haspatch

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 4160bd7976e73d6c7b040ea5746f5535057494aa..5cde60f95979741a431e1f53d3cb2aafc29c49fb 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -34,16 +34,20 @@
 \newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
 
 \renewcommand{\implies}{\Rightarrow}
+\renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\land}{\wedge}
+\renewcommand{\lor}{\vee}
 
 \newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
 \newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
 
 \newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
-
-\renewcommand{\land}{\wedge}
+\newcommand{\baseof}[1]{{\mathcal B} ( #1 ) }
 
 \newcommand{\eqn}[2]{ #2 \tag*{\mbox{#1}} }
 
+\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
+
 \begin{document}
 
 \section{Notation}
@@ -92,14 +96,37 @@ $ \{ E \; | \; E \in \pancs{C}{\set P}
   A \neq E \land E \le A \} $ 
 i.e. all $\le$-maximal commits in $\pancs{C}{\set P}$.
 
+\item[ $ \baseof{C} $ ]
+$ \pends{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
+A partial function from commits to commits.
+See ``unique base'', below.
+
+\item[ $ C \haspatch \p $ ]
+$ \bigforall_{D \in \py} D \isin C \equiv D \le C $.
+Informally, $C$ has the contents of $\p$.
+
+\item[ $ C \nothaspatch \p $ ]
+$ \bigforall_{D \in \py} D \not\isin C $.
+Informally, $C$ has none of the contents of $\p$.
+
 \end{basedescript}
 
 \section{Invariants}
 
 \[ \eqn{No replay:}{
-  C \has D \implies C \ge D } \]
+  C \has D \implies C \ge D
+}\]
 \[\eqn{Unique base:}{
- \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} }\]
+ \bigforall_{C \in \py} \pends{C}{\pn} = \{ B \}
+}\]
+\[\eqn{Tip contents:}{
+  \bigforall_{C \in \py} D \isin C \equiv
+    { D \isin \baseof{C} \lor \atop
+      (D \in \py \land D \le C) }
+}\]
+\[\eqn{Base non-circ:}{
+  \bigforall_{B \in \pn} D \isin B \implies D \notin \py
+}\]
 
 \section{Test more symbols}