LaTeX: change \set macros

docs/constructions.tex

@@ -249,7 +249,7 @@ Given a monoid $M$, we construct a monoid modeling someone owning an \emph{autho
 (If $M$ is an exclusive monoid, the construction is very similar to a half-ownership monoid with two asymmetric halves.)
 Let $\auth{M}$ be the monoid with carrier
 \[
-	\SET{ (x, \melt) }{ x \in \mcarp{\exm{\mcarp{M}}} \land \melt \in \mcarp{M} \land (x = \munit_{\exm{\mcarp{M}}} \lor \melt \leq_M x) }
+	\setComp{ (x, \melt) }{ x \in \mcarp{\exm{\mcarp{M}}} \land \melt \in \mcarp{M} \land (x = \munit_{\exm{\mcarp{M}}} \lor \melt \leq_M x) }
 \]
 and multiplication
 \[
@@ -341,7 +341,7 @@ We first lift the transition relation to $\STSS \times \mathcal{P}(\STST)$ (impl
 \begin{align*}
  (s, T) \ra (s', T') \eqdef&\, s \ra s' \land \STSL(s) \uplus T = \STSL(s') \uplus T' \\
  \textsf{frame}(s, T) \eqdef&\, (s, \STST \setminus (\STSL(s) \uplus T)) \\
- \upclose(S, T) \eqdef&\, \SET{ s' \in \STSS}{\exists s \in S.\; \textsf{frame}(s, T) \ststrans \textsf{frame}(s', T) }
+ \upclose(S, T) \eqdef&\, \setComp{ s' \in \STSS}{\exists s \in S.\; \textsf{frame}(s, T) \ststrans \textsf{frame}(s', T) }
 \end{align*}
 
 \noindent
@@ -358,7 +358,7 @@ This is exactly what we have to show, since we know $\STSL(s) \uplus T = \STSL(s
 
 Let $\STSMon{\STSS}$ be the monoid with carrier
 \[
-	\SET{ (s, S, T) \in \exm{\STSS} \times \mathcal{P}(\STSS) \times \mathcal{P}(\STST) }{ \begin{aligned} &(s = \munit \lor s \in S) \land \upclose(S, T) = S   \land{} \\& S \neq \emptyset \land \All s \in S. \STSL(s) \sep T  \end{aligned} }
+	\setComp{ (s, S, T) \in \exm{\STSS} \times \mathcal{P}(\STSS) \times \mathcal{P}(\STST) }{ \begin{aligned} &(s = \munit \lor s \in S) \land \upclose(S, T) = S   \land{} \\& S \neq \emptyset \land \All s \in S. \STSL(s) \sep T  \end{aligned} }
 \]
 and multiplication
 \[

docs/setup.tex

@@ -152,9 +152,11 @@
 
 \newcommand{\upclose}{\mathord{\uparrow}}
 
-\def\All #1.{\forall #1.\;}%
-\def\Exists #1.{\exists #1.\;}%
-\def\Ret #1.{#1.\;}%
+\newcommand{\spac}{\;} % a space
+
+\def\All #1.{\forall #1.\spac}%
+\def\Exists #1.{\exists #1.\spac}%
+\def\Ret #1.{#1.\spac}%
 
 \newcommand{\any}{{\rule[-.2ex]{1ex}{.4pt}}}%
 \newcommand{\unitval}{()}%
@@ -182,21 +184,8 @@
 \newcommand{\IF}{\mathrel{\text{if}}}
 \newcommand{\WHEN}{\textrm{when }}
 
-
-
-\newcommand{\SET}[2]{
-\left\{%
-#1%
-\;\middle|\;%
-#2%
-\right\}
-}
-\newcommand{\SETB}[1]{
-\left\{%
-#1%
-\right\}
-}
-\newcommand{\SETC}[2]{#1 & #2}
+\newcommand*\setComp[2]{\left\{#1\spac\middle|\spac#2\right\}}
+\newcommand*\set[1]{\left\{#1\right\}}
 
 \newenvironment{inbox}[1][]{
   \begin{array}[#1]{@{}l@{}}
@@ -317,8 +306,8 @@
 %% various pieces of Syntax
 \newcommand{\unitsort}{1}%	\unit is bold.
 
-\def\MU #1.{\mu #1.\;}%
-\def\Lam #1.{\lambda #1.\;}%
+\def\MU #1.{\mu #1.\spac}%
+\def\Lam #1.{\lambda #1.\spac}%
 
 \newcommand{\proves}{\vdash}
 \newcommand{\provesalways}{\vdash_{\!\!\boxempty}}