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List/head Beispiel

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Andreas Stadelmeier 2024-04-24 17:45:14 +02:00
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vortrag.tex
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@ -19,11 +19,11 @@
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\Delta \vdash \expr{v}, \ol{v} : \ol{T}
\Delta \vdash \expr{v}, \ol{v} : [\ol{T'}/\ol{X}]\ol{T}
\\
\hline
\vspace*{-0.3cm}\\
\Delta \vdash \expr{v}.\texttt{m}(\ol{v}) : \type{T}
\Delta \vdash \expr{v}.\generics{\ol{T'}}\texttt{m}(\ol{v}) : [\ol{T'}/\ol{X}]\type{T}
\end{array}
\end{array}$
\end{center}
@ -45,17 +45,61 @@ $\begin{array}{l}
\end{array}$
\end{center}
\textbf{Beispiele:}\\
\begin{verbatim}
X head(List<X> l) { ... }
\end{verbatim}
\begin{itemize}
\item
$\textit{mtype}(\texttt{head}) = \generics{\type{X}}\ \exptype{List}{\type{X}} \to \type{X}$
\end{itemize}
\begin{verbatim}
<X> List<X> emptyList() { ... }
\end{verbatim}
$\textit{mtype}(\texttt{head}) = \generics{\type{X}}\ \exptype{List}{\type{X}} \to \type{X}$
\begin{itemize}
\item
$\textit{mtype}(\texttt{emptyList}) = \generics{\type{X}}\ [] \to \exptype{List}{\type{X}}$
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Java Method Call}
\rulename{T-Call} \\[1em]
\begin{center}
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\Delta \vdash \expr{v}, \ol{v} : [\ol{T'}/\ol{X}]\ol{T}
\\
\hline
\vspace*{-0.3cm}\\
\Delta \vdash \expr{v}.\generics{\ol{T'}}\texttt{m}(\ol{v}) : [\ol{T'}/\ol{X}]\type{T}
\end{array}
\end{array}$
\end{center}
\textbf{Beispiel:}\\
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\texttt{new List<String>}() : [\type{String}/\type{X}]\exptype{List}{\type{X}}
\\
\hline
\vspace*{-0.3cm}\\
\generics{\type{String}}\texttt{head}(\texttt{new List<String>}()) : [\type{String}/\type{X}]\type{X}
\end{array}
\end{array}$
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\texttt{new List<String>}() : \exptype{List}{\type{String}}
\\
\hline
\vspace*{-0.3cm}\\
\generics{\type{String}}\texttt{head}(\texttt{new List<String>}()) : \type{String}
\end{array}
\end{array}$
\end{frame}
\begin{frame}[fragile]