Comments on: PROPs and patches http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/ Because my LiveJournal is too silly Sat, 17 Sep 2011 02:28:35 +0000 hourly 1 http://wordpress.org/?v=3.2.1 By: Michi http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/comment-page-1/#comment-78915 Michi Sat, 16 Feb 2008 09:30:54 +0000 http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/#comment-78915 wren: It sounds like you're talking about combinatorial group theory - where you study groups as given by finite presentation, and where string rewriting systems and rules for precisely manipulation of strings of symbols representing group generators are the tools of the trade. However, Brent does have a good point when he says that we'll probably want to work in a groupoid and not a group with these operations; since a patch A describing the change from P to Q won't be applicable unless the state we're in IS P. wren: It sounds like you’re talking about combinatorial group theory – where you study groups as given by finite presentation, and where string rewriting systems and rules for precisely manipulation of strings of symbols representing group generators are the tools of the trade.

However, Brent does have a good point when he says that we’ll probably want to work in a groupoid and not a group with these operations; since a patch A describing the change from P to Q won’t be applicable unless the state we’re in IS P.

]]> By: wren http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/comment-page-1/#comment-78777 wren Sat, 16 Feb 2008 02:41:01 +0000 http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/#comment-78777 I think this highlights the point of the problem. What does it mean to undo []->[a] without also undoing [a]->[] ? That is, perhaps the proper way to think about things is not in terms of insertions and deletions to a constant state, but rather to think in terms of reachability on a graph of edits. Thus, we have a graph from nil with a cycle to [a] and back before moving on to [b] and so forth. Now what does it mean to "remove [a]"? Rather than thinking of it as removing the arc from nil to [a], think of it as removing the [a] node itself. Alternatively, consider the process of pushing A to the end of AA^-1BCD. Since AA^-1 = [], then AA^-1 = A^-1'A' implies A^-1'A' = []. There's an abstruse study of strings with these sorts of "negative" letters in mathematics, though I forget the name it goes by. I think this highlights the point of the problem. What does it mean to undo []->[a] without also undoing [a]->[] ?

That is, perhaps the proper way to think about things is not in terms of insertions and deletions to a constant state, but rather to think in terms of reachability on a graph of edits. Thus, we have a graph from nil with a cycle to [a] and back before moving on to [b] and so forth. Now what does it mean to “remove [a]“? Rather than thinking of it as removing the arc from nil to [a], think of it as removing the [a] node itself.

Alternatively, consider the process of pushing A to the end of AA^-1BCD. Since AA^-1 = [], then AA^-1 = A^-1′A’ implies A^-1′A’ = []. There’s an abstruse study of strings with these sorts of “negative” letters in mathematics, though I forget the name it goes by.

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