-\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}
%\usepackage{accents}
\renewcommand{\ge}{\geqslant}
\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}
\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}
-$ 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
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 rewind/replay: $ C \has D \implies C \ge D $
+\[ \eqn{No replay:}{
+ C \has D \implies C \ge D
+}\]
+\[\eqn{Unique base:}{
+ \bigforall_{C \in \py} \pends{C}{\pn} = \{ B \}
+}\]
+\[\eqn{Tip contents:}{
+ \bigforall_{C \in \py} D \isin C \equiv
+ { D \isin \baseof{C} \lor \atop
+ (D \in \py \land D \le C) }
+}\]
+\[\eqn{Base non-circ:}{
+ \bigforall_{B \in \pn} D \isin B \implies D \notin \py
+}\]
+
+\section{Test more symbols}
+
+$ C \haspatch \p $
+
+$ C \nothaspatch \p $
+
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
+$ \{ B \} \areparents C $
\end{document}