\newcommand{\py}{\pay{P}}
\newcommand{\pn}{\pan{P}}
+\newcommand{\pq}{\pa{Q}}
+\newcommand{\pqy}{\pay{Q}}
+\newcommand{\pqn}{\pan{Q}}
+
\newcommand{\pr}{\pa{R}}
\newcommand{\pry}{\pay{R}}
\newcommand{\prn}{\pan{R}}
\gathnext
\baseof{C}, \text{ if } C \in \py
\gathnext
- \bigforall_{\pa{Q}}
- \text{ either } C \haspatch \pa{Q} \text{ or } C \nothaspatch \pa{Q}
+ \bigforall_{\pq}
+ \text{ either } C \haspatch \pq \text{ or } C \nothaspatch \pq
\gathnext
- \bigforall_{\pay{Q} \not\ni C} \pendsof{C}{\pay{Q}}
+ \bigforall_{\pqy \not\ni C} \pendsof{C}{\pqy}
\end{gather}
$\patchof{C}$, for each kind of Topbloke-generated commit, is stated
Whether $\baseof{C}$ is required, and if so what the value is, is
stated in the proof of Unique Base for each kind of commit.
-$C \haspatch \pa{Q}$ or $\nothaspatch \pa{Q}$ is represented as the
-set $\{ \pa{Q} | C \haspatch \pa{Q} \}$. Whether $C \haspatch \pa{Q}$
+$C \haspatch \pq$ or $\nothaspatch \pq$ is represented as the
+set $\{ \pq | C \haspatch \pq \}$. Whether $C \haspatch \pq$
is in stated
-(in terms of $I \haspatch \pa{Q}$ or $I \nothaspatch \pa{Q}$
+(in terms of $I \haspatch \pq$ or $I \nothaspatch \pq$
for the ingredients $I$),
in the proof of Coherence for each kind of commit.
-$\pendsof{C}{\pa{Q}^+}$ is computed, for all Topbloke-generated commits,
+$\pendsof{C}{\pq^+}$ is computed, for all Topbloke-generated commits,
using the lemma Calculation of Ends, above.
We do not annotate $\pendsof{C}{\py}$ for $C \in \py$. Doing so would
make it wrong to make plain commits with git because the recorded $\pends$
\gathbegin
B \hasparents \{ L \}
\gathnext
- \patchof{B} = \pan{Q}
+ \patchof{B} = \pqn
\gathnext
D \isin B \equiv D \isin L \lor D = B
\end{gather}
\[ \eqn{ Ingredients }{
\patchof{L} = \pa{L} \lor \patchof{L} = \bot
}\]
-\[ \eqn{ Non-recursion }{
- L \not\in \pa{Q}
+\[ \eqn{ Create Acyclic }{
+ L \not\haspatch \pq
}\]
\subsection{No Replay}
\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.
-
-$\qed$
+Consider some $D \isin B$. If $D = B$, $D \in \pqn$.
+If $D \neq B$, $D \isin L$, and by Create Acyclic
+$D \not\in \pqy$. $\qed$
\subsection{Coherence and Patch Inclusion}
Consider some $D \in \p$.
-$B \not\in \py$ so $D \neq B$. So $D \isin B \equiv D \isin L$.
+$B \not\in \py$ so $D \neq B$. So $D \isin B \equiv D \isin L$
+and $D \le B \equiv D \le L$.
Thus $L \haspatch \p \implies B \haspatch P$
and $L \nothaspatch \p \implies B \nothaspatch P$.
\section{Create Tip}
-xxx tbd
+Given a Topbloke base $B$, create a tip branch initial commit B.
+\gathbegin
+ C \hasparents \{ B \}
+\gathnext
+ \patchof{B} = \pqy
+\gathnext
+ D \isin C \equiv D \isin B \lor D = C
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{B} = \pqn
+}\]
+\[ \eqn{ No Sneak }{
+ \pendsof{B}{\pqy} = \{ \}
+}\]
+
+\subsection{No Replay}
+
+Ingredients Prevent Replay applies. $\qed$
+
+\subsection{Unique Base}
+
+Trivially, $\pendsof{C}{\pqn} = \{B\}$ so $\baseof{C} = B$. $\qed$
+
+\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 $B$, $D \isin B \implies D \not\in \pqy$.
+So $D \isin C \equiv D \isin \baseof{B}$.
+
+$\qed$
+
+\subsection{Base Acyclic}
+
+Not applicable.
+
+\subsection{Coherence and Patch Inclusion}
+
+Consider some $D \in \py$.
+
+\subsubsection{For $\p = \pq$:}
+
+By Base Acyclic, $D \not\isin B$. So $D \isin C \equiv D = C$.
+By No Sneak, $D \le B \equiv D = C$. Thus $C \haspatch \pq$.
+
+xxx up to here
\section{Anticommit}