The next 700 relational program logics

Maillard, Kenji; Hriţcu, Cătălin; Rivas, Exequiel; Muylder, Antoine Van

doi:10.1145/3371072

Cited by 34 publications

(25 citation statements)

References 97 publications

(172 reference statements)

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“…Their Dijkstra monad has a flavor of grading but the structure they use is more complex than a pomonoid. Maillard et al [30] focus on relational program logics for effectful computations. They show how these logics can be derived in a relational dependent type theory, but their logics are not graded.…”

Section: Related Workmentioning

confidence: 99%

Graded Hoare Logic and its Categorical Semantics

Gaboardi

Katsumata

Orchard

et al. 2021

Programming Languages and Systems

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Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by augmenting their rules with additional information to reason about program side-effects. For example, general program logics have been augmented with cost analyses, logics for probabilistic computations have been augmented with estimate measures, and logics for differential privacy with indistinguishability bounds. In this work, we unify these various approaches via the paradigm of grading, adapted from the world of functional calculi and semantics. We propose Graded Hoare Logic (GHL), a parameterisable framework for augmenting program logics with a preordered monoidal analysis. We develop a semantic framework for modelling GHL such that grading, logical assertions (pre- and post-conditions) and the underlying effectful semantics of an imperative language can be integrated together. Central to our framework is the notion of a graded category which we extend here, introducing graded Freyd categories which provide a semantics that can interpret many examples of augmented program logics from the literature. We leverage coherent fibrations to model the base assertion language, and thus the overall setting is also fibrational.

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Section: Related Workmentioning

confidence: 99%

Graded Hoare Logic and its Categorical Semantics

Gaboardi

Katsumata

Orchard

et al. 2021

Programming Languages and Systems

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“…In this section we point out related work and directions for further development. For more extensive reviews of related work on RHLs, some starting points are [14]- [16] and [17]. The latter proposes the idea of alignment completeness but only in vague terms.…”

Section: Discussionmentioning

confidence: 99%

Alignment Completeness for Relational Hoare Logics

Ramana¹,

Naumann²

2021

Preprint

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Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule, Sequential-Product, that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL). A variety of other rules have been found useful in practice, but Sequential-Product is relatively complete on its own (with HL). As a more satisfactory way to evaluate RHLs, a notion of alignment completeness for rules is introduced, in terms of the inductive assertion method and product automata. Alignment completeness results are given to account for several different sets of rules. Applying alignment completeness to richer languages and product notions may serve to guide the design of RHLs.

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“…All of the expected monad laws hold with respect to equality defined as set equivalence (up to ≈), except one direction of bind associativity. This is expected in the presence of nondeterminism[Maillard et al 2020]. Proc.…”

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confidence: 89%

Modular, compositional, and executable formal semantics for LLVM IR

Zakowski

Beck

Yoon

et al. 2021

Proc. ACM Program. Lang.

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This paper presents a novel formal semantics, mechanized in Coq, for a large, sequential subset of the LLVM IR. In contrast to previous approaches, which use relationally-specified operational semantics, this new semantics is based on monadic interpretation of interaction trees, a structure that provides a more compositional approach to defining language semantics while retaining the ability to extract an executable interpreter. Our semantics handles many of the LLVM IR's non-trivial language features and is constructed modularly in terms of event handlers, including those that deal with nondeterminism in the specification. We show how this semantics admits compositional reasoning principles derived from the interaction trees equational theory of weak bisimulation, which we extend here to better deal with nondeterminism, and we use them to prove that the extracted reference interpreter faithfully refines the semantic model. We validate the correctness of the semantics by evaluating it on unit tests and LLVM IR programs generated by HELIX.

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The next 700 relational program logics

Cited by 34 publications

References 97 publications

Graded Hoare Logic and its Categorical Semantics

Graded Hoare Logic and its Categorical Semantics

Alignment Completeness for Relational Hoare Logics

Modular, compositional, and executable formal semantics for LLVM IR

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