wip create tip

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 25b529fe8d1197aa75cfd436a035aa5fe190c2e7..44942ff2e6524da61a2d7cce059d249ab88aec61 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -293,7 +293,7 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
-\[ \eqn{Ingredients Prohibit Replay:}{
+\[ \eqn{Ingredients Prevent Replay:}{
   \left[
     {C \hasparents \set A} \land
    \\
@@ -379,7 +379,7 @@ Topbloke strips the metadata when exporting.
 
 \subsection{No Replay}
 
-Ingredients Prohibit Replay applies.  $\qed$
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 If $A, C \in \py$ then by Calculation of Ends for
@@ -464,7 +464,7 @@ Given $L$, create a Topbloke base branch initial commit $B$.
 \gathbegin
  B \hasparents \{ L \}
 \gathnext
- \patchof{B} = \pan{B}
+ \patchof{B} = \pan{Q}
 \gathnext
  D \isin B \equiv D \isin L \lor D = B
 \end{gather}
@@ -475,12 +475,12 @@ Given $L$, create a Topbloke base branch initial commit $B$.
  \patchof{L} = \pa{L} \lor \patchof{L} = \bot
 }\]
 \[ \eqn{ Non-recursion }{
- L \not\in \pa{B}
+ L \not\in \pa{Q}
 }\]
 
 \subsection{No Replay}
 
-Ingredients Prohibit Replay applies.  $\qed$
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 
@@ -497,6 +497,8 @@ 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.
 
+xxx this is wrong
+
 $\qed$
 
 \subsection{Coherence and Patch Inclusion}
@@ -523,7 +525,40 @@ Not applicable.
 
 \section{Create Tip}
 
-xxx tbd
+Given a Topbloke base $B$, create a tip branch initial commit B.
+\gathbegin
+ C \hasparents \{ B \}
+\gathnext
+ \patchof{B} = \pay{Q}
+\gathnext
+ D \isin C \equiv D \isin B \lor D = C
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{B} = \pan{Q}
+}\]
+
+\subsection{No Replay}
+
+Ingredients Prevent Replay applies.  $\qed$
+
+\subsection{Unique Base}
+
+Trivially, $\pendsof{C}{\pan{Q}} = \{B\}$ so $\baseof{C} = B$.
+
+\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 $B$, $D \isin B \implies D \not\in \pay{Q}$.
+So $D \isin C \equiv D \isin \baseof{B}$.
+
+$\qed$
+
+xxx up to here
 
 \section{Anticommit}
 
@@ -567,7 +602,7 @@ is a descendant, not an ancestor, of the 2nd parent.)
 By definition of $\merge$,
 $D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
 So, by Ordering of Ingredients,
-Ingredients Prohibit Replay applies.  $\qed$
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Desired Contents}
 
@@ -724,7 +759,7 @@ is therefore consistent with our scheme.
 By definition of $\merge$,
 $D \isin C \implies D \isin L \lor D \isin R \lor D = C$.
 So, by Ingredients,
-Ingredients Prohibit Replay applies.  $\qed$
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}