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[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 405dbbd2f47f080002190ddb4989b06a918626e9..fe0996574afbc0f9a569a795aa90f80d3ef10f8a 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -1,22 +1,77 @@
-\documentclass[a4paper]{article}
+\documentclass[a4paper]{strayman}
+\let\numberwithin=\notdef
 \usepackage{MnSymbol}
 \usepackage{stmaryrd}
 \usepackage{slashed}
-\begin{document}
+\usepackage{txfonts}
+\usepackage{amsfonts}
+\usepackage{nath}
+%\usepackage{accents}
+
+\renewcommand{\ge}{\geqslant}
+\renewcommand{\le}{\leqslant}
+
+\newcommand{\has}{\sqsupseteq}
+\newcommand{\isin}{\sqsubseteq}
+
 \newcommand{\nothaspatch}{{%
   \declareslashed{}{\sslash}{-0.04}{0}{\Sqsupset}\slashed{\Sqsupset}}}
-\newcommand{\notinpatch}{{%
+\newcommand{\notpatchisin}{{%
   \declareslashed{}{\sslash}{-0.04}{0}{\Sqsubset}\slashed{\Sqsubset}}}
 \newcommand{\haspatch}{\Sqsupset}
-\newcommand{\inpatch}{\Sqsubset}
-sponge
-$ A \sqsubseteq B $
-$ A \not \sqsubseteq B $
-$ A \nsqsubseteq B $
-$ A \Sqsubset B $
-$ A \Sqsupset B $
-$ A \haspatch B $
-$ A \nothaspatch B $
-$ A \inpatch B $
-$ A \notinpatch B $
+\newcommand{\patchisin}{\Sqsubset}
+
+\newcommand{\set}[1]{\mathbb #1}
+\newcommand{\pa}[1]{\varmathbb #1}
+\newcommand{\pay}[1]{\pa{#1}^+}
+\newcommand{\pan}[1]{\pa{#1}^-}
+
+\newcommand{\p}{\pa{P}}
+\newcommand{\py}{\pay{P}}
+\newcommand{\pn}{\pan{P}}
+
+%\newcommand{\hasparents}{\underaccent{1}{>}}
+%\newcommand{\hasparents}{{%
+%  \declareslashed{}{_{_1}}{0}{-0.8}{>}\slashed{>}}}
+\newcommand{\hasparents}{>_{\mkern-7.0mu _1}}
+\newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
+
+\renewcommand{\implies}{\Rightarrow}
+
+\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
+\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
+
+\begin{document}
+
+\section{Notation}
+
+$ C \hasparents \set X $ The parents of commit $C$ are exactly the set
+$\set X$.
+
+$ C \ge D $ $C$ is a descendant of $D$ in the git commit
+graph.  This is a partial order, namely the transitive closure of 
+$ D \in \set X $ where $ C \hasparents \set X $.
+
+$ C \has D $ Informally, the tree at commit $C$ contains the change
+made in commit $D$.  Does not take account of deliberate reversions by
+the user or in non-Topbloke-controlled branches; these are considered
+normal, forward, commits.  For merges and Topbloke-generated
+anticommits, the ``change made'' is only to be thought of as any
+conflict resolution.  This is not a partial order because it is not
+transitive.
+
+\section{Invariants}
+
+No replay: $ C \has D \implies C \ge D $
+
+Unique base: $ \mathop{\forall}\limits_{C \in \py} \pends{C}{\pn} = \{ B \} $
+
+\section{Test more symbols}
+
+$ C \haspatch \p $
+
+$ C \nothaspatch \p $
+
+$ \{ B \} \areparents C $
+
 \end{document}