Ecrire les raisons de la correction d'algorithmes : perspectives depuis la Chine ancienne

Abstract : This article focuses on three features proofs of the correctness of algorithms found in ancient mathematical sources frequently display. For some texts, the structure of the statement of the algorithm is meaningful in and of itself, insofar as it allows us to interpret, along the text, the meaning of the successive operations, until the meaning of the final result is brought to light. Other writings prescribe operations in a resolutely indirect way, referring to operations by means of terms stating reasons why these operations should be put into play. By contrast, in ancient books, some statements of algorithms don't point out reasons for the correctness of these algorithms. In these cases, the proof seeks, first, to establish a transparent equivalent algorithm, before it discusses meta-operations that enable transforming this other algorithm into the one actors aim to establish. Thus, in these cases we see appearing, in the history of proof, the lineaments of a form of algebraic proof in an algorithmic context.
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https://halshs.archives-ouvertes.fr/halshs-00803428
Contributor : Karine Chemla <>
Submitted on : Thursday, March 21, 2013 - 11:14:53 PM
Last modification on : Thursday, February 21, 2019 - 12:22:02 PM
Long-term archiving on : Monday, June 24, 2013 - 12:00:29 PM

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  • HAL Id : halshs-00803428, version 1

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Karine Chemla. Ecrire les raisons de la correction d'algorithmes : perspectives depuis la Chine ancienne. 2013. ⟨halshs-00803428⟩

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