Make better use of \Val, \State, \Expr macros.

docs/base-logic.tex

@@ -26,7 +26,7 @@ Elements of $\SigAx$ are ranged over by $\sigax$.
 \subsection{Grammar}\label{sec:grammar}
 
 \paragraph{Syntax.}
-Iris syntax is built up from a signature $\Sig$ and a countably infinite set $\textdom{Var}$ of variables (ranged over by metavariables $x$, $y$, $z$).
+Iris syntax is built up from a signature $\Sig$ and a countably infinite set $\Var$ of variables (ranged over by metavariables $\var$, $\varB$, $\varC$).
 Below, $\melt$ ranges over $\monoid$ and $i$ ranges over $\set{1,2}$.
 
 \begin{align*}

docs/derived.tex

@@ -141,7 +141,7 @@
 % We write $x \fgmapsto v$ for $\exists q.\; x \fgmapsto[q] v$ and $x \gmapsto v$ for $x \fgmapsto[1] v$.
 % Note that $x \fgmapsto v$ is duplicable but cannot be boxed (as it depends on resources); \ie we have $x \fgmapsto v \Lra x \fgmapsto v * x \fgmapsto v$ but not $x \fgmapsto v \Ra \always x \fgmapsto v$.
 
-% To implement this interface, allocate an instance $\gname_G$ of $\FHeap(\textdom{Val})$ and define
+% To implement this interface, allocate an instance $\gname_G$ of $\FHeap(\Val)$ and define
 % \[
 % 	x \fgmapsto[q] v \eqdef
 % 	  \begin{cases}

docs/iris.sty

@@ -136,6 +136,8 @@
 \newcommand{\Val}{\textdom{Val}}
 \newcommand{\Loc}{\textdom{Loc}}
 \newcommand{\Expr}{\textdom{Expr}}
+\newcommand{\Var}{\textdom{Var}}
+\newcommand{\ThreadPool}{\textdom{ThreadPool}}
 
 \newcommand{\cofe}{T}
 \newcommand{\cofeB}{U}

docs/language.tex

@@ -3,12 +3,14 @@
 \section{Language}
 \label{sec:language}
 
-A \emph{language} $\Lang$ consists of a set \textdom{Expr} of \emph{expressions} (metavariable $\expr$), a set \textdom{Val} of \emph{values} (metavariable $\val$), and a set \textdom{State} of \emph{states} (metvariable $\state$) such that
+A \emph{language} $\Lang$ consists of a set \Expr{} of \emph{expressions} (metavariable $\expr$), a set \Val{} of \emph{values} (metavariable $\val$), and a set \State of \emph{states} (metavariable $\state$) such that
 \begin{itemize}
-\item There exist functions $\ofval : \textdom{Val} \to \textdom{Expr}$ and $\toval : \textdom{Expr} \pfn \textdom{val}$ (notice the latter is partial), such that
-\begin{mathpar} {\All \expr, \val. \toval(\expr) = \val \Ra \ofval(\val) = \expr} \and {\All\val. \toval(\ofval(\val)) = \val} 
+\item There exist functions $\ofval : \Val \to \Expr$ and $\toval : \Expr \pfn \Val$ (notice the latter is partial), such that
+\begin{mathpar}
+{\All \expr, \val. \toval(\expr) = \val \Ra \ofval(\val) = \expr} \and
+{\All\val. \toval(\ofval(\val)) = \val} 
 \end{mathpar}
-\item There exists a \emph{primitive reduction relation} \[(-,- \step -,-,-) \subseteq \textdom{Expr} \times \textdom{State} \times \textdom{Expr} \times \textdom{State} \times (\cup_n \textdom{Expr}^n)\]
+\item There exists a \emph{primitive reduction relation} \[(-,- \step -,-,-) \subseteq \Expr \times \State \times \Expr \times \State \times (\cup_n \Expr^n)\]
   A reduction $\expr_1, \state_1 \step \expr_2, \state_2, \overline\expr$ indicates that, when $\expr_1$ reduces to $\expr_2$, the new threads in the list $\overline\expr$ is forked off.
   We will write $\expr_1, \state_1 \step \expr_2, \state_2$ for $\expr_1, \state_1 \step \expr_2, \state_2, ()$, \ie when no threads are forked off. \\
 \item All values are stuck:
@@ -26,7 +28,7 @@ A \emph{language} $\Lang$ consists of a set \textdom{Expr} of \emph{expressions}
 \end{defn}
 
 \begin{defn}[Context]
-  A function $\lctx : \textdom{Expr} \to \textdom{Expr}$ is a \emph{context} if the following conditions are satisfied:
+  A function $\lctx : \Expr \to \Expr$ is a \emph{context} if the following conditions are satisfied:
   \begin{enumerate}[itemsep=0pt]
   \item $\lctx$ does not turn non-values into values:\\
     $\All\expr. \toval(\expr) = \bot \Ra \toval(\lctx(\expr)) = \bot $
@@ -43,7 +45,7 @@ For any language $\Lang$, we define the corresponding thread-pool semantics.
 
 \paragraph{Machine syntax}
 \[
-	\tpool \in \textdom{ThreadPool} \eqdef \bigcup_n \textdom{Expr}^n
+	\tpool \in \ThreadPool \eqdef \bigcup_n \Expr^n
 \]
 
 \judgment[Machine reduction]{\cfg{\tpool}{\state} \step

docs/program-logic.tex

@@ -14,7 +14,7 @@ To this end, we use tokens that manage which invariants are currently enabled.
 
 We assume to have the following four CMRAs available:
 \begin{align*}
-  \textmon{State} \eqdef{}& \authm(\exm(\textdom{State})) \\
+  \textmon{State} \eqdef{}& \authm(\exm(\State)) \\
   \textmon{Inv} \eqdef{}& \authm(\mathbb N \fpfn \agm(\latert \iPreProp)) \\
   \textmon{En} \eqdef{}& \pset{\mathbb N} \\
   \textmon{Dis} \eqdef{}& \finpset{\mathbb N}
@@ -249,10 +249,10 @@ The purpose of the adequacy statement is to show that our notion of weakest prec
 There are two properties we are looking for: First of all, the postcondition should reflect actual properties of the values the program can terminate with.
 Second, a proof of a weakest precondition with any postcondition should imply that the program is \emph{safe}, \ie that it does not get stuck.
 
-To express the adequacy statement for functional correctness, we assume we are given some set $V \in \textdom{Val}$ of legal return values.
+To express the adequacy statement for functional correctness, we assume we are given some set $V \subseteq \Val$ of legal return values.
 Furthermore, we assume that the signature $\Sig$ adds a predicate $\pred$ to the logic which reflects $V$ into the logic:
 \[\begin{array}{rMcMl}
-  \Sem\pred &:& \Sem{\textdom{Val}\,} \nfn \Sem\Prop \\
+  \Sem\pred &:& \Sem{\Val\,} \nfn \Sem\Prop \\
   \Sem\pred &\eqdef& \Lam \val. \Lam \any. \setComp{n}{v \in V}
 \end{array}\]
 The signature can of course state arbitrary additional properties of $\pred$, as long as they are proven sound.