Refinement to Imperative HOL

Lammich, Peter

doi:10.1007/s10817-017-9437-1

Cited by 44 publications

(60 citation statements)

References 30 publications

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“…The final step leads into the heap-monad of Imperative HOL [22], which supports imperative data structures. Here, the Sepref tool [6] replaces functional by imperative data structures and generates a refinement theorem automatically.…”

Section: Listing 11 Cyclicity Checkermentioning

confidence: 99%

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Verified Model Checking of Timed Automata

Wimmer

Lammich

2018

Lecture Notes in Computer Science

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Abstract. We have constructed a mechanically verified prototype implementation of a model checker for timed automata, a popular formalism for modeling real-time systems. Our goal is two-fold: first, we want to provide a reference implementation that is fast enough to check other model checkers against it on reasonably sized benchmarks; second, we strive for maximal feature compatibility with the state-of-the-art tool Uppaal. The starting point of our work is an existing highly abstract formalization of reachability checking of timed automata. We reduce checking of Uppaal-style models to the problem of model checking a single automaton in this abstract formalization, while retaining the ability to perform on the fly model-checking. Using the Isabelle Refinement Framework, the abstract specification of the model checker is refined, via multiple intermediate steps, to an actual imperative implementation in Standard ML. The resulting tool is evaluated on a set of standard benchmarks to demonstrate its practical usability.

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Section: Listing 11 Cyclicity Checkermentioning

confidence: 99%

“…Thus, it must provide sufficient performance to check real world examples. To this end, we use the Isabelle Refinement Framework (IRF) [5,6] to obtain efficient imperative implementations of the algorithms required for model checking.…”

Section: Introductionmentioning

confidence: 99%

Verified Model Checking of Timed Automata

Wimmer

Lammich

2018

Lecture Notes in Computer Science

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“…In this section, we review some basic concepts from the Imperative HOL framework in Isabelle and its separation logic. See [3,13,14] for details.…”

Section: Imperative Hol and Its Separation Logicmentioning

confidence: 99%

Efficient Verification of Imperative Programs Using Auto2

Zhan

2018

Lecture Notes in Computer Science

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Auto2 is a recently introduced prover for the proof assistant Isabelle. It is designed to be both highly customizable from within Isabelle, and also have a powerful proof search mechanism. In this paper, we apply auto2 to the verification of imperative programs. We describe the setup of auto2 for both stages of the proof process: verification of a functional version of the program, and refining to the imperative version using separation logic. As examples, we verify several data structures, including red-black trees, interval trees, priority queues, and union-find. We also verify several algorithms making use of these data structures. These examples show that our framework is able to verify complex algorithms efficiently and in a modular manner.

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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%

“…For example, we implement the iterators by indexes into an array of integers that stores both the formula and the lemmas. For many of the abstract types, we use general purpose data structures from the Isabelle Refinement Framework [24,25]. For example, we refine assignments to arrays, using the array_map_default data structure, which implements functions of type nat⇒ a option by arrays of type b array.…”

Section: Bt_assign_rel A0 ≡ { ((At)a) | a T T ⊆ Dom A ∧ A0 = A (-T) }mentioning

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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Refinement to Imperative HOL

Cited by 44 publications

References 30 publications

Verified Model Checking of Timed Automata

Verified Model Checking of Timed Automata

Efficient Verification of Imperative Programs Using Auto2

Efficient Verified (UN)SAT Certificate Checking

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