Synthesis of sorting algorithms using multisets in Theorema

Dramnesc, Isabela; Jebelean, Tudor

doi:10.1016/j.jlamp.2020.100635

Cited by 7 publications

(3 citation statements)

References 13 publications

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“…As a support for teaching subjects related to algorithm synthesis by proving and mathematical theory exploration we developed a prover [20,19] in the Theorema system that synthesizes a large number of algorithms operating on lists and on binary trees, including sorting algorithms as rewrite programs. A prover in Theorema consists of a collection of inference rules (as rewrite rules).…”

Section: Synthesis and Transformation Of Algorithmsmentioning

confidence: 99%

Experiments with Automated Reasoning in the Class

Dramnesc

Ábrahám

Jebelean

et al. 2022

Lecture Notes in Computer Science

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Synthesis and Transformation Of Algorithmsmentioning

confidence: 99%

Experiments with Automated Reasoning in the Class

Dramnesc

Ábrahám

Jebelean

et al. 2022

Lecture Notes in Computer Science

Self Cite

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“…The algorithms Insert-Sort and Merge-Sort have been formally verified by the authors in the Theorema system in [11]. The automated certification in both Theorema and Coq of the sorting algorithms: Quick-Sort, Patience-Sort, Min-Sort, Max-Sort, Min-Max-Sort is submitted for review to [13]. These algorithms have been synthesized in authors' previous research, see [12,10,7,9].…”

Section: Related Work Classical Algorithms On Arrays/listsmentioning

confidence: 99%

“…The automated certification in both Theorema and Coq of the sorting algorithms: Quick-Sort, Patience-Sort, Min-Sort, Max-Sort, Min-Max-Sort is submitted for review to [13]. These algorithms have been synthesized in authors' previous research, see [12,10,7,9]. The tail recursive version of Bubble-Sort that is certified in this paper, was firstly introduced in [8].…”

Section: Related Work Classical Algorithms On Arrays/listsmentioning

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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AlCons : Deductive Synthesis of Sorting Algorithms in Theorema

Dramnesc

Jebelean

2021

Lecture Notes in Computer Science

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Synthesis of sorting algorithms using multisets in Theorema

Cited by 7 publications

References 13 publications

Experiments with Automated Reasoning in the Class

Experiments with Automated Reasoning in the Class

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

AlCons : Deductive Synthesis of Sorting Algorithms in Theorema

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