grained information on the degree of similarity of systems. Behavioural metrics are correspondingly used, e.g., in verification [25], differential privacy [13], and conformance testing of hybrid systems [36].…”

Section: Introductionmentioning

confidence: 99%

A Quantified Coalgebraic van Benthem Theorem

Wild

Schröder

2021

Lecture Notes in Computer Science

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The classical van Benthem theorem characterizes modal logic as the bisimulation-invariant fragment of first-order logic; put differently, modal logic is as expressive as full first-order logic on bisimulation-invariant properties. This result has recently been extended to two flavours of quantitative modal logic, viz. fuzzy modal logic and probabilistic modal logic. In both cases, the quantitative van Benthem theorem states that every formula in the respective quantitative variant of first-order logic that is bisimulation-invariant, in the sense of being nonexpansive w.r.t. behavioural distance, can be approximated by quantitative modal formulae of bounded rank. In the present paper, we unify and generalize these results in three directions: We lift them to full coalgebraic generality, thus covering a wide range of system types including, besides fuzzy and probabilistic transition systems as in the existing examples, e.g. also metric transition systems; and we generalize from real-valued to quantale-valued behavioural distances, e.g. nondeterministic behavioural distances on metric transition systems; and we remove the symmetry assumption on behavioural distances, thus covering also quantitative notions of simulation.

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Quantitative Behavioural Reasoning for Higher-order Effectful Programs

Cited by 26 publications

References 40 publications

The next 700 relational program logics

The next 700 relational program logics

On Generalized Metric Spaces for the Simply Typed Lambda-Calculus

A Quantified Coalgebraic van Benthem Theorem

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