64 lines
1.9 KiB
TeX
64 lines
1.9 KiB
TeX
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\documentclass[11pt,a4paper]{scrartcl}
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\usepackage[a4paper,left=1.5cm,right=3.0cm,top=2.5cm,bottom=2.5cm]{geometry}
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\usepackage[ngerman]{babel}
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\usepackage{amssymb}
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\usepackage{amsthm}
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\usepackage{mathrsfs}
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\usepackage{scrextend}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath}
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\usepackage{enumitem}
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\usepackage{tikz-qtree}
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\usepackage{mathtools}
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\usepackage{latexsym}
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\usepackage{algorithmicx}
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\usepackage{csquotes}
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\usepackage{pdfpages}
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\usepackage{pgfplots}
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\usepackage{hyperref}
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\usepackage{tikz}
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\usetikzlibrary{positioning}
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\usetikzlibrary{arrows.meta}
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\newcommand{\siehe}[1]{\marginpar{\footnotesize \textit{#1}}}
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\newcommand{\app}{\ensuremath{\rightarrow_a}}
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\newcommand{\norm}{\ensuremath{\rightarrow_n}}
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\theoremstyle{definition}
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\newtheorem{definition}{Definition}[section]
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\title{Merkzettel für \enquote{Theorie der Programmierung}}
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\author{Marco Ammon}
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\date{\today}
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\begin{document}
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\maketitle
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\section*{Termersetzungssysteme}
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\subsection*{Terminierung}
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\subsubsection*{Polynomordnungen}
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\subsection*{Konfluenz}
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\subsection*{Critical Pairs}
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\section*{$\lambda$-Kalkül}
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\subsection*{Ungetypt}
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\subsubsection*{Rekursion}
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\subsubsection*{Auswertungsstrategien}
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\begin{itemize}
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\item applikativ (\textit{leftmost-innermost}) \app
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\begin{itemize}
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\item $\lambda x.t \app \lambda x.t'$, wenn $t \app t'$
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\item $ts \app t's$, wenn $t \app t'$
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\item $ts \app ts'$, wenn $s\app s'$ und $t$ normal ist
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\item $(\lambda x.t)s \app t\lbrack s/x\rbrack$, wenn $t$ und $s$ normal sind
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\end{itemize}
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\item normal (\textit{leftmost-outermost}) \norm
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\begin{itemize}
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\item $(\lambda x.t) s \norm t\lbrack s/x\rbrack$
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\item $\lambda x.t \norm \lambda x.t'$, wenn $t\norm t'$
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\item $ts \norm t's$m wenn $t\norm t'$ und $t$ keine $\lambda$-Abstraktion ist
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\item $ts \norm ts'$, wenn $s\norm s'$ und $t$ normal und keine $\lambda$-Abstraktion ist
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\end{itemize}
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\end{itemize}
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\subsection*{Getypt}
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\end{document}
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