From aa9ad81822434edbceb87ed8ece06a2d047a4e95 Mon Sep 17 00:00:00 2001
From: Carlo Zancanaro <carlo@pc-4w14-0.cs.usyd.edu.au>
Date: Mon, 19 Nov 2012 18:06:22 +1100
Subject: Very simple little change to the lit review stuff.

---
 tex/thesis/litreview/litreview.tex | 31 ++++++++++++++++---------------
 1 file changed, 16 insertions(+), 15 deletions(-)

(limited to 'tex/thesis/litreview/litreview.tex')

diff --git a/tex/thesis/litreview/litreview.tex b/tex/thesis/litreview/litreview.tex
index bde7160..f54ed97 100644
--- a/tex/thesis/litreview/litreview.tex
+++ b/tex/thesis/litreview/litreview.tex
@@ -2,6 +2,7 @@
 \newcommand{\PP}{\mathsf{PP}}
 \newcommand{\States}{\mathsf{States}}
 \newcommand{\state}{\mathsf{state}}
+\renewcommand{\b}[1]{\mathbf{#1}}
 
 \chapter{Literature Review} \label{chap:litreview}
 
@@ -23,40 +24,40 @@ assignment, conditional or loop as having the denotation $\llb s \rrb:
 \rrb = \llb s_2 \rrb \circ \llb s_1 \rrb$.
 
 As an example, we'll define some denotational semantics for a simple
-language. Here our $\state$ will be a partial function $\state: I \to N$
+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{
-    $P :: S$
+    $P::= S$
   }{
-    $P: \state \to \state$ \\
-    $P\llb S \rrb = S\llb S \rrb \{\}$
+    $\b{P}: \state \to \state$ \\
+    $\b{P}\llb S \rrb = S\llb S \rrb \{\}$
   }
   \halfpages{
     $S ::= S_1;S_2 \mid if ~B~ then ~S_1~ else ~S_2~ \mid I := E$
   }{
-    $S: \state \to \state$ \\
-    $S\llb S_1;S_2 \rrb = \lambda v . (S\llb S_2 \rrb (S\llb S_1 \rrb(s)))$ \\
-    $S\llb if ~B~ then ~S_1~ else ~S_2~ \rrb = \lambda v . (S \llb S_b \rrb(v))$ \\
-    where $b = B\llb B \rrb (v) + 1$ \\
-    $S\llb I := E \rrb = \lambda v: (v \oplus \{ I \mapsto E \})$
+    $\b{S}: \state \to \state$ \\
+    $\b{S}\llb S_1;S_2 \rrb = \lambda v . (S\llb S_2 \rrb (S\llb S_1 \rrb(s)))$ \\
+    $\b{S}\llb if ~B~ then ~S_1~ else ~S_2~ \rrb = \lambda v . (S \llb S_b \rrb(v))$ \\
+    where $b = \b{B}\llb B \rrb (v) + 1$ \\
+    $\b{S}\llb I := E \rrb = \lambda v: (v \oplus \{ I \mapsto E \})$
   }
   \halfpages{
     $E ::= E_1 + E_2 \mid I \mid N$
   }{
-    $E: \state \to \N$ \\
-    $E\llb E_1 + E_2 \rrb = \lambda v . (E\llb E_1 \rrb(v) + E\llb E_2 \rrb(v))$ \\
-    $E\llb I \rrb = \lambda v . v(I)$ \\
-    $E\llb N \rrb = \lambda v . N$
+    $\b{E}: \state \to \N$ \\
+    $\b{E}\llb E_1 + E_2 \rrb = \lambda v . (E\llb E_1 \rrb(v) + E\llb E_2 \rrb(v))$ \\
+    $\b{E}\llb I \rrb = \lambda v . v(I)$ \\
+    $\b{E}\llb N \rrb = \lambda v . N$
   }
   \halfpages{
     $B ::= E_1 = E_2 \mid \lnot B$
   }{
-    $B: \state \to \{0,1\}$ \\
-    $B\llb E_1 = E_2 \rrb = \lambda v . (if ~\llb E_1 \rrb(v) = \llb E_2 \rrb(v) ~then~ 1 ~else~ 0)$
+    $\b{B}: \state \to \{0,1\}$ \\
+    $\b{B}\llb E_1 = E_2 \rrb = \lambda v . (if ~\llb E_1 \rrb(v) = \llb E_2 \rrb(v) ~then~ 1 ~else~ 0)$
   }
   \halfpages{
     $I ::= $ variable identifier
-- 
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