
diff -r 93bd75031ced -r 4df4404455d0 handouts/scala-ho.tex
--- a/handouts/scala-ho.tex	Thu Aug 21 15:10:53 2014 +0100
+++ b/handouts/scala-ho.tex	Sun Aug 24 10:49:21 2014 +0100
@@ -9,43 +9,51 @@
 \usepackage[scaled=.95]{helvet}
 
 \newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}%
-
+\definecolor{codegray}{gray}{0.9}
+\newcommand{\code}[1]{\colorbox{codegray}{\texttt{#1}}}
 
 \begin{document}
 
 \section*{A Crash-Course on Scala}
 
 Scala is programming language that combines functional and
-object-oriented programming-styles. This language received in
-the last five years quite a bit of attention. One reason is
-that, like the Java programming language, it compiles to the
-Java Virtual Machine (JVM) and therefore can run under MacOSX,
-Linux and Windows.\footnote{There are also experimental
-backends for Android and JavaScript.} The main compiler can be
+object-oriented programming-styles, and has received in the
+last five years quite a bit of attention. One reason for this
+attention is that, like the Java programming language, it
+compiles to the Java Virtual Machine (JVM) and therefore can
+run under MacOSX, Linux and Windows.\footnote{There are also
+experimental backends for Android and JavaScript.} Unlike
+Java, however, Scala often allows programmers to write concise
+and elegant code; some therefore say Scala is the much better
+Java. If you want to try it out, the Scala compiler can be
 downloaded from
 
 \begin{quote}
 \url{http://www.scala-lang.org}
 \end{quote}
 
-\noindent Why do I use Scala in this course? Actually, you can
-do any part of the programming coursework in \emph{any}
-programming language you like. I use Scale because its
-functional programming-style allows for some very small and
-elegant code. Since the compiler is free, you can download it
-and run every example I give. But if you prefer, you can also
-translate the examples into any other functional language, for
-example Haskell, ML, F\# and so on.
+Why do I use Scala in the AFL course? Actually, you can do
+\emph{any} part of the programming coursework in \emph{any}
+programming language you like. I use Scala for showing you
+code during the lectures because its functional
+programming-style allows me to implement some of the functions
+we will discuss with very small and elegant code. Since the
+compiler is free, you can download it and run every example I
+give. But if you prefer, you can also translate the examples
+into any other functional language, for example Haskell, ML,
+F\# and so on.
 
-Writing programs in Scala can be done with Eclipse IDE and
-also with IntelliJ, but I am using just the Emacs-editor and
-run programs on the command line. One advantage of Scala is
-that it has an interpreter (a REPL --- read-eval-print-loop)
-with which you can run and test small code-snippets without
-the need of the compiler. This helps a lot for interactively
+Writing programs in Scala can be done with the Eclipse IDE and
+also with IntelliJ, but for the small programs we will look at
+the Emacs-editor id good for me and I will run programs on the
+command line. One advantage of Scala over Java is that it
+includes an interpreter (a REPL, or Read-Eval-Print-Loop) with
+which you can run and test small code-snippets without the
+need of the compiler. This helps a lot for interactively
 developing programs. Once you installed Scala correctly, you
 can start the interpreter by typing
 
+
 \begin{alltt}
 $ scala\small
 Welcome to Scala version 2.11.2 (Java HotSpot(TM) 64-Bit Server VM).
@@ -55,18 +63,18 @@
 scala>
 \end{alltt}
 
-\noindent At the scala prompt you can type things like {\tt 2 + 3}
-\keys{Ret}. The output will be
+\noindent The precise output may vary due to the platform
+where you installed Scala. At the scala prompt you can type
+things like {\tt 2 + 3} \keys{Ret} and the output will be
 
 \begin{alltt}
 scala> 2 + 3
 res0: Int = 5
 \end{alltt}
 
-\noindent
-indicating that the result is of type {\tt Int} and the result 
-of the addition is {\tt 5}. Another example you can type in 
-immediately is
+\noindent indicating that the result of the addition is of
+type {\tt Int} and the actual result is {\tt 5}. Another
+example you can type in is
 
 \begin{alltt}
 scala> print ("hello world")
@@ -75,20 +83,21 @@
 
 \noindent which prints out a string. Note that in this case
 there is no result: the reason is that {\tt print} does not
-produce any result indicated by {\tt res\_}, rather it is a
-function that causes a \emph{side-effect} of printing out a
-string. Once you are more familiar with the functional
-programming-style, you will immediately see what the
-difference is between a function that returns a result and a
-function that causes a side-effect (the latter always has as
-return type {\tt Unit}).
+actually produce a result (there is no {\tt res\_}), rather it
+is a function that causes the \emph{side-effect} of printing
+out a string. Once you are more familiar with the functional
+programming-style, you will know what the difference is
+between a function that returns a result, like addition, and a
+function that causes a side-effect, like {\tt print}. We shall
+come back to this later, but if you are curious, the latter
+kind of functions always have as return type {\tt Unit}.
 
