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Re: [zzdev] Re: [zzdev] Subspaces & ZZ versioning
- To: Antti-Juhani Kaijanaho <gaia@xxxxxx>
- Subject: Re: [zzdev] Re: [zzdev] Subspaces & ZZ versioning
- From: Benjamin Fallenstein <b.fallenstein@xxxxxx>
- Date: Wed, 27 Dec 2000 11:53:03 +0100
- Cc: zzdev@xxxxxxxxxx
- References: <3A34009B.FB990E0@xxxxxx> <20001211015201.E18012@xxxxxxxxxxxxxx> <3A342176.B03A9B9F@xxxxxx> <20001211035226.B3587@xxxxxxxxxxxxxx> <3A3E67F4.3C00B087@xxxxxx> <20001219124905.A7717@xxxxxxxxxxxxxx> <3A41351B.BA16A23D@xxxxxx> <20001221111527.B29066@xxxxxxxxxxx> <3A425394.C54EF3AC@xxxxxx> <3A478411.4B27CC31@xxxxxx> <20001227113520.A4366@xxxxxxxxxxx>
Antti-Juhani Kaijanaho schrieb:
> Actually, I now think we need to revisit those definitions.
> I can see at least two good definitions for a subspace:
> 1) Let Z be a ZigZag space. Z' is a subspace of Z iff
> * it is a ZigZag space
> * its set of cells is a subset of Z's set of cells
> * its set of connections is a subset of Z's set of connections
> 2) Let Z be a ZigZag space. Z' is a subspace of Z iff
> * it is a subspace of Z (by definition 1) and
> * if d is a dimension in Z' and there is a connection along d
> in Z', then for all cells c and c' in Z', if there is a
> connection from c to c' along d in Z, then there is a connection
> from c to c' along d.
> 1 is your def. 2 is an extension of my earlier def
> (instead of a set of dims defining the subspace, we have two disjoint
> set of dims, one for defining the closure, and another for including
> more connections; I've been calling these hard and soft dimensions in
> my sketches).
For general use in versioning etc., I would not use the closuring: for
example, you'd want to be able to take the whole tree starting at the
"AllViews" cell as a subspace, but it isn't a closed set in any way that
makes sense. (Of course it's a closed set with respect to the dimensions
"d.i-don't-exist" and "d.me-neither", but that doesn't help us. ;))
> Def 1 is nice also theoretically since it mirrors many other subspace
> definitions in mathematics. Def 2 seems more natural: you cannot arbitrarily
> remove connections from a rank where the cells are in the space.
I agree that def 2 is more natural, but there will be cases where we
need 1, so I wouldn't totally lock that out. What about calling
subspaces according to 2 "standard subspace?"
I've been thinking a bit about how to phrase the definitions, and I
think I'd prefer a phrasing that stresses we either select a number of
cells and a number of connections, or a number of cells and a number of
Z' is a subspace of Z with respect to a set of cells C and a set of
connections N iff...
Z' is a standard subspace of Z with respect to a set of cells C and
a set of dimensions D iff...