89 shown below. I have in my implementation the convention that

    89 shown below. I have in my implementation the convention that

    90 regular expressions are written entirely with upper-case

    90 regular expressions are written entirely with upper-case

    91 letters, while values just start with a single upper-case

    91 letters, while values just start with a single upper-case

    92 character and the rest are lower-case letters.

    92 character and the rest are lower-case letters.

    93  

    93  

    95 {../progs/app01.scala}}

    96 {../progs/app01.scala}}

    96 

    97 

    97  

    98  

    99 {../progs/app02.scala}}

   101 {../progs/app02.scala}}

   100 

   102 

   101 

   103 

   102 Graphically the algorithm by Sulzmann \& Lu can be illustrated

   104 Graphically the algorithm by Sulzmann \& Lu can be illustrated

   103 by the picture in Figure~\ref{Sulz} where the path from the

   105 by the picture in Figure~\ref{Sulz} where the path from the

   578 \caption{The simplification function that returns a simplified 

   580 \caption{The simplification function that returns a simplified 

   579 regular expression and a rectification function.\label{simp}}

   581 regular expression and a rectification function.\label{simp}}

   580 \end{figure}

   582 \end{figure}

   581 

   583 

   582 \begin{figure}[p]

   584 \begin{figure}[p]

   584 

   588 

   585 \caption{The Scala code for the simplification function. The

   589 \caption{The Scala code for the simplification function. The

   586 first part defines some auxillary functions for the rectification.

   590 first part defines some auxillary functions for the rectification.

   587 The second part give the simplification function.

   591 The second part give the simplification function.

   588 \label{simprect}}

   592 \label{simprect}}

   637 $(x:r)$, where $x$ is just an identifier (in my implementation

   641 $(x:r)$, where $x$ is just an identifier (in my implementation

   638 a plain string) and $r$ is a regular expression. A record will

   642 a plain string) and $r$ is a regular expression. A record will

   639 be regarded as a regular expression. The extended definition

   643 be regarded as a regular expression. The extended definition

   640 in Scala therefore looks as follows:

   644 in Scala therefore looks as follows:

   641 

   645 

   643 {../progs/app03.scala}}

   648 {../progs/app03.scala}}

   644 

   649 

   645 \noindent Since we regard records as regular expressions we

   650 \noindent Since we regard records as regular expressions we

   646 need to extend the functions $\textit{nullable}$ and $\textit{der}$. Similarly

   651 need to extend the functions $\textit{nullable}$ and $\textit{der}$. Similarly

   647 $\textit{mkeps}$ and $\textit{inj}$ need to be extended. This means we also need

   652 $\textit{mkeps}$ and $\textit{inj}$ need to be extended. This means we also need

   648 to extend the definition of values, which in Scala looks as

   653 to extend the definition of values, which in Scala looks as

   649 follows:

   654 follows:

   650 

   655 

   652 {../progs/app04.scala}}

   658 {../progs/app04.scala}}

   653 

   659 

   654 \noindent Let us now look at the purpose of records more

   660 \noindent Let us now look at the purpose of records more

   655 closely and let us return to our question whether the string

   661 closely and let us return to our question whether the string

   656 terminated in a $b$ or $c$. We can do this as follows: we

   662 terminated in a $b$ or $c$. We can do this as follows: we