\renewcommand{\land}{\wedge}
\renewcommand{\lor}{\vee}
-\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
-\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
+\newcommand{\pancs}{{\mathcal A}}
+\newcommand{\pends}{{\mathcal E}}
+
+\newcommand{\pancsof}[2]{\pancs ( #1 , #2 ) }
+\newcommand{\pendsof}[2]{\pends ( #1 , #2 ) }
\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
\newcommand{\baseof}[1]{{\mathcal B} ( #1 ) }
\item[ $ \patchof{ C } $ ]
Either $\p$ s.t. $ C \in \p $, or $\bot$.
-A function from commits to sets $\p$.
+A function from commits to patches' sets $\p$.
-\item[ $ \pancs{C}{\set P} $ ]
+\item[ $ \pancsof{C}{\set P} $ ]
$ \{ A \; | \; A \le C \land A \in \set P \} $
i.e. all the ancestors of $C$
which are in $\set P$.
-\item[ $ \pends{C}{\set P} $ ]
-$ \{ E \; | \; E \in \pancs{C}{\set P}
- \land \mathop{\not\exists}_{A \in \pancs{C}{\set P}}
+\item[ $ \pendsof{C}{\set P} $ ]
+$ \{ E \; | \; E \in \pancsof{C}{\set P}
+ \land \mathop{\not\exists}_{A \in \pancsof{C}{\set P}}
A \neq E \land E \le A \} $
-i.e. all $\le$-maximal commits in $\pancs{C}{\set P}$.
+i.e. all $\le$-maximal commits in $\pancsof{C}{\set P}$.
\item[ $ \baseof{C} $ ]
-$ \pends{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
+$ \pendsof{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
A partial function from commits to commits.
See ``unique base'', below.
C \has D \implies C \ge D
}\]
\[\eqn{Unique Base:}{
- \bigforall_{C \in \py} \pends{C}{\pn} = \{ B \}
+ \bigforall_{C \in \py} \pendsof{C}{\pn} = \{ B \}
}\]
\[\eqn{Tip Contents:}{
\bigforall_{C \in \py} D \isin C \equiv
\[\eqn{Base Acyclic:}{
\bigforall_{B \in \pn} D \isin B \implies D \notin \py
}\]
+\[\eqn{Coherence:}{
+ \bigforall_{C,\p} C \haspatch \p \lor C \nothaspatch \p
+}\]
\section{Some lemmas}
}\]
\[ \eqn{Transitive Ancestors:}{
- \left[ \bigforall_{ E \in \pends{C}{\set P} } E \le C \right] \implies
- \left[ \bigforall_{ A \in \pancs{C}{\set P} } A \le C \right]
+ \left[ \bigforall_{ E \in \pendsof{C}{\set P} } E \le M \right] \equiv
+ \left[ \bigforall_{ A \in \pancsof{C}{\set P} } A \le M \right]
}\]
\proof{
-By the definition of $\mathcal E$,
-for every such $A$, either $A \in \pends{C}{\set P}$ which implies
-$A \le C$, or $\exists_{A' \in \pancs{C}{\set P}} \; A' \neq A \land A \le C $
+The implication from right to left is trivial because
+$ \pends() \subset \pancs() $.
+For the implication from left to right:
+by the definition of $\mathcal E$,
+for every such $A$, either $A \in \pends()$ which implies
+$A \le C$, or $\exists_{A' \in \pancs()} \; A' \neq A \land A \le A' $
in which case we repeat for $A'$. Since there are finitely many
-commits, this terminates.
+commits, this terminates with $A'' \in \pends()$, ie $A'' \le M$
+by the LHS. And $A \le A''$.
}
+\section{Commit annotation}
+
+We annotate each Topbloke commit $C$ with:
+\begin{gather}
+\tag*{} \patchof{C} \\
+\tag*{} \baseof{C}, \text{ if } C \in \py \\
+\tag*{} \bigforall_{\pa{Q}}
+ \text{ either } C \haspatch \pa{Q} \text{ or } C \nothaspatch \pa{Q} \\
+\tag*{} \bigforall_{\pay{Q} \not\ni C} \pendsof{C}{\pay{Q}}
+\end{gather}
+
+We do not annotate $\pendsof{C}{\py}$ for $C \in \py$ doing so would
+break making plain commits with git because the recorded $\pends$
+would have to be updated. The annotation is not needed because
+$\forall_{\py \ni C} \pendsof{C}{\py} = \{C\}$.
+
\section{Test more symbols}
$ C \haspatch \p $