Camp notation
Daniel Carrera
dcarrera at gmail.com
Sat Apr 18 10:43:57 EDT 2009
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
ASCIIfriendly.
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 "antidistributive" property.
This looks similar to the traditional use of ">" in algebra, where if X
> Y then Y > X.
B) "Quasiassociative" 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.
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