Automatic Data Refinement

Lammich, Peter

doi:10.1007/978-3-642-39634-2_9

Cited by 55 publications

(48 citation statements)

References 16 publications

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“…For the moment, this is done in an ad-hoc way using morphisms between data-structures and explicitly applying rewriting rules for the correctness proof. The use of a more systematic approach such as the ones proposed in [10,19,23] would be a clear improvement.…”

Section: Discussionmentioning

confidence: 97%

Formally Verified Certificate Checkers for Hardest-to-Round Computation

et al. 2014

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In order to derive efficient and robust floating-point implementations of a given function f , it is crucial to compute its hardest-to-round points, i.e. the floating-point numbers x such that f (x) is closest to the midpoint of two consecutive floating-point numbers. Depending on the floating-point format one is aiming at, this can be highly computationally intensive. In this paper, we show how certificates based on Hensel's lemma can be added to an algorithm using lattice basis reduction so that the result of a computation can be formally checked in the Coq proof assistant.

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Section: Discussionmentioning

confidence: 97%

Formally Verified Certificate Checkers for Hardest-to-Round Computation

et al. 2014

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“…For Isabelle/HOL, the Isabelle Refinement Framework [22,24,25,29] provides a powerful stepwise refinement tool chain, featuring a nondeterministic shallowly embedded programming language [29], a library of efficient collection data structures and generic algorithms [24][25][26], and convenience tools to simplify canonical refinement steps [22,24]. It has been used for various software verification projects (e. g. [23,27,28]), including a fully fledged verified LTL model checker [4,12].…”

Section: Program Verification With Isabelle/holmentioning

confidence: 99%

Efficient Verified (UN)SAT Certificate Checking

Lammich

2017

Automated Deduction – CADE 26

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We present an efficient formally verified checker for satisfiability and unsatisfiability certificates for Boolean formulas in conjunctive normal form. It utilizes a two phase approach: Starting from a DRAT certificate, the unverified generator computes an enriched certificate, which is checked against the original formula by the verified checker. Using the Isabelle/HOL Refinement Framework, we verify the actual implementation of the checker, specifying the semantics of the formula down to the integer sequence that represents it. On a realistic benchmark suite drawn from the 2016 SAT competition, our approach is more than two times faster than the unverified standard tool drat-trim. Additionally, we implemented a multi-threaded version of the generator, which further reduces the runtime.

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“…They are useful to express hierarchies of concepts and to reduce the number of parameters and assumptions that must be threaded through a formal development. -The Refinement Framework [30] can be used to express refinements from abstract data structures and algorithms to concrete, optimized implementations. This allows us to reason about simple algebraic objects and yet obtain efficient programs.…”

Section: Introductionmentioning

confidence: 99%

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

Blanchette

Fleury

Weidenbach

2016

Automated Reasoning

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We developed a formal framework for conflict-driven clause learning (CDCL) using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL calculus is connected first to a more concrete calculus, then to a SAT solver expressed in a functional programming language, and finally to a SAT solver in an imperative language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants, including the Davis-Putnam-Logemann-Loveland (DPLL) calculus. The imperative program relies on the two-watched-literal data structure and other optimizations found in modern solvers. We used Isabelle's Refinement Framework to automate the most tedious refinement steps. The most noteworthy aspects of our work are the inclusion of rules for forget, restart, and incremental solving and the application of stepwise refinement.

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Automatic Data Refinement

Cited by 55 publications

References 16 publications

Formally Verified Certificate Checkers for Hardest-to-Round Computation

Formally Verified Certificate Checkers for Hardest-to-Round Computation

Efficient Verified (UN)SAT Certificate Checking

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

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