Prolog_Loesungen.tex

\documentclass{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{amsmath,amssymb}
\usepackage{enumerate}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{wasysym}

\newcommand{\same}{$\stackrel{\eta,\beta}{=}$}
\renewcommand{\l}{$\lambda$}
\newcommand{\rep}{\pointer}

\begin{document}
\shorthandoff{"}
\lstset{language=Prolog}
\section*{Lösungen zu Prolog}
\subsection*{Aufgabe 1}
\begin{lstlisting}
% Aufgabe 1.1
evenLength([]).
evenLength([_|[_|Xs]]):-evenLength(Xs).

% Aufgabe 1.2
pow2Length([1]).
pow2Length(Xs):-Xs=[1|_],append(Ys,Ys,Xs),pow2Length(Ys).
\end{lstlisting}

\subsection*{Aufgabe 2}
\begin{enumerate}[1.]
\item $\sigma$ = [P \rep Q, Y \rep 1, Z \rep 7, W \rep [4], T \rep g(3,X)].
\item $\sigma$ = [P \rep g(Y,7), Z \rep [3,g(Y,7)], Q \rep 4].
\item $\sigma$ = [L \rep 1, X \rep g(1,1), Y \rep g(g(1,1),g(1,1)), Z \rep g(g(g(1,1),g(1,1)),g(g(1,1),g(1,1)))].
\end{enumerate}

\end{document}