198 should mean and do. While our language is rather simple and

   198 should mean and do. While our language is quite simple and the

   199 the meaning of statements, for example, is rather

   199 meaning of statements, for example, is rather straightforward,

   200 straightforward, there are still places where we need to make

   200 there are still places where we need to make real choices. For

   201 real choices. For example consider the conditional jumps, say

   201 example consider the conditional jumps, say the one in the

   202 the one in the factorial program: 

   202 factorial program: 

   228 programs we will transform programs into \emph{snippets}.

   228 programs we will transform programs into \emph{snippets}. A

   229 Their purpose is to simplify the definition of what the

   229 snippet is a label and all the code that comes after the

   230 interpreter should do in case of a jump. A snippet is a label

   230 label. This essentially means a snippet is a \emph{map} from

   231 and all the code that comes after the label. This essentially

   231 labels to code.\footnote{Be sure you know what maps are. In a

   232 means a snippet is a \emph{map} from labels to

   233 code.\footnote{Be sure you know what maps are. In a

   531 \noindent It is interesting to not that our interpreter when

   529 \noindent It is interesting to note that our interpreter when

   537 evaluation of the program)

   535 evaluation of the program and the CPU getting hot). Evaluating 

   538 

   536 the factorial program with our interpreter we receive as

   539 

   537 ``answer''-environment

   540 

   538 

   539 \begin{center}

   540 \begin{tabular}{ll}

   541 $\fbox{\texttt{a}} \mapsto \texttt{120}$ &

   542 $\fbox{\texttt{n}} \mapsto \texttt{0}$

   543 \end{tabular}

   544 \end{center}

   545 

   546 \noindent While the discussion above should have illustrated

   547 the ideas, in order to do some serious calculation we clearly

   548 need to implement the interpreter.

   549 

   550 

   551 \subsubsection*{Code of the Interpreter}

   552 

   553 Functional programming languages are very convenient for

   554 implementations of interpreters. A convenient choice for a

   555 functional programming language is Scala. This is a

   556 programming language that combines functional and

   557 object-oriented programming-styles. It has received in the

   558 last five years or so quite a bit of attention. One reason for

   559 this attention is that, like the Java programming language,

   560 Scala compiles to the Java Virtual Machine (JVM) and therefore

   561 Scala programs can run under MacOSX, Linux and

   562 Windows.\footnote{There are also experimental backends for

   563 Android and JavaScript.} Unlike Java, however, Scala often

   564 allows programmers to write very concise and elegant code.

   565 Some therefore say Scala is the much better Java. A number of

   566 companies, The Guardian, Twitter, Coursera, FourSquare,

   567 LinkedIn to name a few, either use Scala exclusively in

   568 production code, or at least to some substantial degree. If

   569 you want to try out Scala yourself, the Scala compiler can be

   570 downloaded from

   571 

   572 \begin{quote}

   573 \url{http://www.scala-lang.org}

   574 \end{quote}

   575 

   576 

   577 \begin{figure}[t]

   578 \small

   579 \lstinputlisting[language=Scala]{../progs/inter.scala}

   580 \caption{Bla}

   581 \end{figure}

   582 

   583 

   584 \subsubsection*{Static Analysis}

   585 

   586 Finally we can come back to our original problem, namely 

   587 finding out what the signs of variables are 

   588 

   589 \begin{center}

   590 

   591 

   592 \end{center}