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Symbolverzeichnis verschönert

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Martin Thoma 2014-03-20 15:18:50 +01:00
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documents/Programmierparadigmen/Symbolverzeichnis.tex
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@ -6,29 +6,45 @@
% Reguläre Ausdrücke %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Reguläre Ausdrücke}
$\emptyset\;\;\;$ Leere Menge\\
$\epsilon\;\;\;$ Das leere Wort\\
$\alpha, \beta\;\;\;$ Reguläre Ausdrücke\\
$L(\alpha)\;\;\;$ Die durch $\alpha$ beschriebene Sprache\\
$\begin{aligned}[t]
L(\alpha | \beta) &= L(\alpha) \cup L(\beta)\\
L(\alpha \cdot \beta)&= L(\alpha) \cdot L(\beta)
\end{aligned}$\\
$L^0 := \Set{\varepsilon}\;\;\;$ Die leere Sprache\\
$L^{n+1} := L^n \circ L \text{ für } n \in \mdn_0\;\;\;$ Potenz einer Sprache\\
$\begin{aligned}[t]
\alpha^+ &=& L(\alpha)^+ &=& \bigcup_{i \in \mdn} L(\alpha)^i\\
\alpha^* &=& L(\alpha)^* &=& \bigcup_{i \in \mdn_0} L(\alpha)^i
\end{aligned}$
% Set \mylengtha to widest element in first column; adjust
% \mylengthb so that the width of the table is \columnwidth
\settowidth\mylengtha{$\alpha^+ = L(\alpha)^+$}
\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}
\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}
$\emptyset$ & Leere Menge\\
$\epsilon$ & Das leere Wort\\
$\alpha, \beta$ & Reguläre Ausdrücke\\
$L(\alpha)$ & Die durch $\alpha$ beschriebene Sprache\\
$L(\alpha | \beta)$& $L(\alpha) \cup L(\beta)$\\
$L^0$ & Die leere Sprache, also $\Set{\varepsilon}$\\
$L^{n+1}$ & Potenz einer Sprache. Diese ist definiert als\newline $L^n \circ L \text{ für } n \in \mdn_0$\\
$\alpha^+ = L(\alpha)^+$ & $\bigcup_{i \in \mdn} L(\alpha)^i$\\
$\alpha^* = L(\alpha)^*$ & $\bigcup_{i \in \mdn_0} L(\alpha)^i$\\
\end{xtabular}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Logik %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Logik}
$\mathcal{M} \models \varphi\;\;\;$ Im Modell $\mathcal{M}$ gilt das Prädikat $\varphi$.\\
$\psi \vdash \varphi\;\;\;$ Die Formel $\varphi$ kann aus der Menge der Formeln $\psi$ hergeleitet werden.\\
\settowidth\mylengtha{$\mathcal{M} \models \varphi$}
\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}
\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}
$\mathcal{M} \models \varphi$& Im Modell $\mathcal{M}$ gilt das Prädikat $\varphi$.\\
$\psi \vdash \varphi$ & Die Formel $\varphi$ kann aus der Menge der Formeln $\psi$ hergeleitet werden.\\
\end{xtabular}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Weiteres %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Weiteres}
$\bot\;\;\;$ Bottom\\
\settowidth\mylengtha{$\bot$}
\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}
\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}
$\bot$ & Bottom\\
$\vdash$& TODO?
\end{xtabular}