X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=merge.tex;h=b43d30fea899e45b07d47c1aae08d67eb2b7ee2a;hp=2403a49f85ad40bb07e0d502e2057b3fad0175c6;hb=2621bc3962d0f9a3d12b2318aeb3f425fe6a28c7;hpb=35c23b7d2f99196a118cf034c601b42dc31e8815

diff --git a/merge.tex b/merge.tex
index 2403a49..b43d30f 100644
--- a/merge.tex
+++ b/merge.tex
@@ -10,8 +10,9 @@ Merge commits $L$ and $R$ using merge base $M$:
 \end{gather}
 We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
-This can also be used for dependency re-insertion, by setting
-$L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
+This can also be used for dependency re-insertion, by setting $L \in
+\pn$, $R \in \pry$, $M = \baseof{R}$, provided that the Conditions are
+satisfied; in particular, provided that $L \ge \baseof{R}$.
 
 \subsection{Conditions}
 \[ \eqn{ Ingredients }{
@@ -46,24 +47,31 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
     \bigforall_{E \in \pendsof{X}{\py}} E \le Y
    \right]
 }\]
+\[ \eqn{ Suitable Tips }{
+    \bigforall_{\p \neq \patchof{L}, \; C \haspatch \p}
+    \bigexists_T
+      \pendsof{J}{\py} = \{ T \}
+     \land
+      \forall_{E \in \pendsof{K}{\py}} T \ge E
+    , \text{where} \{J,K\} = \{L,R\}
+}\]
 \[ \eqn{ Foreign Merges }{
-    \patchof{L} = \bot \implies \patchof{R} = \bot
+    \isforeign{L} \implies \isforeign{R}
 }\]
 
 \subsection{Non-Topbloke merges}
 
-We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$
+We require both $\isforeign{L}$ and $\isforeign{R}$
 (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.
-By Foreign Contents of $L$, $\patchof{M} = \bot$ as well.
+By Foreign Contents of $L$, $\isforeign{M}$ as well.
 So by Foreign Contents for any $A \in \{L,M,R\}$,
 $\forall_{\p, D \in \py} D \not\le A$
-so by No Replay for $A$, $D \not\isin A$.
-Thus $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends
+so $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends
 conditions are satisifed.
 
 So a plain git merge of non-Topbloke branches meets the conditions and
@@ -112,20 +120,29 @@ $\qed$
 
 \subsection{Coherence and Patch Inclusion}
 
-Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$.
-This involves considering $D \in \py$.
+$$
+\begin{cases}
+  L \nothaspatch \p \land R \nothaspatch \p : & C \nothaspatch \p  \\
+  L \haspatch    \p \land R \haspatch    \p : & C \haspatch    \p  \\
+  \text{otherwise} \land M \haspatch    \p  : & C \nothaspatch \p  \\
+  \text{otherwise} \land M \nothaspatch \p  : & C \haspatch    \p
+\end{cases}
+$$
+\proofstarts
+~ Consider $D \in \py$.
 
 \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 $\neg[ L \nothaspatch \p ]$ by Tip Own Contents for $L$).
+\in \py$ ie $L \haspatch \p$ by Tip Own Contents for $L$).
 So $D \neq C$.
 Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
+OK.
 
 \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 $C \haspatch \p$.
+Consider $D = C$: $D \isin C$, $D \le C$, OK for $C \zhaspatch \p$.
 
 For $D \neq C$: $D \le C \equiv D \le L \lor D \le R
  \equiv D \isin L \lor D \isin R$.
@@ -133,40 +150,41 @@ For $D \neq C$: $D \le C \equiv D \le L \lor D \le R
 
 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 $C \haspatch \p$.
+so $D \le C$.  OK for $C \zhaspatch \p$.
 
 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 $C \haspatch \p$.
+OK for $C \zhaspatch \p$.
 
 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 $C \haspatch \p$.
+OK for $C \zhaspatch \p$.
 
-So indeed $L \haspatch \p \land R \haspatch \p \implies C \haspatch \p$.
+So, in all cases, $C \zhaspatch \p$.
+And by $L \haspatch \p$, $\exists_{F \in \py} F \le L$
+and this $F \le C$ so indeed $C \haspatch \p$.
 
 \subsubsection{For (wlog) $X \not\haspatch \p, Y \haspatch \p$:}
 
-$M \haspatch \p \implies C \nothaspatch \p$.
-$M \nothaspatch \p \implies C \haspatch \p$.
-
-\proofstarts
-
 One of the Merge Ends conditions applies.
 Recall that we are considering $D \in \py$.
 $D \isin Y \equiv D \le Y$.  $D \not\isin X$.
 We will show for each of
-various cases that $D \isin C \equiv M \nothaspatch \p \land D \le C$
-(which suffices by definition of $\haspatch$ and $\nothaspatch$).
+various cases that
+if $M \haspatch \p$, $D \not\isin C$,
+whereas if $M \nothaspatch \p$, $D \isin C \equiv D \le C$.
+And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this
+$F \le C$ so this suffices.
 
 Consider $D = C$:  Thus $C \in \py, L \in \py$.
-By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$,
+By Tip Own Contents, $L \haspatch \p$ so $L \neq X$,
 therefore we must have $L=Y$, $R=X$.
-By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
+Conversely $R \not\in \py$
+so by Tip Merge $M = \baseof{L}$.  Thus $M \in \pn$ so
 by Base Acyclic $M \nothaspatch \p$.  By $\merge$, $D \isin C$,
-and $D \le C$, consistent with $C \haspatch \p$.  OK.
+and $D \le C$.  OK.
 
 Consider $D \neq C, M \nothaspatch \p, D \isin Y$:
 $D \le Y$ so $D \le C$.
@@ -249,9 +267,20 @@ Therefore $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
 $\qed$
 
+\subsection{Unique Tips}
+
+For $L \in \py$, trivially $\pendsof{C}{\py} = C$ so $T = C$ is
+suitable.
+
+For $L \not\in \py$, $\pancsof{C}{\py} = \pancsof{L}{\py} \cup
+\pancsof{R}{\py}$.  So $T$ from Suitable Tips is a suitable $T$ for
+Unique Tips.
+
+$\qed$
+
 \subsection{Foreign Inclusion}
 
-Consider some $D$ s.t. $\patchof{D} = \bot$.
+Consider some $D \in \foreign$.
 By Foreign Inclusion of $L, M, R$:
 $D \isin L \equiv D \le L$;
 $D \isin M \equiv D \le M$;
@@ -282,6 +311,6 @@ $\qed$
 
 \subsection{Foreign Contents}
 
-Only relevant if $\patchof{L} = \bot$, in which case
-$\patchof{C} = \bot$ and by Foreign Merges $\patchof{R} = \bot$,
+Only relevant if $\isforeign{L}$, in which case
+$\isforeign{C}$ and by Foreign Merges $\isforeign{R}$,
 so Totally Foreign Contents applies.  $\qed$