1 files changed, 30 insertions, 35 deletions
diff --git a/tex/thesis/litreview/litreview.tex b/tex/thesis/litreview/litreview.tex
index f54ed97..1ac34d5 100644
--- a/tex/thesis/litreview/litreview.tex
+++ b/tex/thesis/litreview/litreview.tex
@@ -25,46 +25,41 @@ assignment, conditional or loop as having the denotation $\llb s \rrb:
 
 As an example, we'll define some denotational semantics for a simple
 language. Here our $\state$ will be a partial function $\state: I \to \N$
-\newcommand\halfpage[1]{\begin{minipage}{0.45\textwidth}#1\end{minipage}}
-\newcommand\halfpages[2]{\halfpage{#1}\hfill\halfpage{#2}}
-\begin{figure}[here]
-  \halfpages{Syntax:}{Semantics:}
-
-  \halfpages{
-    $P::= S$
-  }{
+\begin{figure}[H]
+  \begin{minipage}{\textwidth}
+    Syntax:
+  \end{minipage} \\[0.1cm]
+  \begin{minipage}{0.8\textwidth}
+    $P ::= S$ \\
+    $S ::= S_1;S_2 \mid \b{if}~ B ~\b{then}~ S_1 ~\b{else~} S_2 \mid I := E$ \\
+    $E ::= E_1 + E_2 \mid I \mid N$ \\
+    $B ::= E_1 = E_2 \mid \lnot B$ \\
+    $I ::= $ variable identifiers \\
+    $N ::= \N$
+  \end{minipage}
+  \\[0.5cm]
+  \begin{minipage}{\textwidth}
+    Semantics:
+  \end{minipage} \\[0.1cm]
+  \begin{minipage}{0.8\textwidth}
     $\b{P}: \state \to \state$ \\
-    $\b{P}\llb S \rrb = S\llb S \rrb \{\}$
-  }
-  \halfpages{
-    $S ::= S_1;S_2 \mid if ~B~ then ~S_1~ else ~S_2~ \mid I := E$
-  }{
+    $\b{P}\llb S \rrb = \b{S}\llb S \rrb \{\}$ \\[0.2cm]
+    
     $\b{S}: \state \to \state$ \\
-    $\b{S}\llb S_1;S_2 \rrb = \lambda v . (S\llb S_2 \rrb (S\llb S_1 \rrb(s)))$ \\
-    $\b{S}\llb if ~B~ then ~S_1~ else ~S_2~ \rrb = \lambda v . (S \llb S_b \rrb(v))$ \\
-    where $b = \b{B}\llb B \rrb (v) + 1$ \\
-    $\b{S}\llb I := E \rrb = \lambda v: (v \oplus \{ I \mapsto E \})$
-  }
-  \halfpages{
-    $E ::= E_1 + E_2 \mid I \mid N$
-  }{
+    $\b{S}\llb S_1;S_2 \rrb = \lambda v . (\b{S}\llb S_2 \rrb (\b{S}\llb S_1 \rrb(v)))$ \\ 
+    $\b{S}\llb \b{if}~ B ~\b{then}~ S_1 ~\b{else~} S_2 \rrb = \lambda v . (\b{S} \llb S_b \rrb(v))$ 
+      where $b = \b{B}\llb B \rrb (v) + 1$ \\
+    $\b{S}\llb I := E \rrb = \lambda v: (v \oplus \{ I \mapsto \b{E}\llb E \rrb(v) \})$ \\[0.2cm]
+
     $\b{E}: \state \to \N$ \\
-    $\b{E}\llb E_1 + E_2 \rrb = \lambda v . (E\llb E_1 \rrb(v) + E\llb E_2 \rrb(v))$ \\
+    $\b{E}\llb E_1 + E_2 \rrb = \lambda v . (\b{E}\llb E_1 \rrb(v) + \b{E}\llb E_2 \rrb(v))$ \\
     $\b{E}\llb I \rrb = \lambda v . v(I)$ \\
-    $\b{E}\llb N \rrb = \lambda v . N$
-  }
-  \halfpages{
-    $B ::= E_1 = E_2 \mid \lnot B$
-  }{
+    $\b{E}\llb N \rrb = \lambda v . N$ \\[0.2cm]
+
     $\b{B}: \state \to \{0,1\}$ \\
-    $\b{B}\llb E_1 = E_2 \rrb = \lambda v . (if ~\llb E_1 \rrb(v) = \llb E_2 \rrb(v) ~then~ 1 ~else~ 0)$
-  }
-  \halfpages{
-    $I ::= $ variable identifier
-  }{~}
-  \halfpages{
-    $N ::= \N$
-  }{~}
+    $\b{B}\llb E_1 = E_2 \rrb = \lambda v . (\b{if}~ \b{E}\llb E_1 \rrb(v) = \b{E}\llb E_2 \rrb(v) ~\b{then}~ 1 ~\b{else}~ 0)$
+  \end{minipage}
+  \caption{Denotational semantics for a simple language.}
   \label{fig:denotational-semantics-example}
 \end{figure}