A Categorical Theory of Patches

Abstract : When working with distant collaborators on the same documents, one often uses a version control system, which is a program tracking the history of files and helping importing modifications brought by others as patches. The implementation of such a system requires to handle lots of situations depending on the operations performed by users on files, and it is thus difficult to ensure that all the corner cases have been correctly addressed. Here, instead of verifying the implementation of such a system, we adopt a complementary approach: we introduce a theoretical model, which is defined abstractly by the universal property that it should satisfy, and work out a concrete description of it. We begin by defining a category of files and patches, where the operation of merging the effect of two coinitial patches is defined by pushout. Since two patches can be incompatible, such a pushout does not necessarily exist in the category, which raises the question of which is the correct category to represent and manipulate files in conflicting state. We provide an answer by investigating the free completion of the category of files under finite colimits, and give an explicit description of this category: its objects are finite sets labeled by lines equipped with a transitive relation and morphisms are partial functions respecting labeling and relations.
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Communication dans un congrès
Dexter Kozen and Michael Mislove. MFPS - Mathematical Foundations of Programming Semantics, Jun 2013, New Orleans, United States. Elsevier, 298, pp.283-307, 2013, Proceedings of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX. 〈http://www.sciencedirect.com/science/article/pii/S1571066113000649〉. 〈10.1016/j.entcs.2013.09.018〉
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Contributeur : Samuel Mimram <>
Soumis le : mercredi 13 novembre 2013 - 19:08:00
Dernière modification le : vendredi 16 mars 2018 - 01:12:10
Document(s) archivé(s) le : vendredi 14 février 2014 - 12:35:29

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Samuel Mimram, Cinzia Di Giusto. A Categorical Theory of Patches. Dexter Kozen and Michael Mislove. MFPS - Mathematical Foundations of Programming Semantics, Jun 2013, New Orleans, United States. Elsevier, 298, pp.283-307, 2013, Proceedings of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX. 〈http://www.sciencedirect.com/science/article/pii/S1571066113000649〉. 〈10.1016/j.entcs.2013.09.018〉. 〈hal-00904156〉

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