 \subsection*{Inductive Datatypes}
 
 The elegance and conciseness of Scala programs stems often
 from the fact that inductive datatypes can be easily defined.
-For example in ``Mathematics'' we would define regular 
-expressions by the grammar
+For example in ``every-day Mathematics'' we would define
+regular expressions simply by the grammar
 
 \begin{center}
 \begin{tabular}{r@{\hspace{2mm}}r@{\hspace{2mm}}l@{\hspace{13mm}}l}
@@ -103,284 +112,86 @@
 
 \noindent This grammar specifies what regular expressions are
 (essentially a kind of tree-structure with three kinds of
-inner nodes and three leave nodes). If you are familiar with
-Java, it might be an instructive exercise to define this
-kind of inductive datatypes in Java.
-
-Implementing the regular expressions from above in Scala
-requires an \emph{abstract class}, say, {\tt Rexp}. The
-different kinds of regular expressions will be instances of
-this abstract class. The cases for $\varnothing$ and
-$\epsilon$ do not require any arguments, while in the other
-cases we do have arguments. For example the character regular
-expressions need to take as argument the character they are
-supposed to recognise.
-
-. is a relative recen programming language
-This course is about the processing of strings. Lets start
-with what we mean by \emph{strings}. Strings (they are also
-sometimes referred to as \emph{words}) are lists of characters
-drawn from an \emph{alphabet}. If nothing else is specified,
-we usually assume the alphabet consists of just the lower-case
-letters $a$, $b$, \ldots, $z$. Sometimes, however, we
-explicitly restrict strings to contain, for example, only the
-letters $a$ and $b$. In this case we say the alphabet is the
-set $\{a, b\}$.
+inner nodes and three kinds of leave nodes). If you are
+familiar with Java, it might be an instructive exercise to
+define this kind of inductive datatypes in
+Java.\footnote{Happy programming! ;o)}
 
-There are many ways how we can write down strings. In programming languages, they are usually 
-written as {\it "hello"} where the double quotes indicate that we dealing with a string. 
-Essentially, strings are lists of characters which can be written for example as follows
-
-\[
-[\text{\it h, e, l, l, o}]
-\]
-
-\noindent
-The important point is that we can always decompose strings. For example, we will often consider the
-first character of a string, say $h$, and the ``rest''  of a string say {\it "ello"} when making definitions 
-about strings. There are some subtleties with the empty string, sometimes written as {\it ""} but also as 
-the empty list of characters $[\,]$. Two strings, for example $s_1$ and $s_2$, can be \emph{concatenated}, 
-which we write as $s_1 @ s_2$. Suppose we are given two strings {\it "foo"} and {\it "bar"}, then their concatenation
-gives {\it "foobar"}.
-
-We often need to talk about sets of strings. For example the set of all strings over the alphabet $\{a, \ldots\, z\}$
-is
-
-\[
-\{\text{\it "", "a", "b", "c",\ldots,"z", "aa", "ab", "ac", \ldots, "aaa", \ldots}\}
-\]
-
-\noindent
-Any set of strings, not just the set-of-all-strings, is often called a \emph{language}. The idea behind
-this choice of terminology is that if we enumerate, say, all words/strings from a dictionary, like 
+Implementing the regular expressions from above in Scala is
+very simple: It first requires an \emph{abstract class}, say,
+{\tt Rexp}. This will act as type for regular expressions.
+Second, it requires some instances. The cases for
+$\varnothing$ and $\epsilon$ do not have any arguments, while
+in the other cases we do have arguments. For example the
+character regular expression needs to take as an argument the
+character it is supposed to recognise. In Scala, the cases
+without arguments are called \emph{case objects}, while the
+ones with arguments are \emph{case classes}. The corresponding
+code is as follows:
 
