The sequential semantics of producer effect systems

Tate, Ross

doi:10.1145/2429069.2429074

Cited by 31 publications

(40 citation statements)

References 36 publications

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“…Atkey introduces parameterized monads and corresponding parameterized Freyd categories [1], demonstrating that parameterized monads naturally model effectful computations with preconditions and postconditions. Tate defines productors with composability of effectful computations controlled by a relational 'effector' structure [53]. Orchard et al define category-graded monads, generalizing graded and parameterised monads via lax functors and sketch a model of Union Bound Logic in this setting (but predicates and graded-predicate interaction are not modelled, as they are here) [41].…”

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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“…He demonstrates that parameterized monads naturally models computational effects involving preconditions and postconditions of computations. Productors in [Tate 2013] are a generalization of monads, and the composability of effectful computations can be controlled by effectors. It is an interesting future work to combine these general models of computational effects and Hoare logic.…”

Section: Related Workmentioning

confidence: 99%

Graded Hoare Logic and its Categorical Semantics

Gaboardi¹,

Katsumata²,

Orchard³

et al. 2020

Preprint

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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 pre-ordered 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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“…Note that, as a by-product, this will provide us with a proof technique to show equivalence between small-step and big-step semantics. Ancona et al [7] Furthermore, it would be interesting to extend such techniques for soundness to big-step semantics with observations, taking inspiration from type and effect systems [36,51].…”

Section: Future Workmentioning

confidence: 99%

A framework for big-step semantics

Dagnino

2019

Proceedings of the Conference Companion of the 3rd International Conference on Art, Science, and Engineering of Programming

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It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type soundness, which cannot even be expressed. To face this problem, we develop a systematic study of big-step semantics: we introduce an abstract definition of what a big-step semantics is, we formalise the evaluation algorithm implicitly associated with any big-step semantics and we identify computations with executions of such an algorithm, thus recovering the distinction between stuckness an non-termination. Then, we define constructions yielding an extended version of a given arbitrary big-step semantics, where such a difference is made explicit. Building on such constructions, we describe a general proof technique to show that a predicate is sound, that is, prevents stuck computation, with respect to a big-step semantics. The extended semantics are exploited in the meta-theory, notably they are necessary to show that the proof technique works. However, they remain transparent when using the proof technique, since it consists in checking three conditions on the original rules only. We illustrate the technique by several examples, showing that it is applicable also in cases where subject reduction does not hold, hence the standard technique for small-step semantics cannot be used.

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The sequential semantics of producer effect systems

Cited by 31 publications

References 36 publications

Graded Hoare Logic and its Categorical Semantics

Graded Hoare Logic and its Categorical Semantics

Graded Hoare Logic and its Categorical Semantics

A framework for big-step semantics

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