A pre-expectation calculus for probabilistic sensitivity

Aguirre, Alejandro; Barthe, Gilles; Hsu, Justin; Kaminski, Benjamin Lucien; Katoen, Joost-Pieter; Matheja, Christoph

doi:10.1145/3434333

Cited by 17 publications

(11 citation statements)

References 33 publications

(36 reference statements)

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“…This noncomposability can be associated to the fact that the monad lifting used in the work is not Cartesian. Their relational pre-expectation operator coincides with our categorical wppt in the Dijkstra structure , where p is the forgetful functor from the category of extended pseudometric spaces, which is a posetal fibration, is the countable probability distribution monad (see Example 40 for the finite case), and is the Kantorovich metric construction: Here is the set of probabilistic couplings between , and E denotes the expectation; see Aguirre et al (2021, Definition 2.2) for details. Since it fails to satisfy the composability, we conclude that the Dijkstra structure is not Cartesian.…”

Section: Dijkstra Structures and Weakest Precondition Predicate Trans...mentioning

confidence: 99%

Weakest preconditions in fibrations

Aguirre

Katsumata

Kura

2022

Math. Struct. Comp. Sci.

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Weakest precondition transformers are useful tools in program verification. One of their key properties is composability, that is, the weakest precondition predicate transformer (wppt for short) associated to program $f;\;g$ should be equal to the composition of the wppts associated to f and g. In this paper, we study the categorical structure behind wppts from a fibrational point of view. We characterize the wppts that satisfy composability as the ones constructed from the Cartesian lifting of a monad. We moreover show that Cartesian liftings of monads along lax slice categories bijectively correspond to Eilenberg–Moore monotone algebras. We then instantiate our techniques by deriving wppts for commonplace effects such as the maybe monad, the nonempty powerset monad, the counter monad, or the distribution monad. We also show how to combine them to derive the wppts appearing in the literature of verification of probabilistic programs.

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Section: Dijkstra Structures and Weakest Precondition Predicate Trans...mentioning

confidence: 99%

Weakest preconditions in fibrations

Aguirre

Katsumata

Kura

2022

Math. Struct. Comp. Sci.

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“…Termination analysis of probabilistic programs [1,24] considers probabilistic reachability properties, but does not consider other program properties as pDL. Other extensions of program logics to probabilistic programs, such as separation logic for probabilistic programs [25], expected run-time analysis for probabilistic programs [26] and relational reasoning over probabilistic programs for sensitivity analysis [27], are orthogonal to pDL. Generally all these approaches rely on the backwards pre-expectation transformer semantics proposed by McIver and Morgan [7].…”

Section: Related Workmentioning

confidence: 99%

A Specification Logic for Programs in the Probabilistic Guarded Command Language (Extended Version)

Pardo¹,

Johnsen²,

Schaefer³

et al. 2022

Preprint

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The semantics of probabilistic languages has been extensively studied, but specification languages for their properties have received little attention. This paper introduces the probabilistic dynamic logic pDL, a specification logic for programs in the probabilistic guarded command language (pGCL) of McIver and Morgan. The proposed logic pDL can express both first-order state properties and probabilistic reachability properties, addressing both the non-deterministic and probabilistic choice operators of pGCL. In order to precisely explain the meaning of specifications, we formally define the satisfaction relation for pDL. Since pDL embeds pGCL programs in its box-modality operator, we first provide a formal MDP semantics for pGCL programs. The satisfaction relation is modeled after PCTL, but extended from propositional to first-order setting of dynamic logic, so also embedding program fragments. We study basic properties of this specification language, such as weakening and distribution, that can support reasoning systems. Finally, we demonstrate the use of pDL to reason about program behavior.

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“…Morgan et al [1996] define a weakest pre-expectation calculus. Aguirre et al [2021] develop a variant of the calculus for relational properties. Kaminski et al [2016] show how similar ideas can be used for reasoning about expected cost.…”

Section: Related Workmentioning

confidence: 99%

Higher-order probabilistic adversarial computations: categorical semantics and program logics

Aguirre

Barthe

Gaboardi

et al. 2021

Proc. ACM Program. Lang.

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Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several domains, including security, privacy and machine learning. In this paper, we develop program logics for reasoning about adversarial computations in a higher-order setting. Our logics are built on top of a simply typed λ-calculus extended with a graded monad for probabilities and state. The grading is used to model and restrict the memory footprint and the cost (in terms of oracle calls) of computations. Under this view, an adversary is a higher-order expression that expects as arguments the code of its oracles. We develop unary program logics for reasoning about error probabilities and expected values, and a relational logic for reasoning about coupling-based properties. All logics feature rules for adversarial computations, and yield guarantees that are valid for all adversaries that satisfy a fixed resource policy. We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish the soundness of proof rules for adversaries. We illustrate the working of our logics with simple but illustrative examples.

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A pre-expectation calculus for probabilistic sensitivity

Cited by 17 publications

References 33 publications

Weakest preconditions in fibrations

Weakest preconditions in fibrations

A Specification Logic for Programs in the Probabilistic Guarded Command Language (Extended Version)

Higher-order probabilistic adversarial computations: categorical semantics and program logics

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