-\[
-\{\text{\it "the", "of", "milk", "name", "antidisestablishmentarianism", \ldots}\}
-\]
-
-\noindent
-then we have essentially described the English language, or more precisely all
-strings that can be used in a sentence of the English language. French would be a
-different set of strings, and so on. In the context of this course, a language might 
-not necessarily make sense from a natural language point of view. For example
-the set of all strings shown above is a language, as is the empty set (of strings). The
-empty set of strings is often written as $\varnothing$ or $\{\,\}$. Note that there is a 
-difference between the empty set, or empty language, and the set that 
-contains only the empty string $\{\text{""}\}$: the former has no elements, whereas 
-the latter has one element.
-
-As seen, there are languages which contain infinitely many strings, like the set of all strings.
-The ``natural'' languages like English, French and so on contain many but only finitely many 
-strings (namely the ones listed in a good dictionary). It might be therefore be surprising that the
-language consisting of all email addresses is infinite provided we assume it is defined by the
-regular expression\footnote{See \url{http://goo.gl/5LoVX7}}
-
-\[
-([\text{\it{}a-z0-9\_.-}]^+)@([\text{\it a-z0-9.-}]^+).([\text{\it a-z.}]^{\{2,6\}})
-\]
+\begin{quote}
+\begin{lstlisting}[language=Scala]
+abstract class Rexp 
+case object NULL extends Rexp
+case object EMPTY extends Rexp
+case class CHAR (c: Char) extends Rexp
+case class SEQ (r1: Rexp, r2: Rexp) extends Rexp 
+case class ALT (r1: Rexp, r2: Rexp) extends Rexp 
+case class STAR (r: Rexp) extends Rexp 
+\end{lstlisting}
+\end{quote}
 
-\noindent
-One reason is that before the $@$-sign there can be any string you want assuming it 
-is made up from letters, digits, underscores, dots and hyphens---clearly there are infinitely many
-of those. Similarly the string after the $@$-sign can be any string. However, this does not mean 
-that every string is an email address. For example
-
-\[
-"\text{\it foo}@\text{\it bar}.\text{\it c}"
-\]
-
-\noindent
-is not, because the top-level-domains must be of length of at least two. (Note that there is
-the convention that uppercase letters are treated in email-addresses as if they were
-lower-case.)
-\bigskip
-
-Before we expand on the topic of regular expressions, let us review some operations on
-sets. We will use capital letters $A$, $B$, $\ldots$ to stand for sets of strings. 
-The union of two sets is written as usual as $A \cup B$. We also need to define the
-operation of \emph{concatenating} two sets of strings. This can be defined as
-
-\[
-A @ B \dn \{s_1@ s_2 | s_1 \in A \wedge s_2 \in B \}
-\]
-
-\noindent
-which essentially means take the first string from the set $A$ and concatenate it with every
-string in the set $B$, then take the second string from $A$ do the same and so on. You might
-like to think about what this definition means in case $A$ or $B$ is the empty set.
-
-We also need to define
-the power of a set of strings, written as $A^n$ with $n$ being a natural number. This is defined inductively as follows
+\noindent Given the grammar above, I hope you can see the
+underlying pattern. In order to be an instance of {\tt Rexp},
+each case object or case class needs to extend {\tt Rexp}. If
+you want to play with such definitions, feel free to define
+for example binary trees.
 
-\begin{center}
-\begin{tabular}{rcl}
-$A^0$ & $\dn$ & $\{[\,]\}$ \\
-$A^{n+1}$ & $\dn$ & $A @ A^n$\\
-\end{tabular}
-\end{center}
-
-\noindent
-Finally we need the \emph{star} of a set of strings, written $A^*$. This is defined as the union
-of every power of $A^n$ with $n\ge 0$. The mathematical notation for this operation is
-
-\[
-A^* \dn \bigcup_{0\le n} A^n
-\]
-
-\noindent
-This definition implies that the star of a set $A$ contains always the empty string (that is $A^0$), one 
-copy of every string in $A$ (that is $A^1$), two copies in $A$ (that is $A^2$) and so on. In case $A=\{"a"\}$ we therefore 
-have 
-
-\[
-A^* = \{"", "a", "aa", "aaa", \ldots\}
-\]
-
-\noindent
-Be aware that these operations sometimes have quite non-intuitive properties, for example
+Once you make a definition like the one above, you can 
+represent, say, the regular expression for $a + b$ as
+{\tt ALT(CHAR('a'), CHAR('b'))}. If you want to assign 
+this regular expression to a variable, you can just type
 
