[darcs-users] Formalizing patch theory

Judah Jacobson judah.jacobson at gmail.com
Thu Oct 15 16:17:22 UTC 2009


Hi all,

I've been thinking for a while about Darcs patch theory and how to
connect it to standard mathematical concepts.  I ended up with a new
formal model which I've written up as a technical report:

http://www.math.ucla.edu/~jjacobson/patch-theory

The main idea is to model patch effects as elements of inverse
semigroups, which generalize the properties of partial injective
functions.  Inverse semigroups turn out to provide clean descriptions
of concepts such as composition, inversion and sensibility.  They also
make a good framework for discussing and proving results about the
commutation and merge operations.  Additionally, they led me to a
novel explanation of conflictors (well, a simplified version of them).

I'm very interested to hear what other Darcs theorists and users think
about all this.  My paper was heavily influenced by the Camp
formalization, so it would be great if we were eventually able to
combine both approaches.

Best,
-Judah


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