no gather

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 4e4a75e3da95ab850d6d64d180225ebc41c8fbc0..4160bd7976e73d6c7b040ea5746f5535057494aa 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -1,9 +1,10 @@
-\documentclass[a4paper]{article}
-\usepackage{MnSymbol}
-\usepackage{stmaryrd}
-\usepackage{slashed}
+\documentclass[a4paper,leqno]{strayman}
+\let\numberwithin=\notdef
+\usepackage{amsmath}
+\usepackage{mathabx}
 \usepackage{txfonts}
 \usepackage{amsfonts}
+\usepackage{mdwlist}
 %\usepackage{accents}
 
 \renewcommand{\ge}{\geqslant}
@@ -12,12 +13,10 @@
 \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{\haspatch}{\Sqsupset}
-\newcommand{\patchisin}{\Sqsubset}
+\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}
@@ -36,20 +35,34 @@
 
 \renewcommand{\implies}{\Rightarrow}
 
-\setlength{\parindent}{0pt}
+\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
+\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
+
+\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
+
+\renewcommand{\land}{\wedge}
+
+\newcommand{\eqn}[2]{ #2 \tag*{\mbox{#1}} }
 
 \begin{document}
 
 \section{Notation}
 
-$ C \hasparents \set X $ The parents of commit $C$ are exactly the set
+\begin{basedescript}{
+\desclabelwidth{5em}
+\desclabelstyle{\nextlinelabel}
+}
+\item[ $ 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
+\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 $.
 
-$ C \has D $ Informally, the tree at commit $C$ contains the change
+\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
@@ -57,8 +70,47 @@ 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}
+
 \section{Invariants}
 
-No rewind/replay: $ C \has D \implies C \ge D $
+\[ \eqn{No replay:}{
+  C \has D \implies C \ge D } \]
+\[\eqn{Unique base:}{
+ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} }\]
+
+\section{Test more symbols}
+
+$ C \haspatch \p $
+
+$ C \nothaspatch \p $
+
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
+$ \{ B \} \areparents C $
 
 \end{document}