| changeset 246 | baf41b05210f |
| parent 242 | 35104ee14f87 |
| child 266 | ae039d6ae3f2 |
| 245:a5fade10c207 | 246:baf41b05210f |
|---|---|
104 |
104 |
105 Occasionally we will use the notation $a^n$ for strings, which |
105 Occasionally we will use the notation $a^n$ for strings, which |
106 stands for the string of $n$ repeated $a$s. So $a^{n}b^{n}$ is |
106 stands for the string of $n$ repeated $a$s. So $a^{n}b^{n}$ is |
107 a string that has as many $a$s as $b$s. |
107 a string that has as many $a$s as $b$s. |
108 |
108 |
109 While for us strings are just lists of characters, programming |
109 Note however that while for us strings are just lists of |
110 languages often differentiate between the two concepts. In |
110 characters, programming languages often differentiate between |
111 Scala, for example, there is the type of \code{String} and the |
111 the two concepts. In Scala, for example, there is the type of |
112 type of lists of characters, \code{List[Char]}. They are not |
112 \code{String} and the type of lists of characters, |
113 the same and we need to explicitly coerce elements between the |
113 \code{List[Char]}. They are not the same and we need to |
114 two types, for example |
114 explicitly coerce elements between the two types, for example |
115 |
115 |
116 \begin{lstlisting}[numbers=none] |
116 \begin{lstlisting}[numbers=none] |
117 scala> "abc".toList |
117 scala> "abc".toList |
118 res01: List[Char] = List(a, b, c) |
118 res01: List[Char] = List(a, b, c) |
119 \end{lstlisting} |
119 \end{lstlisting} |
282 this alphabet $\Sigma^*$. In doing so we also include the |
282 this alphabet $\Sigma^*$. In doing so we also include the |
283 empty string as a possible string over $\Sigma$. So if |
283 empty string as a possible string over $\Sigma$. So if |
284 $\Sigma = \{a, b\}$, then $\Sigma^*$ is |
284 $\Sigma = \{a, b\}$, then $\Sigma^*$ is |
285 |
285 |
286 \[ |
286 \[ |
287 \{[], a, b, ab, ba, aaa, aab, aba, abb, baa, bab, \ldots\} |
287 \{[], a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, \ldots\} |
288 \] |
288 \] |
289 |
289 |
290 \noindent or in other words all strings containing $a$s and |
290 \noindent or in other words all strings containing $a$s and |
291 $b$s only. |
291 $b$s only, plus the empty string. |
292 |
292 |
293 \end{document} |
293 \end{document} |
294 |
294 |
295 %%% Local Variables: |
295 %%% Local Variables: |
296 %%% mode: latex |
296 %%% mode: latex |