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--- a/handouts/ho01.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/handouts/ho01.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -119,8 +119,8 @@
 \ref{crawler3}.\footnote{There is an interesting twist in the
 web-scraper where \pcode{re*?} is used instead of
 \pcode{re*}.} Note, however, the regular expression for
-http-addresses in web-pages in Figure~\ref{crawler1}, Line 15, is 
-intended to be
+http-addresses in web-pages in Figure~\ref{crawler1}, Line 15,
+is intended to be
 
 \[
 \pcode{"https?://[^"]*"}
@@ -128,11 +128,12 @@
 
 \noindent It specifies that web-addresses need to start with a
 double quote, then comes \texttt{http} followed by an optional
-\texttt{s} and so on. Usually we would have to escape the
-double quotes in order to make sure we interpret the double
-quote as character, not as double quote for a string. But
-Scala's trick with triple quotes allows us to omit this kind
-of escaping. As a result we can just write:
+\texttt{s} and so on until the closing double quote comes.
+Usually we would have to escape the double quotes in order to
+make sure we interpret the double quote as character, not as
+double quote for a string. But Scala's trick with triple
+quotes allows us to omit this kind of escaping. As a result we
+can just write:
 
 \[
 \pcode{""""https?://[^"]*"""".r}
@@ -228,7 +229,7 @@
 
 \subsection*{Basic Regular Expressions}
 
-The regular expressions shown above, for example for Scala, we
+The regular expressions shown above for Scala, we
 will call \emph{extended regular expressions}. The ones we
 will mainly study in this module are \emph{basic regular
 expressions}, which by convention we will just call
@@ -521,7 +522,7 @@
 specification and that the corresponding implementations do
 not contain any bugs. We are close, but not yet quite there.
 
-My fascination non withstanding, I am also happy to admit that regular
+Notwithstanding my fascination, I am also happy to admit that regular
 expressions have their shortcomings. There are some well-known
 ``theoretical'' shortcomings, for example recognising strings
 of the form $a^{n}b^{n}$. I am not so bothered by them. What I
@@ -570,7 +571,7 @@
 in ``my'' domain---since these are the ones I am interested in
 to fix. It uses the regular expression \texttt{my\_urls} in
 Line~16 to check for my name in the links. The main change is
-in Lines~26--29 where there is a test whether URL is in ``my''
+in Lines~24--28 where there is a test whether URL is in ``my''
 domain or not.\label{crawler2}}
 
 \end{figure}
@@ -581,8 +582,8 @@
 \caption{A small email harvester---whenever we download a
 web-page, we also check whether it contains any email
 addresses. For this we use the regular expression
-\texttt{email\_pattern} in Line~16. The main change is in Line
-32 where all email addresses that can be found in a page are
+\texttt{email\_pattern} in Line~15. The main change is in Line
+30 where all email addresses that can be found in a page are
 printed.\label{crawler3}}
 \end{figure}
 

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--- a/handouts/ho02.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/handouts/ho02.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -233,7 +233,7 @@
 The other function of our matching algorithm calculates a
 \emph{derivative} of a regular expression. This is a function
 which will take a regular expression, say $r$, and a
-character, say $c$, as argument and return a new regular
+character, say $c$, as argument and returns a new regular
 expression. Be careful that the intuition behind this function
 is not so easy to grasp on first reading. Essentially this
 function solves the following problem: if $r$ can match a
@@ -271,7 +271,7 @@
 straightforward: all strings of the form $c\!::\!s$ are either
 matched by the regular expression $r_1$ or $r_2$. So we just
 have to recursively call $der$ with these two regular
-expressions and compose the results again with $+$. Yes, makes
+expressions and compose the results again with $+$. Makes
 sense? The $\cdot$-case is more complicated: if $r_1\cdot r_2$
 matches a string of the form $c\!::\!s$, then the first part
 must be matched by $r_1$. Consequently, it makes sense to
@@ -332,7 +332,7 @@
 Step 4: & the string is exhausted; test & ($nullable(r_4)$)\\
         & whether $r_4$ can recognise the\\
         & empty string\smallskip\\
-Output: & result of the test $\Rightarrow true \,\text{or}\, \textit{false}$\\        
+Output: & result of this test $\Rightarrow true \,\text{or}\, \textit{false}$\\        
 \end{tabular}
 \end{center}
 

