
diff -r 3c2653fc8b5a -r 53def1fbf472 handouts/ho06.tex
--- a/handouts/ho06.tex	Fri Nov 01 15:56:17 2013 +0000
+++ b/handouts/ho06.tex	Fri Nov 01 23:19:45 2013 +0000
@@ -300,18 +300,59 @@
 to implement and closely resemble grammar rules. Imagine that a grammar
 describes the strings of natural numbers, such as the grammar $N$ shown above.
 For all such strings we want to generate the parse-trees or later on we actually 
-want to extract the meaning of these strings, that is the integers ``behind'' these 
-strings. The parser will therefore be functions of type
+want to extract the meaning of these strings, that is the concrete integers ``behind'' 
+these strings. The parser combinators will be functions of type
 
 \begin{center}
-\texttt{I $\Rightarrow$ (T, I)}
+\texttt{I $\Rightarrow$ Set[(T, I)]}
 \end{center}
 
 \noindent 
-that is they take as input something of type \texttt{I}, typically a list of token or a string,
-and return a pair. 
+that is they take as input something of type \texttt{I}, typically a list of tokens or a string,
+and return a set of pairs. The first component of these pairs corresponds to what the
+parser combinator was able to process from the input and the second is the unprocessed 
+part of the input. As we shall see shortly, a parser combinator might return more than one such pair,
+with the idea that there are potentially several ways how to interpret the input.
+
+The abstract class for parser combinators requires the implementation of the function
+\texttt{parse} taking an argument of type \texttt{I} and returns a set of type  
+\mbox{\texttt{Set[(T, I)]}}.
+
+\begin{center}
+\begin{lstlisting}[language=Scala,basicstyle=\small\ttfamily, numbers=none]
+abstract class Parser[I, T] {
+  def parse(ts: I): Set[(T, I)]
+
+  def parse_all(ts: I): Set[T] =
+    for ((head, tail) <- parse(ts); if (tail.isEmpty)) 
+      yield head
+}
+\end{lstlisting}
+\end{center}
 
+\noindent
+One of the simplest parser combinators recognises just a character, say $c$, 
+from the beginning of strings. Its behaviour is as follows:
 
+\begin{itemize}
+\item if the head of the input string starts with a $c$, it returns 
+	the set $\{(c, \textit{tail of}\; s)\}$
+\item otherwise it returns the empty set $\varnothing$	
+\end{itemize}
+
+\noindent
+The input type of this simple parser combinator for characters is
+\texttt{String} and the output type \mbox{\texttt{Set[(Char, String)]}}. 
+The code in Scala is as follows:
+
+\begin{center}
+\begin{lstlisting}[language=Scala,basicstyle=\small\ttfamily, numbers=none]
+case class CharParser(c: Char) extends Parser[String, Char] {
+  def parse(sb: String) = 
+    if (sb.head == c) Set((c, sb.tail)) else Set()
+}
+\end{lstlisting}
+\end{center}
 
 
 \end{document}




