X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=article.tex;h=0c10bcf095b02696681a91a33539695b10371f9a;hp=703f4d23c510f31f01a49a7938531d8bbcb6f1f3;hb=0c3db5a204f508f8a8a59c74ea8a9bf56d3ab59e;hpb=e83bf31d3532ea138c131241975ca88b71c4f043

diff --git a/article.tex b/article.tex
index 703f4d2..0c10bcf 100644
--- a/article.tex
+++ b/article.tex
@@ -1,4 +1,5 @@
 \documentclass[a4paper,leqno]{strayman}
+\errorcontextlines=50
 \let\numberwithin=\notdef
 \usepackage{amsmath}
 \usepackage{mathabx}
@@ -7,8 +8,20 @@
 \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}
@@ -17,9 +30,15 @@
 \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}^-}
 
@@ -27,87 +46,129 @@
 \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{\pc}{\pa{C}}
+\newcommand{\pcy}{\pay{C}}
+\newcommand{\pcn}{\pan{C}}
 
-\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
-\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
+\newcommand{\pd}{\pa{D}}
+\newcommand{\pdy}{\pay{D}}
+\newcommand{\pdn}{\pan{D}}
 
-\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
+\newcommand{\pl}{\pa{L}}
+\newcommand{\ply}{\pay{L}}
+\newcommand{\pln}{\pan{L}}
 
-\renewcommand{\land}{\wedge}
+\newcommand{\pq}{\pa{Q}}
+\newcommand{\pqy}{\pay{Q}}
+\newcommand{\pqn}{\pan{Q}}
 
-\begin{document}
+\newcommand{\pr}{\pa{R}}
+\newcommand{\pry}{\pay{R}}
+\newcommand{\prn}{\pan{R}}
 
-\section{Notation}
+%\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}}
 
-\begin{basedescript}{
-\desclabelwidth{5em}
-\desclabelstyle{\nextlinelabel}
+\renewcommand{\implies}{\Rightarrow}
+\renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\nequiv}{\nLeftrightarrow}
+\renewcommand{\land}{\wedge}
+\renewcommand{\lor}{\vee}
+
+\newcommand{\pancs}{{\mathcal A}}
+\newcommand{\pends}{{\mathcal E}}
+
+\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{\merge}[4]{{#2 {{\frac{ #1 }{ #3 } #4}}}}
+
+\newcommand{\patch}{{\mathcal P}}
+\newcommand{\base}{{\mathcal B}}
+\newcommand{\depsreq}{{\mathcal D}}
+
+\newcommand{\patchof}[1]{\patch ( #1 ) }
+\newcommand{\baseof}[1]{\base ( #1 ) }
+\newcommand{\depsreqof}[1]{\depsreq ( #1 ) }
+
+\newcommand{\allpatches}{\Upsilon}
+\newcommand{\assign}{\leftarrow}
+\newcommand{\iassign}{\leftarrow}
+%\newcommand{\assign}{' =}
+
+\newcommand{\alg}[1]{\text{\bf #1}}
+\newcommand{\setmerge}{\alg{merge}}
+\newcommand{\setmergeof}[3]{\setmerge\left\langle #1 \;\middle\langle #2 \middle\rangle\; #3 \right\rangle}
+%\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{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
+\newcommand{\bigforall}{%
+  \mathop{\mathchoice%
+    {\hbox{\huge$\forall$}}%
+    {\hbox{\Large$\forall$}}%
+    {\hbox{\normalsize$\forall$}}%
+    {\hbox{\scriptsize$\forall$}}}%
+}
+\newcommand{\bigexists}{%
+  \mathop{\mathchoice%
+    {\hbox{\huge$\exists$}}%
+    {\hbox{\Large$\exists$}}%
+    {\hbox{\normalsize$\exists$}}%
+    {\hbox{\scriptsize$\exists$}}}%
 }
-\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.  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}
+\newcommand{\Largeexists}{\mathop{\hbox{\Large$\exists$}}}
+\newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
 
-\section{Invariants}
+\newcommand{\qed}{\square}
+\newcommand{\proofstarts}{{\it Proof:}}
+\newcommand{\proof}[1]{\proofstarts #1 $\qed$}
 
-\[ C \has D \implies C \ge D \tag*{\mbox{No replay:}} \]
+\newcommand{\gathbegin}{\begin{gather} \tag*{}}
+\newcommand{\gathnext}{\\ \tag*{}}
 
-\[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \tag*{\mbox{Unique base:}} \]
+\newcommand{\true}{t}
+\newcommand{\false}{f}
 
-\section{Test more symbols}
+\begin{document}
 
-$ C \haspatch \p $
+\chapter{Data model}
 
-$ C \nothaspatch \p $
+\input{notation.tex}
+\input{invariants.tex}
+\input{lemmas.tex}
+\input{annotations.tex}
 
-$ \p \patchisin C $
+\input{simple.tex}
+\input{create-base.tex}
+\input{create-tip.tex}
+\input{anticommit.tex}
+\input{merge.tex}
 
-$ \p \notpatchisin C $
+\chapter{Update strategy}
 
-$ \{ B \} \areparents C $
+\input{strategy.tex}
 
 \end{document}