Extracting Purely Functional Contents from Logical Inductive Types

Delahaye, David; Dubois, Catherine; Étienne, Jean-Frédéric

doi:10.1007/978-3-540-74591-4_7

Cited by 8 publications

(5 citation statements)

References 7 publications

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“…We plan to automatize this work for some cases, by taking inspiration from the work of David Delahaye and al. [10], based on a mode consistency analysis of an inductive relation.…”

Section: New Transformationsmentioning

confidence: 99%

Modular pre-processing for automated reasoning in dependent type theory

Blot¹,

Cousineau²,

Crance³

et al. 2022

Preprint

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The power of modern automated theorem provers can be put at the service of interactive theorem proving. But this requires in particular bridging the expressivity gap between the logics these provers are respectively based on. This paper presents the implementation of a modular suite of pre-processing transformations, which incrementally bring certain formulas expressed in the Calculus of Inductive Constructions closer to the first-order logic of Satifiability Modulo Theory solvers. These transformations address issues related to the axiomatization of inductive types, to polymorphic definitions or to the different implementations of a same theory signature. This suite is implemented as a plugin for the Coq proof assistant, and integrated to the SMTCoq toolchain.

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“…We plan to automatize this work for some cases, by taking inspiration from the work of David Delahaye and al. [10], based on a mode consistency analysis of an inductive relation.…”

Section: New Transformationsmentioning

confidence: 99%

Modular pre-processing for automated reasoning in dependent type theory

Blot¹,

Cousineau²,

Crance³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Inductive to Executable Specifications. At a high level, the algorithm described in Section 4 has similarities to earlier attempts at extracting executable specifications from inductive ones [Delahaye et al 2007;Tollitte et al 2012] in the Coq proof assistant. In principle, we could use the algorithm described in this section to obtain a similar transformation.…”

Section: Related Workmentioning

confidence: 99%

Generating good generators for inductive relations

Lampropoulos

Paraskevopoulou

Pierce

2017

Proc. ACM Program. Lang.

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Property-based random testing (PBRT) is widely used in the functional programming and verification communities. For testing simple properties, PBRT tools such as QuickCheck can automatically generate random inputs of a given type. But for more complex properties, effective testing often demands generators for random inputs that belong to a given type and satisfy some logical condition. QuickCheck provides a library of combinators for building such generators by hand, but this can be tedious for simple conditions and error prone for more complex ones. Fortunately, the process can often be automated. The most prominent method, narrowing, works by traversing the structure of the condition, lazily instantiating parts of the data structure as constraints involving them are met. We show how to use ideas from narrowing to compile a large subclass of Coq's inductive relations into efficient generators, avoiding the interpretive overhead of previous implementations. More importantly, the same compilation technique allows us to produce proof terms certifying that each derived generator is goodÐi.e., sound and complete with respect to the inductive relation it was derived from. We implement our algorithm as an extension of QuickChick, an existing tool for property-based testing in Coq. We evaluate our method by automatically deriving good generators for the majority of the specifications in Software Foundations, a formalized textbook on programming language foundations. CCS Concepts: • Software and its engineering → General programming languages;

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“…However, the declarative definition of is_redblack is not well adapted to efficient testing. Even if we were able to automatically give an executable interpretation to the inductive definition of is_redblack' [3,4,21,41], we would still have to guess the existentially quantified black-height h, which would be highly inefficient. So in order to effectively test the is_redblack invariant, we first manually devise an efficiently executable version:…”

Section: Example: Red-black Treesmentioning

confidence: 99%

Foundational Property-Based Testing

Paraskevopoulou

Hriţcu

Dénès

et al. 2015

Lecture Notes in Computer Science

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Integrating property-based testing with a proof assistant creates an interesting opportunity: reusable or tricky testing code can be formally verified using the proof assistant itself. In this work we introduce a novel methodology for formally verified property-based testing and implement it as a foundational verification framework for QuickChick, a port of QuickCheck to Coq. Our framework enables one to verify that the executable testing code is testing the right Coq property. To make verification tractable, we provide a systematic way for reasoning about the set of outcomes a random data generator can produce with non-zero probability, while abstracting away from the actual probabilities. Our framework is firmly grounded in a fully verified implementation of QuickChick itself, using the same underlying verification methodology. We also apply this methodology to a complex case study on testing an information-flow control abstract machine, demonstrating that our verification methodology is modular and scalable and that it requires minimal changes to existing code.

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Extracting Purely Functional Contents from Logical Inductive Types

Cited by 8 publications

References 7 publications

Modular pre-processing for automated reasoning in dependent type theory

Modular pre-processing for automated reasoning in dependent type theory

Generating good generators for inductive relations

Foundational Property-Based Testing

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