Data Refinement in Isabelle/HOL

Haftmann, Florian; Krauß, Alexander; Kunčar, Ondřej; Nipkow, Tobias

doi:10.1007/978-3-642-39634-2_10

Cited by 52 publications

(42 citation statements)

References 18 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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“…We have chosen an existing verified redblack tree implementation for our measurements. Isabelle's code generator supports the transparent replacement of sets by some verified implementation [14].…”

Section: Application: Finite-word Ltlmentioning

confidence: 99%

Verified decision procedures for MSO on words based on derivatives of regular expressions

Traytel

Nipkow

2013

Proceedings of the 18th ACM SIGPLAN International Conference on Functional Programming

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Monadic second-order logic on finite words (MSO) is a decidable yet expressive logic into which many decision problems can be encoded. Since MSO formulas correspond to regular languages, equivalence of MSO formulas can be reduced to the equivalence of some regular structures (e.g. automata). This paper presents a verified functional decision procedure for MSO formulas that is not based on automata but on regular expressions. Functional languages are ideally suited for this task: regular expressions are data types and functions on them are defined by pattern matching and recursion and are verified by structural induction.Decision procedures for regular expression equivalence have been formalized before, usually based on Brzozowski derivatives. Yet, for a straightforward embedding of MSO formulas into regular expressions an extension of regular expressions with a projection operation is required. We prove total correctness and completeness of an equivalence checker for regular expressions extended in that way. We also define a language-preserving translation of formulas into regular expressions with respect to two different semantics of MSO. Our results have been formalized and verified in the theorem prover Isabelle. Using Isabelle's code generation facility, this yields purely functional, formally verified programs that decide equivalence of MSO formulas.

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“…All the operations occurring in checker p could be executed on rational numbers. Under the assumption that all the parameters are rational numbers, checker p can be executed using the standard approach of data-refinement [9] for real numbers in Isabelle/HOL. That is, the code generator is instructed to represent real numbers as a data type with a constructor Ratreal : Q → R. Then, operations on the rational subset of the real numbers are defined by pattern matching on the constructor, and performing the corresponding operation on rational numbers.…”

Section: Executable Checkersmentioning

confidence: 99%

A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

Rizaldi

Immler

Althoff

2016

Lecture Notes in Computer Science

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Abstract. One barrier in introducing autonomous vehicle technology is the liability issue when these vehicles are involved in an accident. To overcome this, autonomous vehicle manufacturers should ensure that their vehicles always comply with traffic rules. This paper focusses on the safe distance traffic rule from the Vienna Convention on Road Traffic. Ensuring autonomous vehicles to comply with this safe distance rule is problematic because the Vienna Convention does not clearly define how large a safe distance is. We provide a formally proved prescriptive definition of how large this safe distance must be, and correct checkers for the compliance of this traffic rule. The prescriptive definition is obtained by: 1) identifying all possible relative positions of stopping (braking) distances; 2) selecting those positions from which a collision freedom can be deduced; and 3) reformulating these relative positions such that lower bounds of the safe distance can be obtained. These lower bounds are then the prescriptive definition of the safe distance, and we combine them into a checker which we prove to be sound and complete. Not only does our work serve as a specification for autonomous vehicle manufacturers, but it could also be used to determine who is liable in court cases and for online verification of autonomous vehicles' trajectory planner.

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Data Refinement in Isabelle/HOL

Cited by 52 publications

References 18 publications

Formally Verified Certificate Checkers for Hardest-to-Round Computation

Formally Verified Certificate Checkers for Hardest-to-Round Computation

Verified decision procedures for MSO on words based on derivatives of regular expressions

A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

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