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--- a/handouts/notation.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/handouts/notation.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -19,7 +19,7 @@
 are composed of \defn{characters}. While characters are surely
 a familiar concept, we will make one subtle distinction in
 this module. If we want to refer to concrete characters, like
-\code{a}, \code{b} and so on, we use a typewriter font.
+\code{a}, \code{b}, \code{c} and so on, we use a typewriter font.
 Accordingly if we want to refer to the concrete characters of
 my email address we shall write
 
@@ -37,7 +37,7 @@
 
 \noindent But often we do not care which particular characters
 we use. In such cases we use the italic font and write $a$,
-$b$ and so on for characters. Therefore if we need a
+$b$, $c$ and so on for characters. Therefore if we need a
 representative string, we might write
 
 \begin{equation}\label{abracadabra}
@@ -67,7 +67,7 @@
 write this string as
 
 \[
-[\text{\it h, e, l, l, o}]
+[\text{\it h, e, l, l, o}] \;\;\text{or simply}\;\; \textit{hello}
 \]
 
 \noindent The important point is that we can always decompose

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--- a/mk	Fri Sep 25 17:39:02 2015 +0100
+++ b/mk	Fri Sep 25 20:59:24 2015 +0100
@@ -1,7 +1,7 @@
 #!/bin/sh
 set -e
 
-subdirs="slides handouts hws coursework" 
+subdirs=${1:-"slides handouts hws coursework"} 
 
 for sd in $subdirs; do
   cd $sd

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--- a/slides/slides01.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/slides/slides01.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -296,8 +296,8 @@
 \frametitle{Today}
 
 \begin{itemize}
-\item the ultimate goal is to implement a small compiler 
-(a really small one for the JVM)\bigskip
+\item While the ultimate goal is to implement a small compiler 
+(a really small one for the JVM)\ldots\bigskip
 \end{itemize}
 
 Let's start with:
@@ -305,7 +305,7 @@
 \begin{itemize}
 \item a web-crawler
 \item an email harvester
-\item \textcolor{gray}{a web-scraper}
+\item \textcolor{gray}{(a web-scraper)}
 \end{itemize}
 
 \end{frame}
@@ -637,7 +637,7 @@
 \bl{$\{[], hello, \textit{foobar}, a, abc\}$}
 \end{center}\bigskip
 
-\item \alert{\bf Concatenation} of strings and sets
+\item \alert{\bf Concatenation} of strings and languages
 
 \begin{center}
 \begin{tabular}{rcl}

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--- a/slides/slides02.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/slides/slides02.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -117,7 +117,7 @@
 \bl{$\{[], hello, \textit{foobar}, a, abc\}$}
 \end{center}\bigskip
 
-\item \alert{\bf Concatenation} of strings and sets
+\item \alert{\bf Concatenation} of strings and languages
 
 \begin{center}
 \begin{tabular}{rcl}
@@ -152,14 +152,7 @@
   \end{tabular}
   \end{textblock}
   
-  
-\only<2->{\footnotesize
-\begin{textblock}{9}(2,0.5)
-\begin{bubble}[9.8cm]
-\lstinputlisting{../progs/app01.scala}
-\end{bubble}
-\end{textblock}}
-  
+
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
@@ -204,6 +197,19 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}
+ When Are Two Regular\\
+ Expressions Equivalent?\end{tabular}}
+\large
+\begin{center}
+\bl{$r_1 \equiv r_2 \;\;\dn\;\; L(r_1) = L(r_2)$}
+\end{center}  
+  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{\begin{tabular}{c}Concrete Equivalences\end{tabular}}
 

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