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Intro Wildcards

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Andreas Stadelmeier 2024-05-07 16:14:48 +02:00
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introduction.tex
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@ -293,19 +293,50 @@ List<?> genList() {
\subsection{Java Wildcards} \subsection{Java Wildcards}
Java has invariant subtyping for polymorphic types Java has invariant subtyping for polymorphic types.
and incooperates use-site variance via so called wildcard types. %but it incooperates use-site variance via so called wildcard types.
A \texttt{List<String>} is not a subtype of \texttt{List<Object>} A \texttt{List<String>} is not a subtype of \texttt{List<Object>}
even though it seems intuitive with \texttt{String} being a subtype of \texttt{Object}. even though it seems intuitive with \texttt{String} being a subtype of \texttt{Object}.
To make the type system more expressive Java incooperates use-site variance by allowing wildcards (\texttt{?}) in type annotations.
For example a type \texttt{List<?>} (short for \texttt{List<? extends Object>}, with \texttt{?} being a placeholder for any type) %with the wildcard \texttt{?} representing a placeholder for any type
is a supertype of \texttt{List<String>} and \texttt{List<Object>}.
%The \texttt{?} is a wildcard type which can be replaced by any type as needed.
%Class instances in Java are mutable and passed by reference. %Class instances in Java are mutable and passed by reference.
Subtyping must be invariant otherwise the integrity of data classes like lists could be Subtyping must be invariant in Java otherwise the integrity of data classes like \texttt{List} could be cannot be guaranteed.
corrupted like shown in listing \ref{lst:invarianceExample}, See listing \ref{lst:invarianceExample} for example,
where an \texttt{Integer} is added to a list of \texttt{String}. where an \texttt{Integer} would be added to a list of \texttt{String}
In listing \ref{lst:invarianceExample} the assignment \texttt{lo = ls} is not semantically correct if not for the Java type system which rejects the assignment \texttt{lo = ls}.
and rejected by Java's type system. Listing \ref{lst:wildcardIntro} shows the use of wildcards rendering the assignment \texttt{lo = ls} correct.
Listing \ref{lst:wildcardIntro} shows the use of wildcards in the type The program still does not compile, because now the addition of an Integer to \texttt{lo} is rightfully deemed incorrect by Java.
\texttt{List<? extends Object>} which is a supertype of \texttt{List<String>}
rendering the assignment \texttt{lo = ls} correct. This behaviour is emulated by our language \TamedFJ{}.
A Featherweight Java \cite{FJ} derivative with added wildcard support
and a global type inference feature.
\TamedFJ{} is basically the language described by \textit{Bierhoff} \cite{WildcardsNeedWitnessProtection} with optional type annotations.
The \texttt{add} call in listing \ref{lst:wildcardIntro} needs to be encased by a \texttt{let} statement in our calculus.
This makes the capture converion explicit.
\begin{lstlisting}
let v : (*@$\wctype{\wildcard{A}{\type{Object}}{\bot}}{List}{\rwildcard{A}}$@*) = lo in v.<A>add(new Integer(1));
\end{lstlisting}
\begin{displaymath}
\begin{array}{l}
\begin{array}{@{}c}
\textit{mtype}(\texttt{concat}) = \generics{\type{X}}\ \exptype{List}{\type{X}} \to \exptype{List}{\type{X}} \to \exptype{List}{\type{X}} \\
\texttt{l1} : \wctype{\rwildcard{A}}{List}{\rwildcard{A}}, \texttt{l2} : \wctype{\rwildcard{B}}{List}{\rwildcard{B}} \\
\exptype{List}{\rwildcard{A}} \nless: [{\color{red}?}/\type{X}]\exptype{List}{\type{X}} \quad \quad
\exptype{List}{\rwildcard{B}} \nless: [{\color{red}?}/\type{X}]\exptype{List}{\type{X}}
\\
\hline
\vspace*{-0.3cm}\\
\texttt{concat}(\expr{l1}, \expr{l2}) : {\color{red}\textbf{Error}}
\end{array}
\end{array}
\end{displaymath}
\begin{figure} \begin{figure}
\begin{minipage}{0.4\textwidth} \begin{minipage}{0.4\textwidth}