X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=85e09e1c470a695becbf92bfa58fcaad0dc000e8;hb=9a2630dee8213479147c4b6a60973c4533de4c32;hp=fda5026a8de1e76d083b9482b537e3d81915147a;hpb=06ac9200d087b074fe60a46fbe186dab4bf653c9;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index fda5026..85e09e1 100644
--- a/article.tex
+++ b/article.tex
@@ -196,6 +196,10 @@ We maintain these each time we construct a new commit. \\
 \[\eqn{Foreign Inclusion:}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
 }\]
+\[\eqn{Foreign Contents:}{
+  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
+    D \le C \implies \patchof{D} = \bot
+}\]
 
 \section{Some lemmas}
 
@@ -289,36 +293,44 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
-\subsection{No Replay for Merge Results}
-
-If we are constructing $C$, with,
-\gathbegin
-  \mergeof{C}{L}{M}{R}
-\gathnext
-  L \le C
-\gathnext
-  R \le C
-\end{gather}
-No Replay is preserved.  \proofstarts
-
-\subsubsection{For $D=C$:} $D \isin C, D \le C$.  OK.
-
-\subsubsection{For $D \isin L \land D \isin R$:}
-$D \isin C$.  And $D \isin L \implies D \le L \implies D \le C$.  OK.
-
-\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
-$D \not\isin C$.  OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \not\isin M$:}
-$D \isin C$.  Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
-R$ so $D \le C$.  OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \isin M$:}
-$D \not\isin C$.  OK.
+\[ \eqn{Ingredients Prevent Replay:}{
+  \left[
+    {C \hasparents \set A} \land
+   \\
+    \left(
+      D \isin C \implies
+       D = C \lor
+       \Largeexists_{A \in \set A} D \isin A
+    \right)
+  \right] \implies \left[
+    D \isin C \implies D \le C
+  \right]
+}\]
+\proof{
+  Trivial for $D = C$.  Consider some $D \neq C$, $D \isin C$.
+  By the preconditions, there is some $A$ s.t. $D \in \set A$
+  and $D \isin A$.  By No Replay for $A$, $D \le A$.  And
+  $A \le C$ so $D \le C$.
+}
 
-$\qed$
+\[ \eqn{Totally Foreign Contents:}{
+  \bigforall_{C \hasparents \set A}
+   \left[
+    \patchof{C} = \bot \land
+      \bigforall_{A \in \set A} \patchof{A} = \bot
+   \right]
+  \implies
+   \left[
+    D \le C
+   \implies
+    \patchof{D} = \bot
+   \right]
+}\]
+\proof{
+Consider some $D \le C$.  If $D = C$, $\patchof{D} = \bot$ trivially.
+If $D \neq C$ then $D \le A$ where $A \in \set A$.  By Foreign
+Contents of $A$, $\patchof{D} = \bot$.
+}
 
 \section{Commit annotation}
 
@@ -366,7 +378,8 @@ This also covers Topbloke-generated commits on plain git branches:
 Topbloke strips the metadata when exporting.
 
 \subsection{No Replay}
-Trivial.
+
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 If $A, C \in \py$ then by Calculation of Ends for
@@ -440,10 +453,111 @@ $\qed$
 If $D = C$, trivial.  For $D \neq C$:
 $D \isin C \equiv D \isin A \equiv D \le A \equiv D \le C$.  $\qed$
 