-\begin{center}
-\begin{tabular}{@{}ccc@{}}
-\begin{tabular}{@{}r@{\hspace{1mm}}c@{\hspace{1mm}}l}
-$A \cup \varnothing$ & $=$ & $A$\\
-$A \cup A$ & $=$ & $A$\\
-$A \cup B$ & $=$ & $B \cup A$\\
-\end{tabular} &
-\begin{tabular}{r@{\hspace{1mm}}c@{\hspace{1mm}}l}
-$A @ B$ & $\not =$ & $B @ A$\\
-$A  @ \varnothing$ & $=$ & $\varnothing @ A = \varnothing$\\
-$A  @ \{""\}$ & $=$ & $\{""\} @ A = A$\\
-\end{tabular} &
-\begin{tabular}{r@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
-$\varnothing^*$ & $=$ & $\{""\}$\\
-$\{""\}^*$ & $=$ & $\{""\}$\\
-$A^\star$ & $=$ & $\{""\} \cup A\cdot A^*$\\
-\end{tabular} 
-\end{tabular}
-\end{center}
-\bigskip
+\begin{alltt}
+scala> val r = ALT(CHAR('a'), CHAR('b'))
+r: ALT = ALT(CHAR(a),CHAR(b))
+\end{alltt}
 
-\noindent
-\emph{Regular expressions} are meant to conveniently describe languages...at least languages
-we are interested in in Computer Science.  For example there is no convenient regular expression
-for describing the English language short of enumerating all English words. 
-But they seem useful for describing all permitted email addresses, as seen above. 
+\noindent In order to make such assignments there is no
+constructor need in the class (like in Java). However, if
+there is the need, you can of course define such a constructor
+in Scala. 
 
-Regular expressions are given by the following grammar:
-
-\begin{center}
-\begin{tabular}{r@{\hspace{1mm}}r@{\hspace{1mm}}l@{\hspace{13mm}}l}
-  $r$ & $::=$ &   $\varnothing$         & null\\
-        & $\mid$ & $\epsilon$              & empty string / "" / []\\
-        & $\mid$ & $c$                         & single character\\
-        & $\mid$ & $r_1 \cdot r_2$      & sequence\\
-        & $\mid$ & $r_1 + r_2$            & alternative / choice\\
-        & $\mid$ & $r^*$                      & star (zero or more)\\
-  \end{tabular}
-\end{center}
-
-\noindent
-Because we overload our notation, there are some subtleties you should be aware of. First, the letter 
-$c$ stands for any character from the
-alphabet at hand. Second, we will use parentheses to disambiguate
-regular expressions. For example we will write $(r_1 + r_2)^*$, which is different from, say $r_1 + (r_2)^*$.
-The former means roughly zero or more times $r_1$ or $r_2$, while the latter means $r_1$ or zero or more times
-$r_2$. We should also write $(r_1 + r_2) + r_3$, which is different from the regular expression $r_1 + (r_2 + r_3)$,
-but in case of $+$ and $\cdot$ we actually do not care about the order and just write $r_1 + r_2 + r_3$, or $r_1 \cdot r_2 \cdot r_3$,
-respectively. The reasons for this will become clear shortly. In the literature you will often find that the choice
-$r_1 + r_2$  is written as $r_1\mid{}r_2$ or $r_1\mid\mid{}r_2$. Also following the convention in the literature, we will in case of $\cdot$ even 
-often omit it all together. For example the regular expression for email addresses shown above is meant to be of the form
+Note that Scala says the variable {\tt r} is of type {\tt
+ALT}, not {\tt Rexp}. Scala always tries to find the most
+general type that is needed for a variable, but does not
+``over-generalise''. In this case there is no need to give
+{\tt r} the more general type of {\tt Rexp}. This is different
+if you want to form a list of regular expressions, for example
 
-\[
-([\ldots])^+ \cdot @ \cdot ([\ldots])^+ \cdot . \cdot \ldots
-\]
-
-\noindent
-meaning first comes a name (specified by the regular expression $([\ldots])^+$), then an $@$-sign, then
-a domain name (specified by the regular expression $([\ldots])^+$), then a dot and then a top-level domain. Similarly if
-we want to specify the regular expression for the string {\it "hello"} we should write
-
-\[
-{\it h} \cdot {\it e} \cdot {\it l} \cdot {\it l} \cdot {\it o}
-\]
+\begin{alltt}
+scala> val ls = List(ALT(CHAR('a'), CHAR('b')), NULL)
+ls: List[Rexp] = List(ALT(CHAR(a),CHAR(b)), NULL)
+\end{alltt}
 
-\noindent
-but often just write {\it hello}.
-
-Another source of confusion might arise from the fact that we use the term \emph{regular expression} for the regular expressions used in ``theory''
-and also the ones used in ``practice''. In this course we refer by default to the regular expressions defined by the grammar above. 
-In ``practice'' we often use $r^+$ to stand for one or more times, $\backslash{}d$ to stand for a digit, $r^?$ to stand for an optional regular
-expression, or ranges such as $[\text{\it a - z}]$ to stand for any lower case letter from $a$ to $z$. They are however mere convenience 
-as they can be seen as shorthand for
+\noindent In this case Scala needs to assign a type to the
+regular expressions, so that it is compatible with the fact
+that list can only contain elements of a single type, in this
+case this is {\tt Rexp}.\footnote{If you type in this example,
+you will notice that the type contains some further
+information, but lets ignore this for the moment.} Note that if a type takes another
+type as argument, this is written for example as
+{\tt List[Rexp]}.
 
