foreign notation: change \bot to \foreign everywhere

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index 7a48a25cf994a282b5c1d74d019af0f45aafb7d2..6ba1387886a8bc6f90fb4cd5254ce544f962e4e7 100644 (file)
--- 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}
 \[ \eqn{ Ingredients }{
@@ -46,20 +47,28 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
     \bigforall_{E \in \pendsof{X}{\py}} E \le Y
    \right]
 }\]
+\[ \eqn{ Suitable Tips }{
+    \bigforall_{\p \neq \patchof{L}, \; C \haspatch \p}
+    \bigexists_T
+      \pendsof{J}{\py} = \{ T \}
+     \land
+      \forall_{E \in \pendsof{K}{\py}} T \ge E
+    , \text{where} \{J,K\} = \{L,R\}
+}\]
 \[ \eqn{ Foreign Merges }{
-    \patchof{L} = \bot \implies \patchof{R} = \bot
+    \patchof{L} = \foreign \implies \patchof{R} = \foreign
 }\]
 
 \subsection{Non-Topbloke merges}
 
-We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$
+We require both $\patchof{L} = \foreign$ and $\patchof{R} = \foreign$
 (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 $L$, $\patchof{M} = \foreign$ as well.
 So by Foreign Contents for any $A \in \{L,M,R\}$,
 $\forall_{\p, D \in \py} D \not\le A$
 so $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends
@@ -170,9 +179,10 @@ 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 $D \le C$.  OK.
 
@@ -257,9 +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 $D$ s.t. $\patchof{D} = \foreign$.
 By Foreign Inclusion of $L, M, R$:
 $D \isin L \equiv D \le L$;
 $D \isin M \equiv D \le M$;
@@ -290,6 +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 $\patchof{L} = \foreign$, in which case
+$\patchof{C} = \foreign$ and by Foreign Merges $\patchof{R} = \foreign$,
 so Totally Foreign Contents applies.  $\qed$