X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=0688c7ad02524d0d5c0d399682f3ac46946d1e1f;hb=26c18196858d61ec8bd051837aa9ccb08f68ccaf;hp=72230e331f1aa22869514bcb957aea9525256982;hpb=2076cf10e9c6db9325923bb35006587fe6a519f4;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index 72230e3..0688c7a 100644
--- a/article.tex
+++ b/article.tex
@@ -46,6 +46,7 @@
 
 \renewcommand{\implies}{\Rightarrow}
 \renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\nequiv}{\nLeftrightarrow}
 \renewcommand{\land}{\wedge}
 \renewcommand{\lor}{\vee}
 
@@ -151,10 +152,13 @@ $\displaystyle \bigforall_{D \in \py} D \isin C \equiv D \le C $.
 $\displaystyle \bigforall_{D \in \py} D \not\isin C $.
 ~ Informally, $C$ has none of the contents of $\p$.  
 
-Non-Topbloke commits are $\nothaspatch \p$ for all $\p$; if a Topbloke
+Non-Topbloke commits are $\nothaspatch \p$ for all $\p$.  This
+includes commits on plain git branches made by applying a Topbloke
+patch.  If a Topbloke
 patch is applied to a non-Topbloke branch and then bubbles back to
-the Topbloke patch itself, we hope that git's merge algorithm will
-DTRT or that the user will no longer care about the Topbloke patch.
+the relevant Topbloke branches, we hope that 
+if the user still cares about the Topbloke patch,
+git's merge algorithm will DTRT when trying to re-apply the changes.
 
 \item[ $\displaystyle \mergeof{C}{L}{M}{R} $ ]
 The contents of a git merge result:
@@ -195,6 +199,23 @@ We maintain these each time we construct a new commit. \\
 
 \section{Some lemmas}
 
+\[ \eqn{Alternative (overlapping) formulations defining
+  $\mergeof{C}{L}{M}{R}$:}{
+ D \isin C \equiv
+  \begin{cases}
+    D \isin L  \equiv D \isin R  : & D = C \lor D \isin L     \\
+    D \isin L \nequiv D \isin R  : & D = C \lor D \not\isin M \\
+    D \isin L  \equiv D \isin M  : & D = C \lor D \isin R     \\
+    D \isin L \nequiv D \isin M  : & D = C \lor D \isin L     \\
+    \text{as above with L and R exchanged}
+  \end{cases}
+}\]
+\proof{
+  Truth table xxx
+
+  Original definition is symmetrical in $L$ and $R$.
+}
+
 \[ \eqn{Exclusive Tip Contents:}{
   \bigforall_{C \in \py} 
     \neg \Bigl[ D \isin \baseof{C} \land ( D \in \py \land D \le C )
@@ -319,6 +340,8 @@ A simple single-parent forward commit $C$ as made by git-commit.
 \tag*{} \patchof{C} = \patchof{A} \\
 \tag*{} D \isin C \equiv D \isin A \lor D = C
 \end{gather}
+This also covers Topbloke-generated commits on plain git branches:
+Topbloke strips the metadata when exporting.
 
 \subsection{No Replay}
 Trivial.
@@ -406,15 +429,15 @@ Used for removing a branch dependency.
 
 \subsection{Conditions}
 
+\[ \eqn{ From Base }{
+ L \in \pn
+}\]
 \[ \eqn{ Unique Tip }{
  \pendsof{L}{\pry} = \{ R^+ \}
 }\]
 \[ \eqn{ Currently Included }{
  L \haspatch \pry
 }\]
-\[ \eqn{ Not Self }{
- L \not\in \{ R^+ \}
-}\]
 
 \subsection{No Replay}
 
@@ -458,7 +481,12 @@ $\qed$
 
 \subsection{Unique Base}
 
-Need to consider only $C \in \py$, ie $L \in \py$.
+From Base means that $C \in \pn$, so Unique Base is not
+applicable. $\qed$
+
+\subsection{Tip Contents}
+
+Again, not applicable. $\qed$
 
 xxx tbd
 
@@ -483,8 +511,7 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
    \begin{cases}
       R \in \py : & \baseof{R} \ge \baseof{L}
               \land [\baseof{L} = M \lor \baseof{L} = \baseof{M}] \\
-      R \in \pn : & R \ge \baseof{L}
-              \land M = \baseof{L} \\
+      R \in \pn : & M = \baseof{L} \\
       \text{otherwise} : & \false
    \end{cases}
 }\]
@@ -509,6 +536,17 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
    \right]
 }\]
 
+\subsection{Non-Topbloke merges}
+
+We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$.
+I.e. not only is it forbidden to merge into a Topbloke-controlled
+branch without Topbloke's assistance, it is also forbidden to
+merge any Topbloke-controlled branch into any plain git branch.
+
+Given those conditions, Tip Merge and Merge Acyclic do not apply.
+And $Y \not\in \py$ so $\neg [ Y \haspatch \p ]$ so neither
+Merge Ends condition applies.  Good.
+
 \subsection{No Replay}
 
 See No Replay for Merge Results.
@@ -539,7 +577,7 @@ That is, $\baseof{C} = \baseof{R}$.
 
