Camp notation

[Daniel Carrera]

Hi Everyone.

I'm a new list member. If you are attending Hac5 then you have already 
met me. Yesterday Mannix demonstrated a new notation for patch theory 
that has several improvements. I wanted to follow that up with some very 
slight alterations that I think will improve clarity and will be more 
ASCII-friendly.

1) The first one I already discussed with Mannix and Ian, but I include 
it for the benefit of other list members:

Mannix proposed an operator for moving a patch over another. I propose 
using the "/" opertor. So that "P/Q" is read "P over Q" and is the 
action of moving patch P over patch Q:

            P
     +------------->
     |
   Q |
     |
     V
     +------------->
          P/Q

2) This one is new: I propose using ">" to denote patch composition. So 
that "X > Y" is read as "X then Y". The ">" is intended to look like an 
arrow, so it indicates direction.

3) Mannix proposed using "-P" to denote the inverse of patch P. On top 
of that, I propose using the number "0 to denote the empty patch.

This leads to nice syntax for several properties:

A) Basic properties:

     P > 0 = 0 > P = 0

     P > -P = 0

     -(X > Y) = -Y > -X   "anti-distributive" property.

This looks similar to the traditional use of ">" in algebra, where if X 
 > Y then -Y > -X.


B) "Quasi-associative" property:  R / (X > Y) = (R / X) / Y

            X
     +------------->+
     |              |
   R |              | Y
     |              |
     V              V

C) Merging:  P > Q/P = Q > P/Q

            P
     +------------->+
     |              |
   Q |              | Q/P
     |              |
     V              V
     +------------->+
          P/Q

Cheers,
Daniel.