X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=052b28b00b62819dc574bb770256bc42a7318355;hb=6424f586088f250e9d5decafdba36b551c28efd0;hp=183744fb3acc1b2c6cc36efa9508ce67e3b8b346;hpb=1760af5bc9551cd1c060b5050d21325d1c1e7a68;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index 183744f..052b28b 100644
--- a/article.tex
+++ b/article.tex
@@ -1,28 +1,44 @@
-\documentclass[a4paper]{strayman}
+\documentclass[a4paper,leqno]{strayman}
+\errorcontextlines=50
 \let\numberwithin=\notdef
+\usepackage{amsmath}
 \usepackage{mathabx}
-\usepackage{stmaryrd}
-\usepackage{slashed}
 \usepackage{txfonts}
 \usepackage{amsfonts}
 \usepackage{mdwlist}
 %\usepackage{accents}
 
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\rhead[\rightmark]{}
+\lhead[]{\rightmark}
+\rfoot[\thepage]{\input{revid.inc}}
+\lfoot[\input{revid.inc}]{\thepage}
+
+\let\stdsection\section
+\renewcommand\section{\newpage\stdsection}
+
 \renewcommand{\ge}{\geqslant}
 \renewcommand{\le}{\leqslant}
+\newcommand{\nge}{\ngeqslant}
+\newcommand{\nle}{\nleqslant}
 
 \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\relax\haspatch}}
+\newcommand{\notpatchisin}{\mathrel{\,\not\!\not\relax\patchisin}}
 \newcommand{\haspatch}{\sqSupset}
 \newcommand{\patchisin}{\sqSubset}
+%\newcommand{\zhaspatch}{\mathrel{\underset{\fullmoon}\sqSupset}}
+\newcommand{\zhaspatch}{\mathrel{\sqSupset_\varnothing\mkern-4mu}}
+
+        \newif\ifhidehack\hidehackfalse
+        \DeclareRobustCommand\hidefromedef[2]{%
+          \hidehacktrue\ifhidehack#1\else#2\fi\hidehackfalse}
+        \newcommand{\pa}[1]{\hidefromedef{\varmathbb{#1}}{#1}}
 
-\newcommand{\set}[1]{\mathbb #1}
-\newcommand{\pa}[1]{\varmathbb #1}
+\newcommand{\set}[1]{\mathbb{#1}}
 \newcommand{\pay}[1]{\pa{#1}^+}
 \newcommand{\pan}[1]{\pa{#1}^-}
 
@@ -30,64 +46,82 @@
 \newcommand{\py}{\pay{P}}
 \newcommand{\pn}{\pan{P}}
 
+\newcommand{\pl}{\pa{L}}
+\newcommand{\ply}{\pay{L}}
+\newcommand{\pln}{\pan{L}}
+
+\newcommand{\pq}{\pa{Q}}
+\newcommand{\pqy}{\pay{Q}}
+\newcommand{\pqn}{\pan{Q}}
+
+\newcommand{\pr}{\pa{R}}
+\newcommand{\pry}{\pay{R}}
+\newcommand{\prn}{\pan{R}}
+
 %\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}}
 
-\newcommand{\implies}{\Rightarrow}
+\renewcommand{\implies}{\Rightarrow}
+\renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\nequiv}{\nLeftrightarrow}
+\renewcommand{\land}{\wedge}
+\renewcommand{\lor}{\vee}
 
-\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
-\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
+\newcommand{\pancs}{{\mathcal A}}
+\newcommand{\pends}{{\mathcal E}}
 
-\begin{document}
-
-\section{Notation}
+\newcommand{\pancsof}[2]{\pancs ( #1 , #2 ) }
+\newcommand{\pendsof}[2]{\pends ( #1 , #2 ) }
 
-\begin{basedescript}{
-\desclabelwidth{5em}
-\desclabelstyle{\nextlinelabel}
-}
-\item[ $ C \hasparents \set X $ ]
-The parents of commit $C$ are exactly the set
-$\set X$.
+\newcommand{\merge}{{\mathcal M}}
+\newcommand{\mergeof}[4]{\merge(#1,#2,#3,#4)}
+%\newcommand{\merge}[4]{{#2 {{\frac{ #1 }{ #3 } #4}}}}
 
-\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 $.
+\newcommand{\patch}{{\mathcal P}}
+\newcommand{\base}{{\mathcal B}}
 
-\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.
+\newcommand{\patchof}[1]{\patch ( #1 ) }
+\newcommand{\baseof}[1]{\base ( #1 ) }
 
-\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.
+\newcommand{\eqntag}[2]{ #2 \tag*{\mbox{#1}} }
+\newcommand{\eqn}[2]{ #2 \tag*{\mbox{\bf #1}} }
 
-\end{basedescript}
+%\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
+\newcommand{\bigforall}{%
+  \mathop{\mathchoice%
+    {\hbox{\huge$\forall$}}%
+    {\hbox{\Large$\forall$}}%
+    {\hbox{\normalsize$\forall$}}%
+    {\hbox{\scriptsize$\forall$}}}%
+}
 
-\section{Invariants}
+\newcommand{\Largeexists}{\mathop{\hbox{\Large$\exists$}}}
+\newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
 
-No replay: \[ C \has D \implies C \ge D \]
+\newcommand{\qed}{\square}
+\newcommand{\proofstarts}{{\it Proof:}}
+\newcommand{\proof}[1]{\proofstarts #1 $\qed$}
 
-Unique base: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]
+\newcommand{\gathbegin}{\begin{gather} \tag*{}}
+\newcommand{\gathnext}{\\ \tag*{}}
 
-\section{Test more symbols}
+\newcommand{\true}{t}
+\newcommand{\false}{f}
 
-$ C \haspatch \p $
+\begin{document}
 
-$ C \nothaspatch \p $
+\input{notation.tex}
+\input{invariants.tex}
+\input{lemmas.tex}
+\input{annotations.tex}
 
-$ \{ B \} \areparents C $
+\input{simple.tex}
+\input{create-base.tex}
+\input{create-tip.tex}
+\input{anticommit.tex}
+\input{merge.tex}
 
 \end{document}