From e6e07a7cef3baaf2751438efa0b70828ef1b1da5 Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Fri, 27 Apr 2012 12:51:59 +0100
Subject: [PATCH] strategy: wip

---
 article.tex  | 18 ++++++++++++++----
 strategy.tex | 28 ++++++++++++++++++++++++++--
 2 files changed, 40 insertions(+), 6 deletions(-)

diff --git a/article.tex b/article.tex
index b37edd5..8ecdbc3 100644
--- a/article.tex
+++ b/article.tex
@@ -99,10 +99,20 @@
 \newcommand{\hasdep}{\succ}
 \newcommand{\isdep}{\prec}
 
-\newcommand{\grefzc}{ T^0_{\pc} }
-\newcommand{\grefcc}{ T_{\pc} }
-\newcommand{\grefuc}{ T'_{\pc} }
-\newcommand{\greffc}{ T^*_{\pc} }
+\newcommand{\grefz}{ T^0 }
+\newcommand{\grefc}{ T }
+\newcommand{\grefu}{ T' }
+\newcommand{\greff}{ T^* }
+
+\newcommand{\grefza}[1]{ \grefz_{#1} }
+\newcommand{\grefca}[1]{ \grefc_{#1} }
+\newcommand{\grefua}[1]{ \grefu_{#1} }
+\newcommand{\greffa}[1]{ \greff_{#1} }
+
+\newcommand{\grefzc}{ \grefza \pc }
+\newcommand{\grefcc}{ \grefca \pc }
+\newcommand{\grefuc}{ \grefua \pc }
+\newcommand{\greffc}{ \greffa \pc }
 
 %\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
 \newcommand{\bigforall}{%
diff --git a/strategy.tex b/strategy.tex
index a718aec..532b24e 100644
--- a/strategy.tex
+++ b/strategy.tex
@@ -98,8 +98,32 @@ for $\pc' = \p$.
 
 \section{Execution phase}
 
-
-
+We process commit sets from the bottom up according to the relation
+$\hasdep$.  For each commit set $\pc$ we construct $\greffc$ from
+$\grefzc$, as planned.  By construction, $\hasdep$ has $\patchof{L}$
+as its maximum, so this operation will finish by updating
+$\greffa{\patchof{L}}$.
+
+After we are done, the result has the following properties:
+\[ \eqn{Best Tip}{
+  \bigforall_{E_i \in \set E_{\pc}} \greffc \ge E_i
+}\]
+\[ \eqn{Perfect Contents}{
+  \greffc \haspatch \p \equiv \pc \hasdep \py
+}\]
+
+For brevity we will write $\grefu$ for $\grefuc$, etc.  We will start
+out with $\grefc = \grefz$, and at each step of the way construct some
+$\grefu$ from $\grefc$.  The final $\grefu$ becomes $\greff$.
+
+\subsection{Preparation}
+
+Firstly, we will check each $E_i$ for being $\ge \grefc$.  If
+it is, are we fast forward to $E_i$
+--- formally, $\grefu = \text{max}(\grefc, E_i)$ ---
+and drop $E_i$ from the planned ordering.
+
+\subsection{Merge Contributors for UP TO HERE}
 
 with $M=M_j, L=T_{\pc,j-1}, R=E_j$,
 and calculate what the resulting desired direct dependencies file
-- 
2.30.2