no gather

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index aac71afd06c5ee23b0d19afd563a6ec50f3858ea..4160bd7976e73d6c7b040ea5746f5535057494aa 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -2,8 +2,6 @@
 \let\numberwithin=\notdef
 \usepackage{amsmath}
 \usepackage{mathabx}
-\usepackage{stmaryrd}
-\usepackage{slashed}
 \usepackage{txfonts}
 \usepackage{amsfonts}
 \usepackage{mdwlist}
@@ -15,10 +13,8 @@
 \newcommand{\has}{\sqsupseteq}
 \newcommand{\isin}{\sqsubseteq}
 
-\newcommand{\nothaspatch}{{%
-  \declareslashed{}{\sslash}{-0.04}{0}{\sqSupset}\slashed{\sqSupset}}}
-\newcommand{\notpatchisin}{{%
-  \declareslashed{}{\sslash}{-0.04}{0}{\sqSubset}\slashed{\sqSubset}}}
+\newcommand{\nothaspatch}{\mathrel{\,\not\!\not\relax\haspatch}}
+\newcommand{\notpatchisin}{\mathrel{\,\not\!\not\relax\patchisin}}
 \newcommand{\haspatch}{\sqSupset}
 \newcommand{\patchisin}{\sqSubset}
 
@@ -42,8 +38,12 @@
 \newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
 \newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
 
+\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
+
 \renewcommand{\land}{\wedge}
 
+\newcommand{\eqn}[2]{ #2 \tag*{\mbox{#1}} }
+
 \begin{document}
 
 \section{Notation}
@@ -75,15 +75,31 @@ A patch $\p$ consists of two sets of commits $\pn$ and $\py$, which
 are respectively the base and tip git branches.  $\p$ may be used
 where the context requires a set, in which case the statement
 is to be taken as applying to both $\py$ and $\pn$.
-All these sets are distinct.
+All these sets are distinct.  Hence:
+
+\item[ $ \patchof{ C } $ ]
+Either $\p$ s.t. $ C \in \p $, or $\bot$.  
+A function from commits to sets $\p$.
+
+\item[ $ \pancs{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}}
+  A \neq E \land E \le A \} $ 
+i.e. all $\le$-maximal commits in $\pancs{C}{\set P}$.
 
 \end{basedescript}
 
 \section{Invariants}
 
-\[ C \has D \implies C \ge D \tag*{\mbox{No replay:}} \]
-
-Unique base: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]
+\[ \eqn{No replay:}{
+  C \has D \implies C \ge D } \]
+\[\eqn{Unique base:}{
+ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} }\]
 
 \section{Test more symbols}
 
@@ -91,6 +107,10 @@ $ C \haspatch \p $
 
 $ C \nothaspatch \p $
 
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
 $ \{ B \} \areparents C $
 
 \end{document}