Re: How to extend a patch theory to fully commute

Am 01.07.20 um 18:45 schrieb James Cook:
>> Just to check I understood the idea (up to this point): roughly
>> speaking, you represent "unrepresentable" states by formally commuting
>> patches.
>>
>> That is, if we regard the primitive states as vertices and primitive
>> (named) patches as edges in a graph, then you extend the graph with new
>> nodes and edges.
> 
> That's exactly the intuition.
> 
> If you had n patches that all commuted, this graph would be a
> hypercube, i.e. the nodes are the 2^n subsets of patches and each edge
> adds one patch.
> 
> I think my theory always extends this graph exactly to that hypercube,
> filling in exactly those nodes and edges that are missing. I haven't
> thought carefully about that point of view so maybe that's not true.
> 
>> The construction works by inductively taking any pair of incommutable
>> patches (in sequence, i.e. with a common middle state) and then
>> "formally" commuting it. The new node is represented as that pair of
>> patches. Is that, essentially, the idea?
> 
> Yes, that's exactly what happens when there are only two patches
> involved and they don't commute.
> 
>> It reminds me of the darcs-1 patch format, where a "merger" patch is
>> defined as the ordered pair consisting of both conflicting patches.
> 
> I think I read about darcs-1 conflictors a long time ago, so that
> general idea has been on my mind for a while.

Okay, I guess I'll need to read on, then. I wonder how you define
commutation for the extended set of patches...

Cheers
Ben