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\section*{A Crash-Course on Scala}

Scala is programming language that combines functional and
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}

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 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).
Type in expressions to have them evaluated.
Type :help for more information.\normalsize

scala>
\end{alltt}

\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 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")
hello world
\end{alltt}

\noindent which prints out a string. Note that in this case
there is no result: the reason is that {\tt print} does not
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 ``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}
  $r$ & $::=$ &   $\varnothing$         & 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 This grammar specifies what regular expressions are
(essentially a kind of tree-structure with three kinds of
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)}

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:

\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 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.

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{alltt}
scala> val r = ALT(CHAR('a'), CHAR('b'))
r: ALT = ALT(CHAR(a),CHAR(b))
\end{alltt}

\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. 

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

\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 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]}.

\subsection*{Functions and Pattern-Matching}




\subsection*{Types}

\subsection*{Cool Stuff}


\end{document}

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