 \subsubsection{For $R \in \pn$:}
 
-By Tip Merge condition on $R$,
+By Tip Merge condition on $R$ and since $M \le R$,
 $A \le \baseof{L} \implies A \le R$, so
 $A \le R \lor A \le \baseof{L} \equiv A \le R$.  
 Thus $A \le C \equiv A \le R$.  
@@ -547,7 +585,7 @@ That is, $\baseof{C} = R$.
 
 $\qed$
 
-\subsection{Coherence and patch inclusion}
+\subsection{Coherence and Patch Inclusion}
 
 Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$.
 This involves considering $D \in \py$.  
@@ -635,16 +673,17 @@ R$.  And $D \neq C$.  So $D \not\isin C$.  $\qed$
 
 We need worry only about $C \in \py$.  
 And $\patchof{C} = \patchof{L}$
-so $L \in \py$ so $L \haspatch \p$.  We will use the coherence and
-patch inclusion of $C$ as just proved.
+so $L \in \py$ so $L \haspatch \p$.  We will use the Unique Base
+of $C$, and its Coherence and Patch Inclusion, as just proved.
 
 Firstly we show $C \haspatch \p$: If $R \in \py$, then $R \haspatch
-\p$ and by coherence/inclusion $C \haspatch \p$ .  If $R \not\in \py$
+\p$ and by Coherence/Inclusion $C \haspatch \p$ .  If $R \not\in \py$
 then by Tip Merge $M = \baseof{L}$ so by Base Acyclic and definition
-of $\nothaspatch$, $M \nothaspatch \p$.  So by coherence/inclusion $C
+of $\nothaspatch$, $M \nothaspatch \p$.  So by Coherence/Inclusion $C
 \haspatch \p$ (whether $R \haspatch \p$ or $\nothaspatch$).
 
-We will consider some $D$ and prove the Exclusive Tip Contents form.
+We will consider an arbitrary commit $D$
+and prove the Exclusive Tip Contents form.
 
 \subsubsection{For $D \in \py$:}
 $C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D
@@ -654,30 +693,58 @@ $C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D
 
 $D \neq C$.  By Tip Contents of $L$,
 $D \isin L \equiv D \isin \baseof{L}$, and by Tip Merge condition,
-$D \isin L \equiv D \isin M$.  xxx up to here
-
+$D \isin L \equiv D \isin M$.  So by definition of $\merge$, $D \isin
+C \equiv D \isin R$.  And $R = \baseof{C}$ by Unique Base of $C$.
+Thus $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
 \subsubsection{For $D \not\in \py, R \in \py$:}
 
+$D \neq C$.
+
+By Tip Contents
+$D \isin L \equiv D \isin \baseof{L}$ and
+$D \isin R \equiv D \isin \baseof{R}$.
 
-%D \in \py$:}
+If $\baseof{L} = M$, trivially $D \isin M \equiv D \isin \baseof{L}.$
+Whereas if $\baseof{L} = \baseof{M}$, by definition of $\base$,
+$\patchof{M} = \patchof{L} = \py$, so by Tip Contents of $M$,
+$D \isin M \equiv D \isin \baseof{M} \equiv D \isin \baseof{L}$.
 
+So $D \isin M \equiv D \isin L$ and by $\merge$,
+$D \isin C \equiv D \isin R$.  But from Unique Base,
+$\baseof{C} = R$ so $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
+$\qed$
+
+\subsection{Foreign Inclusion}
+
+Consider some $D$ s.t. $\patchof{D} = \bot$.
+By Foreign Inclusion of $L, M, R$:
+$D \isin L \equiv D \le L$;
+$D \isin M \equiv D \le M$;
+$D \isin R \equiv D \le R$.
 
-xxx the coherence is not that useful ?
+\subsubsection{For $D = C$:}
+
+$D \isin C$ and $D \le C$.  OK.
 
-$L \haspatch \p$ by 
+\subsubsection{For $D \neq C, D \isin M$:}
 
-xxx need to recheck this
+Thus $D \le M$ so $D \le L$ and $D \le R$ so $D \isin L$ and $D \isin
+R$.  So by $\merge$, $D \isin C$.  And $D \le C$.  OK.
 
-$C \in \py$ $C \haspatch P$ so $D \isin C \equiv D \le C$.  OK.
+\subsubsection{For $D \neq C, D \not\isin M, D \isin X$:}
 
-\subsubsection{For $L \in \py, D \not\in \py, R \in \py$:}
+By $\merge$, $D \isin C$.
+And $D \isin X$ means $D \le X$ so $D \le C$.
+OK.
 
-Tip Contents for $L$: $D \isin L \equiv D \isin \baseof{L}$.
+\subsubsection{For $D \neq C, D \not\isin M, D \not\isin L, D \not\isin R$:}
 
-Tip Contents for $R$: $D \isin R \equiv D \isin \baseof{R}$.
+By $\merge$, $D \not\isin C$.
+And $D \not\le L, D \not\le R$ so $D \not\le C$.
+OK
 
-But by Tip Merge, $\baseof{R} \ge \baseof{L}$
+$\qed$
 
 \end{document}