# Theory/Questions

**See first of all** David Roundy’s explanation of the theory of patches.

See Motivation and Example.

A patch is a partial function that maps trees to trees, yes? So P_2 P_1 is just partial function composition? What does P <—> P’ mean - is it P = P’ ie they are exactly the same maps, or just that P(x) == P’(x) for the context x and P and P’ are somehow “similar”? Is the inverse required to be an inverse for all inputs to the partial function, or just the context?

More precisely, what is unwinding?

*Motivation - Uses the word commute without saying what it means (in this context).*

About ‘commute’: In algebra, the commutator of two elements is [A, B] = AB - BA, thus if [A, B] = 0 then AB = BA holds, which means you can change the order of AB to BA, you can commute both elements.

This turned out to be a very important property in quantum physics: one can only measure two quantities simultaneously if they commute. Some important pairs like momentum and position don’t commute. (see Heisenberg’s uncertainty relation). The mathematical background is that you can’t find a basis to represent two quantities simultaneously in Hilbert space (think: linear vector space in infinite dimensions) if they don’t commute.

If one would say that patch theory relied on algebra, it wouldn’t sound as sexy. If I oversaw any deeper connection to quantum mechanics, please correct me. :-)

By the way, where is patch theory described on this wiki? Can’t find more than those few examples.

Marc

# Link with OT and so6 work?

There seems to be a strong connection between what darcs does, and scientific work on collaborative editing (e.g. “Operational Transformation” http://doi.acm.org/10.1145/289444.289469 resp. http://citeseer.ist.psu.edu/sun98operational.html, including confluent, causality and intention preserving combination of operations. There is also related work in Software Configuration Management, e.g. “Operation-Based Merging” http://doi.acm.org/10.1145/142868.143753. Does darcs do anything *more* than they do, or is it the same theoretical foundation?

Axel

‘’In a footnote of the manual: « Alas, I don’t know how to prove that the two constraints even can be satisfied. The best I have been able to do is to believe that they can be satisfied, and to be unable to find an case in which my implementation fails to satisfy them. »’’

‘’What are the implications of this? Is it possible that darcs doesn’t restore a tagged version correctly because at the time of restoring there are new patches in the repository which it tries to merge?’’

No, it simply means that it might be the case that a merge is not possible, *i.e.* that « darcs pull » will fail sometimes.

When you try to reconstruct a tag, you’re trying to commute back to a configuration that once existed, so we already know that the commutation is possible.

*Can someone show me a transformation of a token name that is represented as such in the patches? When i change token names and look at whatsnew, i see line diffs via hunks.*

Reading the darcs manual suggests that you need to use “darcs rename”: it isn’t “sufficiently smart” to “just realize” that all you’ve done is change a token name; I don’t know anything about the Darcs internals, so I don’t know how hard it would be to make darcs “sufficiently smart.”