-\begin{center}
-\begin{tabular}{rcl}
-$r^+$ & $\mapsto$ & $r\cdot r^*$\\
-$r^?$ & $\mapsto$ & $\epsilon + r$\\
-$\backslash d$ & $\mapsto$ & $0 + 1 + 2 + \ldots + 9$\\
-$[\text{\it a - z}]$ & $\mapsto$ & $a + b + \ldots + z$\\
-\end{tabular}
-\end{center}
+\subsection*{Functions and Pattern-Matching}
 
 
-We will see later that the \emph{not}-regular-expression can also be seen as convenience. This regular
-expression is supposed to stand for every string \emph{not} matched by a regular expression. We will write
-such not-regular-expressions as $\sim{}r$. While being ``convenience'' it is often not so clear what the shorthand for
-these kind of not-regular-expressions is. Try to write down the regular expression which can match any
-string except the two strings {\it "hello"} and {\it "world"}. It is possible in principle, but often it is easier to just include
-$\sim{}r$ in the definition of regular expressions. Whenever we do so, we will state it explicitly.
 
-So far we have only considered informally what the \emph{meaning} of a regular expression is.  
-To do so more formally we will associate with every regular expression a set of strings 
-that is supposed to be matched by this
-regular expression. This can be defined recursively  as follows
-
-\begin{center}
-\begin{tabular}{rcl}
-$L(\varnothing)$  & $\dn$ & $\{\,\}$\\
-$L(\epsilon)$       & $\dn$ & $\{""\}$\\
-$L(c)$                  & $\dn$ & $\{"c"\}$\\
-$L(r_1+ r_2)$      & $\dn$ & $L(r_1) \cup L(r_2)$\\
-$L(r_1 \cdot r_2)$  & $\dn$ & $\{s_1@ s_2 | s_1 \in L(r_1) \wedge s_2 \in L(r_2) \}$\\
-$L(r^*)$                   & $\dn$ & $\bigcup_{n \ge 0} L(r)^n$\\
-\end{tabular}
-\end{center}
 
-\noindent
-As a result we can now precisely state what the meaning, for example, of the regular expression 
-${\it h} \cdot {\it e} \cdot {\it l} \cdot {\it l} \cdot {\it o}$ is, namely 
-$L({\it h} \cdot {\it e} \cdot {\it l} \cdot {\it l} \cdot {\it o}) = \{\text{\it"hello"}\}$...as expected. Similarly if we have the 
-choice-regular-expression $a + b$, its meaning is $L(a + b) = \{\text{\it"a"}, \text{\it"b"}\}$, namely the only two strings which can possibly
-be matched by this choice. You can now also see why we do not make a difference
-between the different regular expressions $(r_1 + r_2) + r_3$ and $r_1 + (r_2 + r_3)$....they 
-are not the same regular expression, but have the same meaning. 
-
-The point of the definition of $L$ is that we can use it to precisely specify when a string $s$ is matched by a
-regular expression $r$, namely only when $s \in L(r)$. In fact we will write a program {\it match} that takes any string $s$ and
-any regular expression $r$ as argument and returns \emph{yes}, if $s \in L(r)$ and \emph{no},
-if $s \not\in L(r)$. We leave this for the next lecture.
+\subsection*{Types}
 
-\begin{figure}[p]
-{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/crawler1.scala}}}
-\caption{Scala code for a web-crawler that can detect broken links in a web-page. It uses
-the regular expression {\tt http\_pattern} in Line~15 for recognising URL-addresses. It finds
-all links using the library function {\tt findAllIn} in Line~21.}
-\end{figure}
+\subsection*{Cool Stuff}
 
-\begin{figure}[p]
-{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/crawler2.scala}}}
-\caption{A version of the web-crawler which only follows links in ``my'' domain---since these are the
-ones I am interested in to fix. It uses the regular expression {\tt my\_urls} in Line~16.
-The main change is in Line~26 where there is a test whether URL is in ``my'' domain or not.}
-
-\end{figure}
-
-\begin{figure}[p]
-{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/crawler3.scala}}}
-\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 {\tt email\_pattern} in
-Line~17.  The main change is in Lines 33 and 34 where all email addresses that can be found in a page are printed.}
-\end{figure}
 
 \end{document}
 




