strategy: rename \gref macros: perl -i~ -pe 's/gref([zcuf])/tip$1/g' *.tex

[topbloke-formulae.git] / strategy.tex

diff --git a/strategy.tex b/strategy.tex
index a718aecc8b7040f46ee459715344548da5086ec5..0ac03fa119ebb0a65c201352c9c8123136bc4a8e 100644 (file)
--- a/strategy.tex
+++ b/strategy.tex
@@ -27,7 +27,7 @@ partial order.
 $ \bigcup_i \pendsof{S_i}{\pc} $.
 All the ends of $\pc$ in the sources.
 
-\item[ $ \grefzc, \grefcc, \grefuc, \greffc $ ]
+\item[ $ \tipzc, \tipcc, \tipuc, \tipfc $ ]
 The git ref for the Topbloke commit set $\pc$: respectively,
 the original, current, updated, and final values.
 
@@ -49,7 +49,7 @@ processing at each step $\pc$.
 At each recursive step 
 we make a plan to merge all $\set E_{\pc} = \{ E_{\pc,j \ldots} \}$
 and all the direct contributors of $\pc$ (as determined below)
-into $\grefzc$, to make $\greffc$.
+into $\tipzc$, to make $\tipfc$.
 
 We start with $\pc = \pl$ where $\pl = \patchof{L}$.
 
@@ -67,7 +67,7 @@ For brevity we will write $E_j$ for $E_{\pc,j}$.
 Remove from that set (and ordering) any $E_j$ which
 are $\le$ and $\neq$ some other $E_k$.
 
-Initially let $\set D_0 = \depsreqof{\grefzc}$.
+Initially let $\set D_0 = \depsreqof{\tipzc}$.
 For each $E_j$ starting with $j=1$ choose a corresponding intended
 merge base $M_j$ such that $M_j \le E_j \land M_j \le T_{\pc,j-1}$.
 Calculate $\set D_j$ as the 3-way merge of the sets $\set D_{j-1}$ and
@@ -98,7 +98,58 @@ 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 $\tipfc$ from
+$\tipzc$, as planned.  By construction, $\hasdep$ has $\patchof{L}$
+as its maximum, so this operation will finish by updating
+$\tipfa{\patchof{L}}$.
+
+After we are done, the result has the following properties:
+\[ \eqn{Tip Inputs}{
+  \bigforall_{E_i \in \set E_{\pc}} \tipfc \ge E_i
+}\]
+\[ \eqn{Tip Dependencies}{
+  \bigforall_{\pc \hasdep \p} \tipfc \ge \tipfa \p
+}\]
+\[ \eqn{Perfect Contents}{
+  \tipfc \haspatch \p \equiv \pc \hasdep \py
+}\]
+
+For brevity we will write $\tipu$ for $\tipuc$, etc.  We will start
+out with $\tipc = \tipz$, and at each step of the way construct some
+$\tipu$ from $\tipc$.  The final $\tipu$ becomes $\tipf$.
+
+\subsection{Preparation}
+
+Firstly, we will check each $E_i$ for being $\ge \tipc$.  If
+it is, are we fast forward to $E_i$
+--- formally, $\tipu = \text{max}(\tipc, E_i)$ ---
+and drop $E_i$ from the planned ordering.
+
+\subsection{Merge Contributors for $\pcy$}
+
+Merge $\pcn$ into $\tipc$.  That is, merge with
+$L = \tipc, R = \tipfa{\pcn}, M = \baseof{\tipc}$.
+to construct $\tipu$.
+
+Merge conditions: Ingredients satisfied by construction.
+Tip Merge satisfied by construction.  Merge Acyclic follows
+from Perfect Contents and $\hasdep$ being acyclic.
+
+Removal Merge Ends: For $\p = \pc$, $M \nothaspatch \p$.
+For $p \neq \pc$, by Tip Contents,
+$M \haspatch \p \equiv L \haspatch \p$, so we need only
+worry about $X = R, Y = L$; ie $L \haspatch \p$,
+$M = \baseof{L} \haspatch \p$.
+By Tip Contents for $L$, $D \le L \equiv D \le M$.  $\qed$
+
+WIP UP TO HERE
+
+Addition Merge Ends: If $\py \isdep \pcn$, we have already
+done the execution phase for $\pcn$ and $\py$.  By
+Perfect Contents for $\pcn$, $\tipfa \pcn \haspatch \p$.
+
+computed $\tipfa \py$, and by Perfect Contents for $\py$
 
 
 with $M=M_j, L=T_{\pc,j-1}, R=E_j$,