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%!TEX root = Programmierparadigmen.tex

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\markboth{Symbolverzeichnis}{Symbolverzeichnis}

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\chapter*{Symbolverzeichnis}

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\addcontentsline{toc}{chapter}{Symbolverzeichnis}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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% Reguläre Ausdrücke                                                %

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\section*{Reguläre Ausdrücke}

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% Set \mylengtha to widest element in first column; adjust

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% \mylengthb so that the width of the table is \columnwidth

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\settowidth\mylengtha{$\alpha^+ = L(\alpha)^+$}

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\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}

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\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}

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 $\emptyset$        & Leere Menge\\

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 $\epsilon$         & Das leere Wort\\

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 $\alpha, \beta$    & Reguläre Ausdrücke\\

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 $L(\alpha)$        & Die durch $\alpha$ beschriebene Sprache\\

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 $L(\alpha | \beta)$& $L(\alpha) \cup L(\beta)$\\

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 $L^0$              & Die leere Sprache, also $\Set{\varepsilon}$\\

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 $L^{n+1}$          & Potenz einer Sprache. Diese ist definiert als\newline $L^n \circ L \text{ für } n \in \mdn_0$\\

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 $\alpha^+ = L(\alpha)^+$ & $\bigcup_{i \in \mdn} L(\alpha)^i$\\

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 $\alpha^* = L(\alpha)^*$ & $\bigcup_{i \in \mdn_0} L(\alpha)^i$\\

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\end{xtabular}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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% Logik                                                             %

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\section*{Logik}

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\settowidth\mylengtha{$\mathcal{M} \models \varphi$}

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\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}

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\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}

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$\mathcal{M} \models \varphi$& Semantische Herleitbarkeit\newline Im Modell $\mathcal{M}$ gilt das Prädikat $\varphi$.\\

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$\psi \vdash \varphi$        & Syntaktische Herleitbarkeit\newline Die Formel $\varphi$ kann aus der Menge der Formeln $\psi$ hergeleitet werden.\\

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\end{xtabular}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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% Typinferenz                                                       %

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\section*{Typinferenz}

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\settowidth\mylengtha{$\tau \succeq \tau'$}

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\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}

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\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}

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$\Gamma \vdash t: \tau$   & Im Typkontext $\Gamma$ hat der Term $t$ den Typ $\tau$\\

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$a \Parr b$  & $a$ wird zu $b$ unifiziert\\

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$\tau \succeq \tau'$& $\tau$ wird durch $\tau'$ instanziiert\\\

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\end{xtabular}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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% Weiteres                                                          %

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\section*{Weiteres}

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\settowidth\mylengtha{$\tau \succeq \tau'$}

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\setlength\mylengthb{\dimexpr\columnwidth-\mylengtha-2\tabcolsep\relax}

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\begin{xtabular}{@{} p{\mylengtha} P{\mylengthb} @{}}

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$\bot$   & Bottom\\

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$a \Parr b$  & $a$ wird zu $b$ unifiziert\\

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$\tau \succeq \tau'$& $\tau$ wird durch $\tau'$ instanziiert\\\

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\end{xtabular}

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