X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=29d8ca96c97c0f679d842e9c99d133a28b710742;hb=63f907df8c8d67156359a4a384dd0060d3de31d3;hp=5ee7f9d7c2210830c4ff05415ae5273737ec80f9;hpb=f720043e63417535be69f72bb737e44b10562daa;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index 5ee7f9d..29d8ca9 100644
--- a/article.tex
+++ b/article.tex
@@ -34,6 +34,10 @@
 \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}}
@@ -196,6 +200,10 @@ We maintain these each time we construct a new commit. \\
 \[\eqn{Foreign Inclusion:}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
 }\]
+\[\eqn{Foreign Contents:}{
+  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
+    D \le C \implies \patchof{D} = \bot
+}\]
 
 \section{Some lemmas}
 
@@ -289,36 +297,62 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
-\subsection{No Replay for Merge Results}
-
-If we are constructing $C$, with,
-\gathbegin
-  \mergeof{C}{L}{M}{R}
-\gathnext
-  L \le C
-\gathnext
-  R \le C
-\end{gather}
-No Replay is preserved.  \proofstarts
-
-\subsubsection{For $D=C$:} $D \isin C, D \le C$.  OK.
-
-\subsubsection{For $D \isin L \land D \isin R$:}
-$D \isin C$.  And $D \isin L \implies D \le L \implies D \le C$.  OK.
-
-\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
-$D \not\isin C$.  OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \not\isin M$:}
-$D \isin C$.  Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
-R$ so $D \le C$.  OK.
+\[ \eqn{Ingredients Prevent Replay:}{
+  \left[
+    {C \hasparents \set A} \land
+   \\
+    \left(
+      D \isin C \implies
+       D = C \lor
+       \Largeexists_{A \in \set A} D \isin A
+    \right)
+  \right] \implies \left[
+    D \isin C \implies D \le C
+  \right]
+}\]
+\proof{
+  Trivial for $D = C$.  Consider some $D \neq C$, $D \isin C$.
+  By the preconditions, there is some $A$ s.t. $D \in \set A$
+  and $D \isin A$.  By No Replay for $A$, $D \le A$.  And
+  $A \le C$ so $D \le C$.
+}
 
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \isin M$:}
-$D \not\isin C$.  OK.
+\[ \eqn{Simple Foreign Inclusion:}{
+  \left[
+    C \hasparents \{ L \}
+   \land
+    \bigforall_{D} D \isin C \equiv D \isin L \lor D = C
+  \right]
+ \implies
+   \bigforall_{D \text{ s.t. } \patchof{D} = \bot}
+     D \isin C \equiv D \le C
+}\]
+\proof{
+Consider some $D$ s.t. $\patchof{D} = \bot$.
+If $D = C$, trivially true.  For $D \neq C$,
+by Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+And by Exact Ancestors $D \le L \equiv D \le C$.
+So $D \isin C \equiv D \le C$.
+}
 
-$\qed$
+\[ \eqn{Totally Foreign Contents:}{
+  \bigforall_{C \hasparents \set A}
+   \left[
+    \patchof{C} = \bot \land
+      \bigforall_{A \in \set A} \patchof{A} = \bot
+   \right]
+  \implies
+   \left[
+    D \le C
+   \implies
+    \patchof{D} = \bot
+   \right]
+}\]
+\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 $A$, $\patchof{D} = \bot$.
+}
 
 \section{Commit annotation}
 
@@ -328,10 +362,10 @@ We annotate each Topbloke commit $C$ with:
 \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
@@ -340,14 +374,14 @@ in the summary in the section for that kind of commit.
 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 $\pends$
@@ -366,7 +400,8 @@ This also covers Topbloke-generated commits on plain git branches:
 Topbloke strips the metadata when exporting.
 
 \subsection{No Replay}
-Trivial.
+
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 If $A, C \in \py$ then by Calculation of Ends for
@@ -435,10 +470,14 @@ So:
 \[ A \nothaspatch P \implies C \nothaspatch P \]
 $\qed$
 
-\subsection{Foreign inclusion:}
+\subsection{Foreign Inclusion:}
 
-If $D = C$, trivial.  For $D \neq C$:
-$D \isin C \equiv D \isin A \equiv D \le A \equiv D \le C$.  $\qed$
+Simple Foreign Inclusion applies.  $\qed$
+
+\subsection{Foreign Contents:}
+
+Only relevant if $\patchof{C} = \bot$, and in that case Totally
+Foreign Contents applies. $\qed$
 
