330 

   330 \subsection*{Background}

   331 \noindent

   331 

   332 \textbf{Background} Although easily implementable in Scala, the idea

   332 Although easily implementable in Scala, the idea behind the derivative

   333 behind the derivative function might not so easy to be seen. To

   333 function might not so easy to be seen. To understand its purpose

   334 understand its purpose better, assume a regular expression $r$ can

   334 better, assume a regular expression $r$ can match strings of the form

   335 match strings of the form $c::cs$ (that means strings which start with

   335 $c::cs$ (that means strings which start with a character $c$ and have

   336 a character $c$ and have some rest, or tail, $cs$). If you now take the

   336 some rest, or tail, $cs$). If you now take the derivative of $r$ with

   337 derivative of $r$ with respect to the character $c$, then you obtain a

   337 respect to the character $c$, then you obtain a regular expressions

   338 regular expressions that can match all the strings $cs$.  In other

   338 that can match all the strings $cs$.  In other words, the regular

   339 words, the regular expression $\textit{der}\;c\;r$ can match the same

   339 expression $\textit{der}\;c\;r$ can match the same strings $c::cs$

   340 strings $c::cs$ that can be matched by $r$, except that the $c$ is

   340 that can be matched by $r$, except that the $c$ is chopped off.

   341 chopped off.