simple commit unique base clarification

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 9a0cf07790e56d6f778ce8ff8ee244b546533fd7..e6447d92380b854b40c0c1bf9d61825564f79a4d 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -95,8 +95,6 @@
 
 \section{Notation}
 
-xxx make all conditions be in conditions, not in (or also in) intro
-
 \begin{basedescript}{
 \desclabelwidth{5em}
 \desclabelstyle{\nextlinelabel}
@@ -254,6 +252,7 @@ $ \bigforall_{C \in \py}\bigforall_{D \in \py}
     ( \mathop{\hbox{\huge{$\vee$}}}_{R \in \set R} D \le R )
     \lor D = C
 }\]
+xxx proof tbd
 
 \[ \eqn{Transitive Ancestors:}{
   \left[ \bigforall_{ E \in \pendsof{C}{\set P} } E \le M \right] \equiv
@@ -272,17 +271,23 @@ in which case we repeat for $A'$.  Since there are finitely many
 commits, this terminates with $A'' \in \pends()$, ie $A'' \le M$
 by the LHS.  And $A \le A''$.
 }
+
 \[ \eqn{Calculation Of Ends:}{
   \bigforall_{C \hasparents \set A}
     \pendsof{C}{\set P} =
+      \begin{cases}
+       C \in \p : & \{ C \}
+      \\
+       C \not\in \p : & \displaystyle
        \left\{ E \Big|
            \Bigl[ \Largeexists_{A \in \set A} 
                        E \in \pendsof{A}{\set P} \Bigr] \land
            \Bigl[ \Largenexists_{B \in \set A} 
                        E \neq B \land E \le B \Bigr]
        \right\}
+      \end{cases}
 }\]
-XXX proof TBD.
+xxx proof tbd
 
 \subsection{No Replay for Merge Results}
 
@@ -317,8 +322,6 @@ $\qed$
 
 \section{Commit annotation}
 
-xxx need to compute annotation for every commit type
-
 We annotate each Topbloke commit $C$ with:
 \gathbegin
  \patchof{C}
@@ -331,10 +334,25 @@ We annotate each Topbloke commit $C$ with:
  \bigforall_{\pay{Q} \not\ni C} \pendsof{C}{\pay{Q}}
 \end{gather}
 
+$\patchof{C}$, for each kind of Topbloke-generated commit, is stated
+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 $C \haspatch \pa{Q}$
+is in stated
+(in terms of $I \haspatch \pa{Q}$ or $I \nothaspatch \pa{Q}$
+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,
+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 $\pends$
-would have to be updated.  The annotation is not needed because
-$\forall_{\py \ni C} \; \pendsof{C}{\py} = \{C\}$.
+would have to be updated.  The annotation is not needed in that case
+because $\forall_{\py \ni C} \; \pendsof{C}{\py} = \{C\}$.
 
 \section{Simple commit}
 
@@ -351,7 +369,10 @@ Topbloke strips the metadata when exporting.
 Trivial.
 
 \subsection{Unique Base}
-If $A, C \in \py$ then $\baseof{C} = \baseof{A}$. $\qed$
+If $A, C \in \py$ then by Calculation of Ends for
+$C, \py, C \not\in \py$:
+$\pendsof{C}{\pn} = \pendsof{A}{\pn}$ so
+$\baseof{C} = \baseof{A}$. $\qed$
 
 \subsection{Tip Contents}
 We need to consider only $A, C \in \py$.  From Tip Contents for $A$: