X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=article.tex;h=1cf0e76e61e8b48c3eb083eafdcf590929e74891;hp=714fbd167e00d67c850ccf69d0942e9a8b3b116a;hb=0b0cb39339f1f3c4fd43e8dbfa2efd3f5b5eddf2;hpb=cc1fe9b52fdc03805d305fe1e0b74063661d5e2a

diff --git a/article.tex b/article.tex
index 714fbd1..1cf0e76 100644
--- a/article.tex
+++ b/article.tex
@@ -1,21 +1,109 @@
-\documentclass[a4paper]{article}
-\usepackage{MnSymbol}
+\documentclass[a4paper,leqno]{strayman}
+\let\numberwithin=\notdef
+\usepackage{amsmath}
+\usepackage{mathabx}
 \usepackage{stmaryrd}
 \usepackage{slashed}
+\usepackage{txfonts}
+\usepackage{amsfonts}
+\usepackage{mdwlist}
+%\usepackage{accents}
+
+\renewcommand{\ge}{\geqslant}
+\renewcommand{\le}{\leqslant}
+
+\newcommand{\has}{\sqsupseteq}
+\newcommand{\isin}{\sqsubseteq}
+
+\newcommand{\nothaspatch}{\mathrel{\,\not\!\not\relax\haspatch}}
+\newcommand{\notpatchisin}{\mathrel{\,\not\!\not\relax\patchisin}}
+\newcommand{\haspatch}{\sqSupset}
+\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 ) }
+
+\renewcommand{\land}{\wedge}
+
 \begin{document}
-\def\iwjtest{{/\mkern-9mu\Sqsupset}}
-\newcommand{\iwjtestx}{\mathrel{\ooalign{$\Sqsubset$ $\sslash$}}}
-\newcommand{\iwjtesty}{{%
-  \declareslashed{}{\sslash}{-0.04}{0}{\Sqsubset}\slashed{\Sqsubset}}}
-sponge
-$ A \sqsubseteq B $
-$ A \not \sqsubseteq B $
-$ A \nsqsubseteq B $
-$ A \Sqsubset B $
-$ A \Sqsupset B $
-$ \sslash $
-$ \iwjtest $
-$ \iwjtestx $
-$ \iwjtesty $
-$ A \iwjtesty B $
+
+\section{Notation}
+
+\begin{basedescript}{
+\desclabelwidth{5em}
+\desclabelstyle{\nextlinelabel}
+}
+\item[ $ C \hasparents \set X $ ]
+The parents of commit $C$ are exactly the set
+$\set X$.
+
+\item[ $ 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 $.
+
+\item[ $ 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.
+
+\item[ $ \p, \py, \pn $ ]
+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.
+
+\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: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]
+
+\section{Test more symbols}
+
+$ C \haspatch \p $
+
+$ C \nothaspatch \p $
+
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
+$ \{ B \} \areparents C $
+
 \end{document}