Using Isabelle/UTP for the Verification of Sorting Algorithms: A Case Study

Bockenek, Joshua; Lammich, Peter; Nemouchi, Yakoub; Wolff, Burkhart

doi:10.29007/ddqm

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…This seems mainly due to missing lemmas, and so in future the proof should be more automated (cf. [12]). Nevertheless, for now we omit details of the proof steps.…”

Section: Insertion Sortmentioning

confidence: 99%

“…Lenses [8][9][10] allow us to characterise variables as abstract algebraic objects, which can be composed and manipulated. They provide a generic foundation for verification tools that can maximise proof automation in tools like Isabelle [11,12]. Although originating from a different intellectual stream [8], lenses are essentially Back and von Wright's variable manipulation functions [13].…”

Section: Introductionmentioning

confidence: 99%

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Automated Algebraic Reasoning for Collections and Local Variables with Lenses

Foster

Baxter

2020

Relational and Algebraic Methods in Computer Science

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Lenses are a useful algebraic structure for giving a unifying semantics to program variables in a variety of store models. They support efficient automated proof in the Isabelle/UTP verification framework. In this paper, we expand our lens library with (1) dynamic lenses, that support mutable indexed collections, such as arrays, and (2) symmetric lenses, which allow partitioning of a state space into disjoint local and global regions to support variable scopes. From this basis, we provide an enriched program model in Isabelle/UTP for collection variables and variable blocks. For the latter, we adopt an approach first used by Back and von Wright, and derive weakest precondition and Hoare calculi. We demonstrate several examples, including verification of insertion sort.

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“…This seems mainly due to missing lemmas, and so in future the proof should be more automated (cf. [12]). Nevertheless, for now we omit details of the proof steps.…”

Section: Insertion Sortmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automated Algebraic Reasoning for Collections and Local Variables with Lenses

Foster

Baxter

2020

Relational and Algebraic Methods in Computer Science

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“…In contrast, in Coq the user needs the computer to run the proof scripts step by step and to display the current state of the proof. [16,24,20,26,6,3,21] have been certified in formal certification environments like Coq [1] and Isabelle/HOL [19]. [14] proves the correctness of various sorting algorithms using the Why3 [15] platform.…”

Section: Introductionmentioning

confidence: 99%

Certification of Tail Recursive Bubble--Sort in Theorema and Coq

Dramnesc,

Jebelean,

Stratulat

Kalpa Publications in Computing

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Algorithm certification or program verification have an increasing importance in the current technological landscape, due to the sharp increase in the complexity of software and software using systems and the high potential of adverse effects in case of failure. For instance robots constitute a particular class of systems that can present high risks of such failures. Sorting on the other hand has a growing area of applications, in particular the ones where organizing huge data collections is critical, as for instance in environmental applications.We present an experiment in formal certification of an original version of the Bubble- Sort algorithm that is functional and tail recursive. The certification is performed in parallel both in Theorema and in Coq, this allows to compare the characteristics and the performance of the two systems. In Theorema the proofs are produced automatically in natural style (similar to human proofs), while in Coq they are based on scripts. However, the background theory, the algorithms, and the proof rules in Theorema are composed by the user without any restrictions – thus error prone, while in Coq one can only use the theories and the proof rules that are rigurously checked by the system, and the algorithms are checked for termination.The goal of our experiments is to contribute to a better understanding and estimation of the complexity of such certification tasks and to create a basis for further increase of the level of automation in the two systems and for their possible integration.

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