mdw's bigforall

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index ac351fb6366734cafd90fc5357cc59c7bc267c64..3512d9c5418954713d1ea10b36c82c829ce29308 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -1,8 +1,7 @@
-\documentclass[a4paper]{strayman}
+\documentclass[a4paper,leqno]{strayman}
 \let\numberwithin=\notdef
-\usepackage{MnSymbol}
-\usepackage{stmaryrd}
-\usepackage{slashed}
+\usepackage{amsmath}
+\usepackage{mathabx}
 \usepackage{txfonts}
 \usepackage{amsfonts}
 \usepackage{mdwlist}
@@ -14,12 +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}
@@ -37,10 +34,27 @@
 \newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
 
 \renewcommand{\implies}{\Rightarrow}
+\renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\land}{\wedge}
+\renewcommand{\lor}{\vee}
 
 \newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
 \newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
 
+\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
+\newcommand{\baseof}[1]{{\mathcal B} ( #1 ) }
+
+\newcommand{\eqn}[2]{ #2 \tag*{\mbox{#1}} }
+
+%\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
+\newcommand{\bigforall}{%
+  \mathop{\mathchoice%
+    {\hbox{\huge$\forall$}}%
+    {\hbox{\Large$\forall$}}%
+    {\hbox{\normalsize$\forall$}}%
+    {\hbox{\scriptsize$\forall$}}}%
+}
+
 \begin{document}
 
 \section{Notation}
@@ -67,13 +81,59 @@ 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 $\pancs{C}{\set P}$.
+
+\item[ $ \baseof{C} $ ]
+$ \pends{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
+A partial function from commits to commits.
+See ``unique base'', below.
+
+\item[ $ C \haspatch \p $ ]
+$ \bigforall_{D \in \py} D \isin C \equiv D \le C $.
+Informally, $C$ has the contents of $\p$.
+
+\item[ $\displaystyle C \nothaspatch \p $ ]
+$\displaystyle \bigforall_{D \in \py} D \not\isin C $.
+~ Informally, $C$ has none of the contents of $\p$.
+
 \end{basedescript}
 
 \section{Invariants}
 
-No replay: \[ C \has D \implies C \ge D \]
-
-Unique base: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]
+\[ \eqn{No replay:}{
+  C \has D \implies C \ge D
+}\]
+\[\eqn{Unique base:}{
+ \bigforall_{C \in \py} \pends{C}{\pn} = \{ B \}
+}\]
+\[\eqn{Tip contents:}{
+  \bigforall_{C \in \py} D \isin C \equiv
+    { D \isin \baseof{C} \lor \atop
+      (D \in \py \land D \le C) }
+}\]
+\[\eqn{Base non-circ:}{
+  \bigforall_{B \in \pn} D \isin B \implies D \notin \py
+}\]
 
 \section{Test more symbols}
 
@@ -81,6 +141,10 @@ $ C \haspatch \p $
 
 $ C \nothaspatch \p $
 
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
 $ \{ B \} \areparents C $
 
 \end{document}