-\documentclass[a4paper]{strayman}
+\documentclass[a4paper,leqno]{strayman}
\let\numberwithin=\notdef
+\usepackage{amsmath}
\usepackage{mathabx}
-\usepackage{stmaryrd}
-\usepackage{slashed}
\usepackage{txfonts}
\usepackage{amsfonts}
\usepackage{mdwlist}
\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}
\newcommand{\hasparents}{>_{\mkern-7.0mu _1}}
\newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
-\newcommand{\implies}{\Rightarrow}
+\renewcommand{\implies}{\Rightarrow}
\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}
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.
+is to be taken as applying to both $\py$ and $\pn$.
+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}
-No replay: \[ C \has D \implies C \ge D \]
-
-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}
$ C \nothaspatch \p $
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
$ \{ B \} \areparents C $
\end{document}