notation: fixes from annotations

[topbloke-formulae.git] / trav-alg.tex

diff --git a/trav-alg.tex b/trav-alg.tex
index 4b6796a3e97110b88072f0206949eaae253f6484..df5e4cd8fb3b5e47532215b754ea66b6816fb0c1 100644 (file)
--- a/trav-alg.tex
+++ b/trav-alg.tex
@@ -1,7 +1,7 @@
 \section{Traversal phase --- algorithm}
 
 (In general, unless stated otherwise below, when we generate a new
-commit $C$ using one of the commit kind algorith, we update
+commit $C$ using one of the commit kind recipies, we update
 $W \assign C$.  In any such case where we say we're going to Merge
 with $L = W$, if $R \ge W$ we do not Merge but instead simply set
 $W \assign R$.)
@@ -29,12 +29,20 @@ such that:
 \statement{Correct Base}{
   \baseof{\tipcy} = \tipcn
 }
-\statement{Base Ends Supreme}{
-  \tipcn \ge \pendsof{\allsrcs}{\pcn}
+\statement{Base Correct Contents}{
+  \tipcn \haspatch \pa E
+   \equiv
+  \pa E \isdep \pc
 }
-\statement{Tip Ends Supreme}{
+\statement{Tip Exceeds Inputs}{
   \tipcy \ge \pendsof{\allsrcs}{\pcy}
 }
+\statement{Base Exceeds Inputs' Bases}{
+  \bigforall_{E \in \pendsof{\allsrcs}{\pcy}} \tipcn \ge \baseof{E}
+}
+\statement{Base Exceeds Base Inputs}{
+  \bigforall_{H \in \set H^{\pn}} \tipcn \ge H
+}
 
 \subsection{$\alg{Merge-Base}(\pc)$}
 
@@ -63,10 +71,10 @@ In some order, perhaps interleaving the two kinds of merge:
 
 \begin{enumerate}
 
-\item For each $\pd \isdirdep \pc$, find a merge base
+\item For each $\hasdep$-maximal $\pd \isdirdep \pc$, find a merge base
 $M \le W,\; \le \tipdy$ and merge $\tipdy$ into $W$.
 That is, use $\alg{Merge}$ with $L = W,\; R = \tipdy$.
-(Dependency Merge.)
+(Base Dependency Merge.)
 
 \item For each $S \in S^{\pcn}_i$, merge it into $W$.
 That is, use $\alg{Merge}$ with $L = W,\; R = S,\; M = M^{\pcn}_i$.
@@ -78,6 +86,11 @@ That is, use $\alg{Merge}$ with $L = W,\; R = S,\; M = M^{\pcn}_i$.
 
 Execute $\alg{Fixup-Base}(W,\pc)$.
 
+TODO define Fixup-Base
+
+\subsubsection{Result}
+
+If all of that was successful, let $\tipcn = W$.
 
 \subsection{$\alg{Recreate-Base}(\pc)$}
 
@@ -89,7 +102,7 @@ Choose a $\hasdep$-maximal direct dependency $\pd$ of $\pc$.
 
 \item
 
-Use $\alg{Create Base}$ with $L$ = $\pdy,\; \pq = \pc$ to generate $C$
+Use $\alg{Create Base}$ with $L$ = $\tipdy,\; \pq = \pc$ to generate $C$
 and set $W \iassign C$.  (Recreate Base Beginning.)
 
 \item
@@ -99,7 +112,7 @@ Execute the subalgorithm $\alg{Recreate-Recurse}(\pc)$.
 \item
 
 Declare that we contain all of the relevant information from the
-sources.  That is, use $\alg{Pseudo-merge}$ with $L = W, \;
+sources.  That is, use $\alg{Pseudo-Merge}$ with $L = W, \;
 \set R = \{ W \} \cup \set S^{\pcn}$.
 (Recreate Base Final Declaration.)
 
@@ -113,12 +126,12 @@ sources.  That is, use $\alg{Pseudo-merge}$ with $L = W, \;
 
 \item TODO what about non-Topbloke base branches
 
-\item Use $\alg{Pseudo-Merge}$ with $L = W,\; \set R = \{ \tipdn \}$.
-(Recreate Base Dependency Base Declaration.)
-
 \item For all $\hasdep$-maximal $\pd' \isdirdep \pd$,
 execute $\alg{Recreate-Recurse}(\pd')$.
 
+\item Use $\alg{Pseudo-Merge}$ with $L = W,\; \set R = \{ \tipdn \}$.
+(Recreate Base Dependency Base Declaration.)
+
 \item Use $\alg{Merge}$ to apply $\pd$ to $W$.  That is,
 $L = W, \; R = \tipdy, \; M = \baseof{R} = \tipdn$.
 (Recreate Reapply.)