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Computer Science > Logic in Computer Science

arXiv:1311.3903 (cs)
[Submitted on 13 Nov 2013]

Title:A Categorical Theory of Patches

Authors:Samuel Mimram (LIST), Cinzia Di Giusto (LIST)
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    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.

Subjects:          Logic in Computer Science (cs.LO); Category Theory
                   (math.CT)
Journal reference: MFPS - Mathematical Foundations of Programming
                   Semantics 298 (2013) 283-307
DOI:               10.1016/j.entcs.2013.09.018
Cite as:           arXiv:1311.3903 [cs.LO]
                   (or arXiv:1311.3903v1 [cs.LO] for this version)

Submission history

From: Samuel Mimram [view email] [via CCSD proxy]
[v1] Wed, 13 Nov 2013 20:19:47 UTC (73 KB)
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