strategy: define W in Notation

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index d5e73b1a7e19da4ee9041dcb04a1bebcf5a7b4d4..45510aa70d507d9daddd33c5b01306e983f40848 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -5,12 +5,18 @@
 \usepackage{mathabx}
 \usepackage{txfonts}
 \usepackage{amsfonts}
+\usepackage{eufrak}
 \usepackage{mdwlist}
+\usepackage{hyperref}
+%\usepackage{lastpage}
 %\usepackage{accents}
 
 \usepackage{fancyhdr}
-\pagestyle{fancy}
-\lhead[\rightmark]{}
+\pagestyle{fancyplain}
+\rhead[\rightmark]{}
+\lhead[]{\rightmark}
+\rfoot[\thepage]{\input{revid.inc}}
+\lfoot[\input{revid.inc}]{\thepage}
 
 \let\stdsection\section
 \renewcommand\section{\newpage\stdsection}
@@ -27,12 +33,16 @@
 \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{\stmt}[1]{\mathfrak{#1}}
+
 \newcommand{\set}[1]{\mathbb{#1}}
 \newcommand{\pay}[1]{\pa{#1}^+}
 \newcommand{\pan}[1]{\pa{#1}^-}
@@ -41,6 +51,18 @@
 \newcommand{\py}{\pay{P}}
 \newcommand{\pn}{\pan{P}}
 
+\newcommand{\pc}{\pa{C}}
+\newcommand{\pcy}{\pay{C}}
+\newcommand{\pcn}{\pan{C}}
+
+\newcommand{\pd}{\pa{D}}
+\newcommand{\pdy}{\pay{D}}
+\newcommand{\pdn}{\pan{D}}
+
+\newcommand{\pl}{\pa{L}}
+\newcommand{\ply}{\pay{L}}
+\newcommand{\pln}{\pan{L}}
+
 \newcommand{\pq}{\pa{Q}}
 \newcommand{\pqy}{\pay{Q}}
 \newcommand{\pqn}{\pan{Q}}
@@ -52,8 +74,11 @@
 %\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{\hasparent}{>_{\mkern-7.0mu _{1}}}
+\newcommand{\isparent}{<_{\mkern-18.0mu _{1}\mkern+9.0mu}}
+
+\newcommand{\hasparents}{>_{\mkern-7.0mu _{1:}}}
+\newcommand{\areparents}{<_{\mkern-14.0mu _{1:}\mkern+5.0mu}}
 
 \renewcommand{\implies}{\Rightarrow}
 \renewcommand{\equiv}{\Leftrightarrow}
@@ -67,19 +92,60 @@
 \newcommand{\pancsof}[2]{\pancs ( #1 , #2 ) }
 \newcommand{\pendsof}[2]{\pends ( #1 , #2 ) }
 
-\newcommand{\merge}{{\mathcal M}}
-\newcommand{\mergeof}[4]{\merge(#1,#2,#3,#4)}
+%\newcommand{\commitmerge}{\text{\commitmergename}}
+\newcommand{\commitmergeof}[4]{#1 \has \stmtmergeof{#2}{#3}{#4}}
 %\newcommand{\merge}[4]{{#2 {{\frac{ #1 }{ #3 } #4}}}}
+\newcommand{\commitmergename}{Git Merge}
 
 \newcommand{\patch}{{\mathcal P}}
 \newcommand{\base}{{\mathcal B}}
+\newcommand{\depsreq}{{\mathcal G}}
+
+\newcommand{\allsrcs}{\set U}
+\newcommand{\allreach}{\set O}
+\newcommand{\allreachof}[1]{\set O^{#1}}
 
