strategy: wip

[topbloke-formulae.git] / strategy.tex

diff --git a/strategy.tex b/strategy.tex
index a718aecc8b7040f46ee459715344548da5086ec5..532b24e86ef0be422888ab8f51ea973c369f8bd7 100644 (file)
--- 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