X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=6a5023c3ceaf24813e16dfbe0d309a2a38e22178;hb=e600e19a18c0f5b4595c68dd305f093b62fed9e4;hp=20ab3613b294a18dd8bf09d8f49e4f7bc9ab8700;hpb=72c5bcbd461d01b5afe57fe9f58e809202b2bb62;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index 20ab361..6a5023c 100644
--- a/article.tex
+++ b/article.tex
@@ -55,7 +55,8 @@
 \newcommand{\pancsof}[2]{\pancs ( #1 , #2 ) }
 \newcommand{\pendsof}[2]{\pends ( #1 , #2 ) }
 
-\newcommand{\merge}[4]{{\mathcal M}(#1,#2,#3,#4)}
+\newcommand{\merge}{{\mathcal M}}
+\newcommand{\mergeof}[4]{\merge(#1,#2,#3,#4)}
 %\newcommand{\merge}[4]{{#2 {{\frac{ #1 }{ #3 } #4}}}}
 
 \newcommand{\patch}{{\mathcal P}}
@@ -80,7 +81,8 @@
 \newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
 
 \newcommand{\qed}{\square}
-\newcommand{\proof}[1]{{\it Proof.} #1 $\qed$}
+\newcommand{\proofstarts}{{\it Proof:}}
+\newcommand{\proof}[1]{\proofstarts #1 $\qed$}
 
 \newcommand{\gathbegin}{\begin{gather} \tag*{}}
 \newcommand{\gathnext}{\\ \tag*{}}
@@ -154,7 +156,7 @@ 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.
 
-\item[ $\displaystyle \merge{C}{L}{M}{R} $ ]
+\item[ $\displaystyle \mergeof{C}{L}{M}{R} $ ]
 The contents of a git merge result:
 
 $\displaystyle D \isin C \equiv
@@ -261,15 +263,15 @@ XXX proof TBD.
 
 \subsection{No Replay for Merge Results}
 
-If we are constructing $C$, given
+If we are constructing $C$, with,
 \gathbegin
-  \merge{C}{L}{M}{R}
+  \mergeof{C}{L}{M}{R}
 \gathnext
   L \le C
 \gathnext
   R \le C
 \end{gather}
-No Replay is preserved.  {\it Proof:}
+No Replay is preserved.  \proofstarts
 
 \subsubsection{For $D=C$:} $D \isin C, D \le C$.  OK.
 
@@ -399,7 +401,7 @@ Used for removing a branch dependency.
 \gathnext
  \patchof{C} = \patchof{L}
 \gathnext
- \merge{C}{L}{R^+}{R^-}
+ \mergeof{C}{L}{R^+}{R^-}
 \end{gather}
 
 \subsection{Conditions}
@@ -422,19 +424,37 @@ Merge Results applies. $\qed$
 
 \subsection{Desired Contents}
 
-\[ $D \isin C \equiv [ D \not\in \pry \land D \isin L$ ] \lor D = C \]
-{\it Proof.}
+\[ D \isin C \equiv [ D \notin \pry \land D \isin L ] \lor D = C \]
+\proofstarts
 
 \subsubsection{For $D = C$:}
 
 Trivially $D \isin C$.  OK.
 
-\subsubsection{For $D \not\le C$:}
+\subsubsection{For $D \neq C, D \not\le L$:}
 
+By No Replay $D \not\isin L$.  Also $D \not\le R^-$ hence
+$D \not\isin R^-$.  Thus $D \not\isin C$.  OK.
 
+\subsubsection{For $D \neq C, D \le L, D \in \pry$:}
 
-\subsubsection{For $D \in R^+$:}
-By Currently Included, 
+By Currently Included, $D \isin L$.
+
+By Tip Self Inpatch, $D \isin R^+ \equiv D \le R^+$, but by
+by Unique Tip, $D \le R^+ \equiv D \le L$.  
+So $D \isin R^+$.
+
+By Base Acyclic, $D \not\isin R^-$.
+
+Apply $\merge$: $D \not\isin C$.  OK.
+
+\subsubsection{For $D \neq C, D \le L, D \notin \pry$:}
+
+By Tip Contents for $R^+$, $D \isin R^+ \equiv D \isin R^-$.
+
+Apply $\merge$: $D \isin C \equiv D \isin L$.  OK.
+
+$\qed$
 
 \subsection{Unique Base}
 
@@ -442,6 +462,8 @@ Need to consider only $C \in \py$, ie $L \in \py$.
 
 xxx tbd
 
+xxx need to finish anticommit
+
 \section{Merge}
 
 Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
@@ -450,8 +472,9 @@ Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
 \gathnext
  \patchof{C} = \patchof{L}
 \gathnext
- \merge{C}{L}{M}{R}
+ \mergeof{C}{L}{M}{R}
 \end{gather}
+We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
 \subsection{Conditions}
 
@@ -465,6 +488,13 @@ Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
       \text{otherwise} : & \false
    \end{cases}
 }\]
+\[ \eqn{ Merge Ends }{
+    X \not\haspatch \p \land
+    Y \haspatch \p \land
+    E \in \pendsof{X}{\py}
+  \implies
+    E \le Y
+}\]
 
 \subsection{No Replay}
 
@@ -504,4 +534,46 @@ That is, $\baseof{C} = R$.
 
 $\qed$
 
+\subsection{Coherence and patch inclusion}
+
+Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$.
+This involves considering $D \in \py$.  
+
+\subsubsection{For $L \nothaspatch \p, R \nothaspatch \p$:}
+$D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
+\in \py$ ie $L \haspatch \p$ by Tip Self Inpatch).  So $D \neq C$.
+Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
+
+\subsubsection{For $L \haspatch \p, R \haspatch \p$:}
+$D \isin L \equiv D \le L$ and $D \isin R \equiv D \le R$.
+(Likewise $D \isin X \equiv D \le X$ and $D \isin Y \equiv D \le Y$.)
+
+Consider $D = C$: $D \isin C$, $D \le C$, OK for $C \haspatch \p$.
+
+For $D \neq C$: $D \le C \equiv D \le L \lor D \le R
+ \equiv D \isin L \lor D \isin R$.  
+(Likewise $D \le C \equiv D \le X \lor D \le Y$.)
+
+Consider $D \neq C, D \isin X \land D \isin Y$:
+By $\merge$, $D \isin C$.  Also $D \le X$ 
+so $D \le C$.  OK for $C \haspatch \p$.
+
+Consider $D \neq C, D \not\isin X \land D \not\isin Y$:
+By $\merge$, $D \not\isin C$.  
+And $D \not\le X \land D \not\le Y$ so $D \not\le C$.  
+OK for $C \haspatch \p$.
+
+Remaining case, wlog, is $D \not\isin X \land D \isin Y$.
+$D \not\le X$ so $D \not\le M$ so $D \not\isin M$.  
+Thus by $\merge$, $D \isin C$.  And $D \le Y$ so $D \le C$.
+OK for $C \haspatch \p$.
+
+So indeed $L \haspatch \p \land R \haspatch \p \implies C \haspatch \p$.
+
+\subsubsection{For (wlog) $X \not\haspatch \p, Y \haspatch \p$:}
+
+$C \haspatch \p \equiv C \nothaspatch M$.
+
+\proofstarts
+
 \end{document}