# 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
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.

```