merge: prove bases' children

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index b43d30fea899e45b07d47c1aae08d67eb2b7ee2a..5bb0db2b79feffdd0be6452064c36c631b65385a 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -6,7 +6,7 @@ Merge commits $L$ and $R$ using merge base $M$:
 \gathnext
  \patchof{C} = \patchof{L}
 \gathnext
- \mergeof{C}{L}{M}{R}
+ \commitmergeof{C}{L}{M}{R}
 \end{gather}
 We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
@@ -27,6 +27,16 @@ satisfied; in particular, provided that $L \ge \baseof{R}$.
       \text{otherwise} : & \false
    \end{cases}
 }\]
+\[ \eqn{ Base Merge }{
+ L \in \pn \implies
+  \big[
+   R \in \pn
+     \lor
+   R \in \foreign
+     \lor
+   R \in \pqy
+  \big]
+}\]
 \[ \eqn{ Merge Acyclic }{
     L \in \pn
    \implies
@@ -79,7 +89,7 @@ is therefore consistent with our model.
 
 \subsection{No Replay}
 
-By definition of $\merge$,
+By definition of \commitmergename,
 $D \isin C \implies D \isin L \lor D \isin R \lor D = C$.
 So, by Ingredients,
 Ingredients Prevent Replay applies.  $\qed$
@@ -135,7 +145,7 @@ $$
 $D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
 \in \py$ ie $L \haspatch \p$ by Tip Own Contents for $L$).
 So $D \neq C$.
-Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
+Applying \commitmergename gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
 OK.
 
 \subsubsection{For $L \haspatch \p, R \haspatch \p$:}
@@ -149,17 +159,17 @@ For $D \neq C$: $D \le C \equiv D \le L \lor D \le 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 $D \le X$
+By \commitmergename, $D \isin C$.  Also $D \le X$
 so $D \le C$.  OK for $C \zhaspatch \p$.
 
 Consider $D \neq C, D \not\isin X \land D \not\isin Y$:
-By $\merge$, $D \not\isin C$.
+By \commitmergename, $D \not\isin C$.
 And $D \not\le X \land D \not\le Y$ so $D \not\le C$.
 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 $D \le C$.
+Thus by \commitmergename, $D \isin C$.  And $D \le Y$ so $D \le C$.
 OK for $C \zhaspatch \p$.
 
 So, in all cases, $C \zhaspatch \p$.
@@ -183,26 +193,26 @@ By Tip Own Contents, $L \haspatch \p$ so $L \neq X$,
 therefore we must have $L=Y$, $R=X$.
 Conversely $R \not\in \py$
 so by Tip Merge $M = \baseof{L}$.  Thus $M \in \pn$ so
-by Base Acyclic $M \nothaspatch \p$.  By $\merge$, $D \isin C$,
+by Base Acyclic $M \nothaspatch \p$.  By \commitmergename, $D \isin C$,
 and $D \le C$.  OK.
 
 Consider $D \neq C, M \nothaspatch \p, D \isin Y$:
 $D \le Y$ so $D \le C$.
-$D \not\isin M$ so by $\merge$, $D \isin C$.  OK.
+$D \not\isin M$ so by \commitmergename, $D \isin C$.  OK.
 
 Consider $D \neq C, M \nothaspatch \p, D \not\isin Y$:
 $D \not\le Y$.  If $D \le X$ then
 $D \in \pancsof{X}{\py}$, so by Addition Merge Ends and
 Transitive Ancestors $D \le Y$ --- a contradiction, so $D \not\le X$.
-Thus $D \not\le C$.  By $\merge$, $D \not\isin C$.  OK.
+Thus $D \not\le C$.  By \commitmergename, $D \not\isin C$.  OK.
 
 Consider $D \neq C, M \haspatch \p, D \isin Y$:
 $D \le Y$ so $D \in \pancsof{Y}{\py}$ so by Removal Merge Ends
 and Transitive Ancestors $D \in \pancsof{M}{\py}$ so $D \le M$.
-Thus $D \isin M$.  By $\merge$, $D \not\isin C$.  OK.
+Thus $D \isin M$.  By \commitmergename, $D \not\isin C$.  OK.
 
 Consider $D \neq C, M \haspatch \p, D \not\isin Y$:
-By $\merge$, $D \not\isin C$.  OK.
+By \commitmergename, $D \not\isin C$.  OK.
 
 $\qed$
 
@@ -242,7 +252,7 @@ $C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D
 
 $D \neq C$.  By Tip Contents of $L$,
 $D \isin L \equiv D \isin \baseof{L}$, so by Tip Merge condition,
-$D \isin L \equiv D \isin M$.  So by $\merge$, $D \isin
+$D \isin L \equiv D \isin M$.  So by \commitmergename, $D \isin
 C \equiv D \isin R$.  And $R = \baseof{C}$ by Unique Base of $C$.
 Thus $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
@@ -260,7 +270,7 @@ 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 $D \isin M \equiv D \isin L$ so by $\merge$,
+So $D \isin M \equiv D \isin L$ so by \commitmergename,
 $D \isin C \equiv D \isin R$.  But from Unique Base,
 $\baseof{C} = \baseof{R}$.
 Therefore $D \isin C \equiv D \isin \baseof{C}$.  OK.
@@ -293,17 +303,17 @@ $D \isin C$ and $D \le C$.  OK.
 \subsubsection{For $D \neq C, D \isin M$:}
 
 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.
+R$.  So by \commitmergename, $D \isin C$.  And $D \le C$.  OK.
 
 \subsubsection{For $D \neq C, D \not\isin M, D \isin X$:}
 
-By $\merge$, $D \isin C$.
+By \commitmergename, $D \isin C$.
 And $D \isin X$ means $D \le X$ so $D \le C$.
 OK.
 
 \subsubsection{For $D \neq C, D \not\isin M, D \not\isin L, D \not\isin R$:}
 
-By $\merge$, $D \not\isin C$.
+By \commitmergename, $D \not\isin C$.
 And $D \not\le L, D \not\le R$ so $D \not\le C$.
 OK
 
@@ -314,3 +324,24 @@ $\qed$
 Only relevant if $\isforeign{L}$, in which case
 $\isforeign{C}$ and by Foreign Merges $\isforeign{R}$,
 so Totally Foreign Contents applies.  $\qed$
+
+\subsection{Bases' Children}
+
+If $L \in \py, R \in \py$: not applicable for either $D=L$ or $D=R$.
+
+If $L \in \py, R \in \pn$: not applicable for $L$, OK for $R$.
+
+Other possibilities for $L \in \py$ are excluded by Tip Merge.
+
+If $L \in \pn, R \in \pn$: satisfied for both $L$ and $R$.
+
+If $L \in \pn, R \in \foreign$: satisfied for $L$, not applicable for
+$R$.
+
+If $L \in \pn, R \in \pqy$: satisfied for $L$, not applicable for
+$R$.
+
+Other possibilities for $L \in \pn$ are excluded by Base Merge.
+
+If $L \in \foreign$: not applicable for $L$; nor for $R$, by Foreign Merges.
+