\[\eqn{Foreign Inclusion:}{
\bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
}\]
+\[\eqn{Foreign Contents:}{
+ \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
+ D \le C \implies \patchof{D} = \bot
+}\]
\section{Some lemmas}
}\]
xxx proof tbd
+\[ \eqn{Totally Foreign Contents:}{
+ \bigforall_{C \hasparents \set A}
+ \left[
+ \patchof{C} = \bot \land
+ \bigforall_{A \in \set A} \patchof{A} = \bot
+ \right]
+ \implies
+ \left[
+ D \le C
+ \implies
+ \patchof{D} = \bot
+ \right]
+}\]
+\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 $A$, $\patchof{D} = \bot$.
+}
+
\subsection{No Replay for Merge Results}
If we are constructing $C$, with,
For $D = C$: $D \in \pn$ so $D \not\in \py$. OK.
For $D \neq C$: $D \isin C \equiv D \isin A$, so by Base Acyclic for
-$A$, $D \isin C \implies D \not\in \py$. $\qed$
+$A$, $D \isin C \implies D \not\in \py$.
+
+$\qed$
\subsection{Coherence and patch inclusion}
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{B}
+\gathnext
+ D \isin B \equiv D \isin L \lor D = B
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{L} = \pa{L} \lor \patchof{L} = \bot
+}\]
+\[ \eqn{ Non-recursion }{
+ L \not\in \pa{B}
+}\]
+
+\subsection{No Replay}
+
+If $\patchof{L} = \pa{L}$, trivial by Base Acyclic for $L$.
+
+If $\patchof{L} = \bot$, consider some $D \isin B$. $D \neq B$.
+Thus $D \isin L$. So by No Replay of $D$ in $L$, $D \le L$.
+Thus $D \le B$.
+
+\subsection{Unique Base}
+
+Not applicable. $\qed$
+
+\subsection{Tip Contents}
+
+Not applicable. $\qed$
+
+\subsection{Base Acyclic}
+
+Consider some $D \isin B$. If $D = B$, $D \in \pn$, OK.
+
+If $D \neq B$, $D \isin L$. By No Replay of $D$ in $L$, $D \le L$.
+Thus by Foreign Contents of $L$, $\patchof{D} = \bot$. OK.
+
+$\qed$
+
+\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 $D$ xxx up to here
+
+\section{Create Tip}
+
+xxx tbd
+
\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
\subsection{Conditions}
+\[ \eqn{ Ingredients }{
+R^+ \in \pry \land R^- = \baseof{R^+}
+}\]
\[ \eqn{ Into Base }{
L \in \pn
}\]
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}
Whereas if $L \haspatch \p$, $D \isin L \equiv D \le L$.
so $L \haspatch \p \implies C \haspatch \p$.
-\section{Foreign Inclusion}
+$\qed$
+
+\subsection{Foreign Inclusion}
Consider some $D$ s.t. $\patchof{D} = \bot$. $D \neq C$.
So by Desired Contents $D \isin C \equiv D \isin L$.
By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
And $D \le C \equiv D \le L$.
-Thus $D \isin C \equiv D \le C$. $\qed$
+Thus $D \isin C \equiv D \le C$.
+
+$\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable. $\qed$
\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
We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
\subsection{Conditions}
-
+\[ \eqn{ Ingredients }{
+ M \le L, M \le R
+}\]
\[ \eqn{ Tip Merge }{
L \in \py \implies
\begin{cases}
\bigforall_{E \in \pendsof{X}{\py}} E \le Y
\right]
}\]
+\[ \eqn{ Foreign Merges }{
+ \patchof{L} = \bot \equiv \patchof{R} = \bot
+}\]
\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}
Consider some $D \in \py$.
By Base Acyclic of $L$, $D \not\isin L$. By the above, $D \not\isin
-R$. And $D \neq C$. So $D \not\isin C$. $\qed$
+R$. And $D \neq C$. So $D \not\isin C$.
+
+$\qed$
\subsection{Tip Contents}
$\qed$
+\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}
~ian / topbloke-formulae.git / blobdiff