Re: [zzdev] Re: [zzdev] Subspaces & ZZ versioning

[Benjamin Fallenstein <b.fallenstein@xxxxxx>]

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
dimensions, i.e.:

    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...

- Benja