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Beispiel für Wildcard Anwendung

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JanUlrich 2024-04-25 14:49:47 +02:00
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vortrag.tex
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@ -19,17 +19,37 @@
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\Delta \vdash \expr{v}, \ol{v} : [\ol{T'}/\ol{X}]\ol{T}
\Delta \vdash \ol{v} : [\ol{T'}/\ol{X}]\ol{T}
\\
\hline
\vspace*{-0.3cm}\\
\Delta \vdash \expr{v}.\generics{\ol{T'}}\texttt{m}(\ol{v}) : [\ol{T'}/\ol{X}]\type{T}
\Delta \vdash \generics{\ol{T'}}\texttt{m}(\ol{v}) : [\ol{T'}/\ol{X}]\type{T}
\end{array}
\end{array}$
\end{center}
\textbf{Example:}
$\generics{\type{String}}\texttt{emptyList}() : \exptype{List}{\type{String}}$
\\[2em]
\rulename{TI-Call} \\[1em]
\begin{center}
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
\Delta \vdash \expr{v}, \ol{v} : [\ol{T'}/\ol{X}]\ol{T}
\\
\hline
\vspace*{-0.3cm}\\
\Delta \vdash \expr{v}.\texttt{m}(\ol{v}) : [\ol{T'}/\ol{X}]\type{T}
\end{array}
\end{array}$
\end{center}
\textbf{Example:}
$\texttt{emptyList}() : \exptype{List}{\type{String}}$
\end{frame}
\begin{frame}[fragile]
\frametitle{Java Method Call}
\rulename{M-Class} \\[1em]
@ -89,7 +109,7 @@ $\begin{array}{l}
\generics{\type{String}}\texttt{head}(\texttt{new List<String>}()) : [\type{String}/\type{X}]\type{X}
\end{array}
\end{array}$
\pause
$\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{m}) = \generics{\ol{X}}\ \ol{T} \to \type{T} \quad \quad
@ -120,6 +140,43 @@ $
$
\end{frame}
\begin{frame}[fragile]
\frametitle{Java Method Call}
$
\begin{array}[b]{c}
\texttt{emptyList()} : \exptype{List}{\exptype{List}{\type{String}}} \\
\quad \textit{mtype}(\texttt{get}) = \generics{X}\ \exptype{List}{\type{X}} \to \type{X}
\\
\hline
\generics{\exptype{List}{\exptype{List}{\type{String}}}}\texttt{head(emptyList())} : \exptype{List}{\type{String}}
\end{array} \rulenameAfter{T-Call}
$
$
\begin{array}[b]{c}
\texttt{emptyList()} : \exptype{List}{\exptype{List}{\type{String}}} \\
\quad \textit{mtype}(\texttt{get}) = \generics{X}\ \exptype{List}{\type{X}} \to \type{X}
\\
\hline
\generics{\exptype{List}{\type{String}}}\texttt{head(emptyList())} : \exptype{List}{\type{String}}
\end{array} \rulenameAfter{T-Call}
$
\end{frame}
\begin{frame}[fragile]
\frametitle{Java Method Call}
$
\begin{array}[b]{c}
\texttt{emptyList()} : \exptype{List}{\exptype{List}{\type{String}}} \\
\quad \textit{mtype}(\texttt{get}) = \generics{X}\ \exptype{List}{\type{X}} \to \type{X}
\\
\hline
\generics{\exptype{List}{\type{String}}}\texttt{head(emptyList())} : \exptype{List}{\type{String}}
\end{array} \rulenameAfter{T-Call}
$
\end{frame}
\begin{frame}[fragile]
\frametitle{Java Method Call}
$
@ -147,4 +204,68 @@ Dieser muss ausgepackt werden.
Die entstehende freie Typvariable kann nun als Typ benutzt werden.
\end{frame}
\begin{frame}[fragile]
%Wildcard Capture
\begin{verbatim}
List<List<?>> l;
head(l) : List<?>
\end{verbatim}
%why do we need capture constraints?
% List<List<?>> not a subtype of List<List<X>> for any X
$\wctype{\rwildcard{A}}{List}{\rwildcard{A}}$
\end{frame}
\begin{frame}[fragile]
%Explain why ? cannot be used as a regular type
\begin{verbatim}
<X> List<X> concat(List<X> l1, List<X> l2){
return l1.addAll(l2);
}
List<?> l1;
List<?> l2;
concat(l1, l2); //Error
\end{verbatim}
\begin{verbatim}
List<String> ls = new List<String>();
List<?> l1 = ls; //korrekt!
List<?> l2 = new List<Integer>(1);
concat(l1, l2); //Error (würde l2 an ls anfügen!)
// ls.getLast() -> 1 (ein Int obwohl ls : List<String>)
\end{verbatim}
\end{frame}
\begin{frame}[fragile]
%Wildcard Capture
\begin{verbatim}
<X> void shuffle(List<List<X>> l){
//randomly exchange every element
// in the two dimensional list l
}
List<List<?>> l;
shuffle(l); // Error
\end{verbatim}
$\wctype{\rwildcard{A}}{List}{\rwildcard{A}}$
\end{frame}
% TODO:
% Folie zu aktueller Stand Unify: Es gibt <. Constraints. Unify löst diese
% Folie zu <? constraints: sie werden benötigt, weil unify während der Lösungsfindung Capture Conversion durchführen muss
%why do we need capture constraints?
% List<List<?>> not a subtype of List<List<X>> for any X
\end{document}