+\subsection{Foreign Contents:}
+
+Only relevant if $\patchof{C} = \bot$, and in that case Totally
+Foreign Contents applies. $\qed$
+
+\section{Create Base}
+
+Given $L$, create a Topbloke base branch initial commit $B$.
+\gathbegin
+ B \hasparents \{ L \}
+\gathnext
+ \patchof{B} = \pan{Q}
+\gathnext
+ D \isin B \equiv D \isin L \lor D = B
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{L} = \pa{L} \lor \patchof{L} = \bot
+}\]
+\[ \eqn{ Non-recursion }{
+ L \not\haspatch \pa{Q}
+}\]
+
+\subsection{No Replay}
+
+Ingredients Prevent Replay applies.  $\qed$
+
+\subsection{Unique Base}
+
+Not applicable.
+
+\subsection{Tip Contents}
+
+Not applicable.
+
+\subsection{Base Acyclic}
+
+Consider some $D \isin B$.  If $D = B$, $D \in \pan{Q}$.
+If $D \neq B$, $D \isin L$, and by Non-recursion
+$D \not\in \pay{Q}$.  $\qed$
+
+\subsection{Coherence and Patch Inclusion}
+
+Consider some $D \in \p$.
+$B \not\in \py$ so $D \neq B$.  So $D \isin B \equiv D \isin L$.
+
+Thus $L \haspatch \p \implies B \haspatch P$
+and $L \nothaspatch \p \implies B \nothaspatch P$.
+
+$\qed$.
+
+\subsection{Foreign Inclusion}
+
+Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq B$
+so $D \isin B \equiv D \isin L$.
+By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+And by Exact Ancestors $D \le L \equiv D \le B$.
+So $D \isin B \equiv D \le B$.  $\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable.
+
+\section{Create Tip}
+
+Given a Topbloke base $B$, create a tip branch initial commit B.
+\gathbegin
+ C \hasparents \{ B \}
+\gathnext
+ \patchof{B} = \pay{Q}
+\gathnext
+ D \isin C \equiv D \isin B \lor D = C
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{B} = \pan{Q}
+}\]
+
+\subsection{No Replay}
+
+Ingredients Prevent Replay applies.  $\qed$
+
+\subsection{Unique Base}
+
+Trivially, $\pendsof{C}{\pan{Q}} = \{B\}$ so $\baseof{C} = B$.
+
+\subsection{Tip Contents}
+
+Consider some arbitrary commit $D$.  If $D = C$, trivially satisfied.
+
+If $D \neq C$, $D \isin C \equiv D \isin B$.
+By Base Acyclic of $B$, $D \isin B \implies D \not\in \pay{Q}$.
+So $D \isin C \equiv D \isin \baseof{B}$.
+
+$\qed$
+
+xxx up to here
+
 \section{Anticommit}
 
-Given $L, R^+, R^-$ where
-$R^+ \in \pry, R^- = \baseof{R^+}$.  
+Given $L$ and $\pr$ as represented by $R^+, R^-$.
 Construct $C$ which has $\pr$ removed.
 Used for removing a branch dependency.
 \gathbegin
@@ -456,6 +570,9 @@ Used for removing a branch dependency.
 
 \subsection{Conditions}
 
+\[ \eqn{ Ingredients }{
+R^+ \in \pry \land R^- = \baseof{R^+}
+}\]
 \[ \eqn{ Into Base }{
  L \in \pn
 }\]
@@ -466,18 +583,21 @@ Used for removing a branch dependency.
  L \haspatch \pry
 }\]
 
-\subsection{Ordering of ${L, R^+, R^-}$:}
+\subsection{Ordering of Ingredients:}
 
 By Unique Tip, $R^+ \le L$.  By definition of $\base$, $R^- \le R^+$
 so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$.
 $\qed$
 
-(Note that the merge base $R^+ \not\le R^-$, i.e. the merge base is
-later than one of the branches to be merged.)
+(Note that $R^+ \not\le R^-$, i.e. the merge base
+is a descendant, not an ancestor, of the 2nd parent.)
 
 \subsection{No Replay}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
+So, by Ordering of Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Desired Contents}
 
@@ -550,7 +670,7 @@ so $L \haspatch \p \implies C \haspatch \p$.
 
 $\qed$
 
-\section{Foreign Inclusion}
+\subsection{Foreign Inclusion}
 
 Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.
 So by Desired Contents $D \isin C \equiv D \isin L$.
@@ -561,9 +681,13 @@ Thus $D \isin C \equiv D \le C$.
 
 $\qed$
 
+\subsection{Foreign Contents}
+
+Not applicable.
+
 \section{Merge}
 
-Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
+Merge commits $L$ and $R$ using merge base $M$:
 \gathbegin
  C \hasparents \{ L, R \}
 \gathnext
@@ -574,7 +698,9 @@ Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
 We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
 \subsection{Conditions}
-
+\[ \eqn{ Ingredients }{
+ M \le L, M \le R
+}\]
 \[ \eqn{ Tip Merge }{
  L \in \py \implies
    \begin{cases}
@@ -604,21 +730,31 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
     \bigforall_{E \in \pendsof{X}{\py}} E \le Y
    \right]
 }\]
+\[ \eqn{ Foreign Merges }{
+    \patchof{L} = \bot \equiv \patchof{R} = \bot
+}\]
 
 \subsection{Non-Topbloke merges}
 
-We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$.
+We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$
+(Foreign Merges, above).
 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.
+Merge Ends condition applies.
+
+So a plain git merge of non-Topbloke branches meets the conditions and
+is therefore consistent with our scheme.
 
 \subsection{No Replay}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R \lor D = C$.
+So, by Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 
@@ -819,4 +955,10 @@ OK
 
 $\qed$
 
+\subsection{Foreign Contents}
+
+Only relevant if $\patchof{L} = \bot$, in which case
+$\patchof{C} = \bot$ and by Foreign Merges $\patchof{R} = \bot$,
+so Totally Foreign Contents applies.  $\qed$
+
 \end{document}