Proof Synthesis and Reflection for Linear Arithmetic

Chaieb, Amine; Nipkow, Tobias

doi:10.1007/s10817-008-9101-x

Cited by 19 publications

(14 citation statements)

References 39 publications

(67 reference statements)

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“…Interactive theorem provers like Isabelle [33] and HOL Light [21] now incorporate various such methods, either constructing correctness proofs along the way, or reconstructing them from appropriate certificates. (For a small sample, see [10] [12] [22] [27].) Such systems provide powerful tools to support interactive theorem proving.…”

Section: Introductionmentioning

confidence: 99%

A Heuristic Prover for Real Inequalities

2016

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We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with respect to a particular language or class of formulas, our method establishes claims that require heterogeneous forms of reasoning, relying on a Nelson-Oppen-style architecture in which special-purpose modules collaborate and share information. The framework is thus modular and extensible. A prototype implementation shows that the method works well on a variety of examples, and complements techniques that are used by contemporary interactive provers.

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Section: Introductionmentioning

confidence: 99%

A Heuristic Prover for Real Inequalities

2016

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“…This mechanism was replaced in 2016 with a reflection mechanism based on Idris' elaborator reflection. Other proof assistants that support proofs by reflection include HOL4 (Fallenstein and Kumar, 2015), Isabelle/HOL (Chaieb and Nipkow, 2008), and Milawa (Davis and Myreen, 2015).…”

Section: Between the Engineer And The Kernel: Languages And Automationmentioning

confidence: 99%

QED at Large: A Survey of Engineering of Formally Verified Software

Ringer

Palmskog

Sergey

et al. 2019

FNT in Programming Languages

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Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have been available for over 40 years, but have only recently seen wide practical use. Projects based on construction of machine-checked formal proofs are now reaching an unprecedented scale, comparable to large software projects, which leads to new challenges in proof development and maintenance. Despite its increasing importance, the field of proof engineering is seldom considered in its own right; related theories, techniques, and tools span many fields and venues. This survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.

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“…This tactic works over terms in the commutative semiring of integers (int_csr) using proof-by-reflection [13,21,37,39]. Internally, it is composed of a simpler, also proof-by-reflection based tactic canon_monoid that works over monoids, which is then "stacked" on itself to build canon_semiring.…”

Section: Tactics For Individual Assertions and Partial Canonicalizationmentioning

confidence: 99%

Meta-F $$^\star $$ : Proof Automation with SMT, Tactics, and Metaprograms

Martínez

Ahman

Dumitrescu³

et al. 2019

Programming Languages and Systems

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We introduce Meta-F , a tactics and metaprogramming framework for the F program verifier. The main novelty of Meta-F is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F can be used to generate verified code automatically. Meta-F is implemented as an F effect, which, given the powerful effect system of F , heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F provides substantial gains in proof development, efficiency, and robustness.

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Proof Synthesis and Reflection for Linear Arithmetic

Cited by 19 publications

References 39 publications

A Heuristic Prover for Real Inequalities

A Heuristic Prover for Real Inequalities

QED at Large: A Survey of Engineering of Formally Verified Software

Meta-F $$^\star $$ : Proof Automation with SMT, Tactics, and Metaprograms

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