
diff -r f7c6512bb85a -r ff496c243d10 handouts/ho06.tex
--- a/handouts/ho06.tex	Fri Oct 26 17:13:41 2018 +0100
+++ b/handouts/ho06.tex	Sat Oct 27 12:17:03 2018 +0100
@@ -27,7 +27,7 @@
 
 \begin{center}
 $\underbrace{\text{list of tokens}}_{\text{input}}$ 
-$\Rightarrow$
+$\quad\Rightarrow\quad$
 $\underbrace{\text{set of (parsed part, unprocessed part)}}_{\text{output}}$
 \end{center} 
 
@@ -82,20 +82,21 @@
 something ``went wrong''\ldots or more precisely, nothing could be
 parsed.
 
-Also important to note is that the type \texttt{T} for the processed
-part is different from the input type \texttt{I} in the parse. In the
-example above is just happens to be the same. The reason for the
-difference is that in general we are interested in
-transforming our input into something ``different''\ldots for example
-into a tree; or if we implement the grammar for arithmetic
-expressions, we might be interested in the actual integer number the
-arithmetic expression, say \texttt{1 + 2 * 3}, stands for. In this way
-we can use parser combinators to implement relatively easily a
-calculator, for instance.
+Also important to note is that the output type \texttt{T} for the
+processed part can potentially be different from the input type
+\texttt{I} in the parser. In the example above is just happens to be
+the same. The reason for the difference is that in general we are
+interested in transforming our input into something
+``different''\ldots for example into a tree; or if we implement the
+grammar for arithmetic expressions, we might be interested in the
+actual integer number the arithmetic expression, say \texttt{1 + 2 *
+  3}, stands for. In this way we can use parser combinators to
+implement relatively easily a calculator, for instance (we shall do
+this later on).
 
-The main idea of parser combinators is that we can easily build parser
-combinators out of smaller components following very closely the
-structure of a grammar. In order to implement this in a
+The main driving force behind parser combinators is that we can easily
+build parser combinators out of smaller components following very
+closely the structure of a grammar. In order to implement this in a
 functional/object-oriented programming language, like Scala, we need
 to specify an abstract class for parser combinators. In the abstract
 class we specify that \texttt{I} is the \emph{input type} of the
@@ -878,7 +879,7 @@
 \end{center}
 
 \noindent
-Let us try out on some examples:
+Let us try out some examples:
 
 \begin{center}
 \begin{tabular}{rcl}
@@ -886,18 +887,24 @@
   \texttt{\Grid{1+2+3}} & $\rightarrow$ & \texttt{Set(6)}\\
   \texttt{\Grid{4*2+3}} & $\rightarrow$ & \texttt{Set(11)}\\
   \texttt{\Grid{4*(2+3)}} & $\rightarrow$ & \texttt{Set(20)}\\
+  \texttt{\Grid{(4)*((2+3))}} & $\rightarrow$ & \texttt{Set(20)}\\
   \texttt{\Grid{4/2+3}} & $\rightarrow$ & \texttt{Set()}\\
   \texttt{\Grid{1\VS +\VS 2\VS +\VS 3}} & $\rightarrow$ & \texttt{Set()}\\                      
 \end{tabular}
 \end{center}
 
 \noindent
-All examples should be quite self-explanatory: the last two do not
-produce any result because our parser did not define what to do in
-case of division (could be easily added) but also has no idea what to
-do with whitescpaces. To deal with them is the task of the lexer. We
-can deal with them inside the grammar, but that would render many
-grammars becoming unintelligible.
+Note that we call \pcode{parse_all}, not \pcode{parse}.  The examples
+should be quite self-explanatory. The last two example do not produce
+any integer result because our parser does not define what to do in
+case of division (could be easily added), but also has no idea what to
+do with whitescpaces. To deal with them is the task of the lexer! Yes,
+we can deal with them inside the grammar, but that would render many
+grammars becoming unintelligible, including this one.\footnote{If you
+  think an easy solution is to extend the notion of what a number
+  should be, then think again---you still would have to deal with
+  cases like \texttt{\Grid{(\VS (\VS 2+3)\VS )}}. Jusat think you have
+  a grammar for a full-blown language where there are numerous such cases.}
 
 \end{document}
 