 \newcommand{\patchof}[1]{\patch ( #1 ) }
 \newcommand{\baseof}[1]{\base ( #1 ) }
+\newcommand{\depsreqof}[1]{\depsreq ( #1 ) }
+
+\newcommand{\foreign}{\pa F}
+\newcommand{\isforeign}[1]{#1 \in \foreign}
+
+\newcommand{\allpatches}{\Upsilon}
+\newcommand{\assign}{\leftarrow}
+\newcommand{\iassign}{\leftarrow}
+%\newcommand{\assign}{' =}
+
+\newcommand{\mergeof}[3]{\left\langle #1 \;\middle\langle #2 \middle\rangle\; #3 \right\rangle}
+
+\newcommand{\alg}[1]{\text{\bf #1}}
+\newcommand{\setmerge}{\mergeof{}{}{}}
+\newcommand{\setmergeof}[3]{\mergeof{#1}{#2}{#3}}
+\newcommand{\stmtmergeof}[3]{\mergeof{#1}{#2}{#3}}
+
+%\newcommand{\setmergeof}[3]{\setmerge\left\lgroup #1 \;\middle\lmoustache\; #2 \;\middle\rmoustache\; #3 \right\rgroup}
+%\newcommand{\setmergeof}[3]{\setmerge\left\rmoustache #1 \middle\rmoustache #2 \middle\lmoustache #3 \right\lmoustache}
+%\newcommand{\setmergeof}[3]{\setmerge\left\lfloor #1 \middle\lfloor #2 \middle\rfloor #3 \right\rfloor}
 
 \newcommand{\eqntag}[2]{ #2 \tag*{\mbox{#1}} }
 \newcommand{\eqn}[2]{ #2 \tag*{\mbox{\bf #1}} }
 
+\newcommand{\hasdirdep}{\succ_{\mkern-7.0mu _1}}
+\newcommand{\hasdep}{\succ}
+\newcommand{\isdep}{\prec}
+\newcommand{\isdirdep}{\prec_{\mkern-18.0mu _1}{\mkern+10mu}}
+
+\newcommand{\tip}{ T }
+\newcommand{\tipa}[1]{ \tip^{#1} }
+\newcommand{\tipcn}{ \tipa \pcn }
+\newcommand{\tipcy}{ \tipa \pcy }
+\newcommand{\tipdn}{ \tipa \pdn }
+\newcommand{\tipdy}{ \tipa \pdy }
+
+\newcommand{\tippn}{ \tipa \pn }
+\newcommand{\tippy}{ \tipa \py }
+
 %\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
 \newcommand{\bigforall}{%
   \mathop{\mathchoice%
@@ -88,6 +154,13 @@
     {\hbox{\normalsize$\forall$}}%
     {\hbox{\scriptsize$\forall$}}}%
 }
+\newcommand{\bigexists}{%
+  \mathop{\mathchoice%
+    {\hbox{\huge$\exists$}}%
+    {\hbox{\Large$\exists$}}%
+    {\hbox{\normalsize$\exists$}}%
+    {\hbox{\scriptsize$\exists$}}}%
+}
 
 \newcommand{\Largeexists}{\mathop{\hbox{\Large$\exists$}}}
 \newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
@@ -96,6 +169,16 @@
 \newcommand{\proofstarts}{{\it Proof:}}
 \newcommand{\proof}[1]{\proofstarts #1 $\qed$}
 
+\newcommand{\commitproof}[1]{{\bf Proof of commit generation conditions:}
+ #1 $\qed$}
+\newcommand{\condproof}[2]{
+
+{\it #1:} #2
+
+}
+
+\newcommand{\statement}[2]{\[\eqn{ #1 }{ #2 }\]}
+
 \newcommand{\gathbegin}{\begin{gather} \tag*{}}
 \newcommand{\gathnext}{\\ \tag*{}}
 
@@ -104,6 +187,8 @@
 
 \begin{document}
 
+\chapter{Data model}
+
 \input{notation.tex}
 \input{invariants.tex}
 \input{lemmas.tex}
@@ -114,5 +199,16 @@
 \input{create-tip.tex}
 \input{anticommit.tex}
 \input{merge.tex}
+\input{pseudomerge.tex}
+
+\chapter{Update strategy}
+
+\input{strategy.tex}
+\input{ranking.tex}
+\input{traversal.tex}
+
+%\AtEndDocument{\par\bigskip\centerline{\Large\bfseries Document ends here}}
+
+\par$\bigboxdot$
 
 \end{document}