 \section{Create Base}
 
@@ -446,7 +485,7 @@ Given $L$, create a Topbloke base branch initial commit $B$.
 \gathbegin
  B \hasparents \{ L \}
 \gathnext
- \patchof{B} = \pa{B}
+ \patchof{B} = \pqn
 \gathnext
  D \isin B \equiv D \isin L \lor D = B
 \end{gather}
@@ -456,35 +495,120 @@ Given $L$, create a Topbloke base branch initial commit $B$.
 \[ \eqn{ Ingredients }{
  \patchof{L} = \pa{L} \lor \patchof{L} = \bot
 }\]
-\[ \eqn{ Non-recursion }{
- L \not\in \pa{B}
+\[ \eqn{ Create Acyclic }{
+ L \not\haspatch \pq
 }\]
 
 \subsection{No Replay}
 
-If $\patchof{L} = \pa{L}$, trivial by Base Acyclic for $L$.
+Ingredients Prevent Replay applies.  $\qed$
+
+\subsection{Unique Base}
+
+Not applicable.
 
-If $\patchof{L} = \bot$, xxx
+\subsection{Tip Contents}
+
+Not applicable.
+
+\subsection{Base Acyclic}
+
+Consider some $D \isin B$.  If $D = B$, $D \in \pqn$.
+If $D \neq B$, $D \isin L$, and by Create Acyclic
+$D \not\in \pqy$.  $\qed$
 
-Trivial from Base Acyclic for $L$.  $\qed$
+\subsection{Coherence and Patch Inclusion}
+
+Consider some $D \in \p$.
+$B \not\in \py$ so $D \neq B$.  So $D \isin B \equiv D \isin L$
+and $D \le B \equiv D \le L$.
+
+Thus $L \haspatch \p \implies B \haspatch P$
+and $L \nothaspatch \p \implies B \nothaspatch P$.
+
+$\qed$.
+
+\subsection{Foreign Inclusion}
+
+Simple Foreign Inclusion applies. $\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable.
+
+\section{Create Tip}
+
+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}
 
-Not applicable. $\qed$
+Trivially, $\pendsof{C}{\pqn} = \{B\}$ so $\baseof{C} = B$.  $\qed$
 
 \subsection{Tip Contents}
 
-Not applicable. $\qed$
+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}
 
-xxx
+Not applicable.
 
-xxx unfinished
+\subsection{Coherence and Patch Inclusion}
 
-\section{Create Tip}
+$$
+\begin{cases}
+  \p = \pq    \lor B \haspatch \p : & C \haspatch \p \\
+  \p \neq \pq \land B \nothaspatch \p : & C \nothaspatch \p
+\end{cases}
+$$
+
+\proofstarts
+~ 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 tbd
+\subsubsection{For $\p \neq \pq$:}
+
+$D \neq C$.  So $D \isin C \equiv D \isin B$,
+and $D \le C \equiv D \le B$.
+
+$\qed$
+
+\subsection{Foreign Inclusion}
+
+Simple Foreign Inclusion applies.  $\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable.
 
 \section{Anticommit}
 
@@ -514,7 +638,7 @@ R^+ \in \pry \land R^- = \baseof{R^+}
  L \haspatch \pry
 }\]
 
-\subsection{Ordering of ${L, R^+, R^-}$:}
+\subsection{Ordering of Ingredients:}
 
 By Unique Tip, $R^+ \le L$.  By definition of $\base$, $R^- \le R^+$
 so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$.
@@ -525,7 +649,10 @@ is a descendant, not an ancestor, of the 2nd parent.)
 
 \subsection{No Replay}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
+So, by Ordering of Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Desired Contents}
 
@@ -598,7 +725,7 @@ so $L \haspatch \p \implies C \haspatch \p$.
 
 $\qed$
 
-\section{Foreign Inclusion}
+\subsection{Foreign Inclusion}
 
 Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.
 So by Desired Contents $D \isin C \equiv D \isin L$.
@@ -609,6 +736,10 @@ Thus $D \isin C \equiv D \le C$.
 
 $\qed$
 
+\subsection{Foreign Contents}
+
+Not applicable.
+
 \section{Merge}
 
 Merge commits $L$ and $R$ using merge base $M$:
@@ -654,21 +785,31 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
     \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}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R \lor D = C$.
+So, by Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 
@@ -869,4 +1010,10 @@ OK
 
 $\qed$
 
+\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}