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Start Wildcard Elimination Beispiel

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JanUlrich 2024-04-27 23:39:02 +02:00
parent 22a8f80484
commit e92d008a6c
1 changed files with 63 additions and 10 deletions
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vortrag.tex
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@ -22,9 +22,9 @@
}
\input{einstellungen_liste} % verfügbare Einstellungen
%\input{einstellungen} % lese Einstellungen
\setzetitel{Scala-like function types in Featherweight Java}
\setzeuntertitel{Bad Honnef 2022}
\setzedatum{2. Mai 2022}
\setzetitel{Typeinferenz für Java mit Wildcards}
\setzeuntertitel{Bad Honnef 2024}
\setzedatum{30. April 2024}
\setzestudiengang{Stuidengang Informatik}
\setzedhbw{DHBW Stuttgart Campus Horb}
\setzeinternetadresse{www.dhbw-stuttgart.de/horb}
@ -625,9 +625,9 @@ shuffle2D(l); // Fehler!
\begin{lstlisting}
(*@\only<2>{$\color{red}\tv{r}$ }@*)someList(){
if(Math.random > 0.5){
return new List<String>();
return new List("String");
} else {
return new List<Integer>();
return new List(42);
}
}
\end{lstlisting}
@ -642,10 +642,11 @@ $\\[1em]
\wildcardEnv \vdash C \cup \wctype{\Delta}{C}{\ol{T}} \lessdot \ntv{a}\\
\hline
\wildcardEnv \vdash C \cup \set{\wctype{\Delta}{C}{\ol{T}} \lessdot \ntv{a},
\ntv{a} \doteq \wctype{\overline{\rwildcard{X}}}{C}{\overline{\rwildcard{X}}}
\ntv{a} \doteq \wctype{\overline{\wildcard{A}{\tv{u}}{\tv{l}}}}{C}{\overline{\rwildcard{A}}}
}
\end{array} \quad \begin{array}[c]{l}
\texttt{class} \ \exptype{C}{\ol{X \triangleleft \type{S}}} \triangleleft \exptype{D}{\ol{N}} \\
\texttt{class} \ \exptype{C}{\ol{X}} \set{\ldots }\\%\triangleleft \exptype{D}{\ol{N}} \\
\tv{u}, \tv{l}\ \text{fresh}
\end{array}
$
\\[1em]
@ -653,19 +654,71 @@ $\\[1em]
$
\exptype{List}{String} \lessdot {\tv{r}},
\exptype{List}{Integer} \lessdot {\tv{r}},
\highlight{\tv{r} \doteq \wctype{\rwildcard{X}}{List}{\rwildcard{X}}}
\highlight{\tv{r} \doteq \wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}}
$
\pause
\\[0.5em]
\textbf{Substitution:}
$
\exptype{List}{String} \lessdot \highlight{\wctype{\rwildcard{X}}{List}{\rwildcard{X}}},
\exptype{List}{Integer} \lessdot \highlight{\wctype{\rwildcard{X}}{List}{\rwildcard{X}}},
\exptype{List}{String} \lessdot \highlight{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}},
\exptype{List}{Integer} \lessdot \highlight{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}}
$
\end{frame}
\begin{frame}[fragile]
$
\begin{array}{l}
\exptype{List}{String} \lessdot \highlight{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}},
\exptype{List}{Integer} \lessdot \highlight{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}}
\\
\hline
\type{String} \doteq \wtv{x1}, \type{Integer} \doteq \wtv{x2}
\end{array}
\rulenameAfter{Reduce}
$
\end{frame}
\begin{frame}[fragile]{Wildcard Elminiation}
\begin{lstlisting}
<X> List<X> concat(List<X> l1, List<X> l2){ ... }
someList(){
if(Math.random > 0.5){
return new List("String");
} else {
return new List(42);
}
}
concat(someList(), someList())
\end{lstlisting}
\only<1>{\textbf{Input}:}
$\only<2>{\highlight{\rulename{General}}}$
$\only<3>{\highlight{\rulename{Reduce}}}$
$
\begin{array}{l}
\exptype{List}{String} \lessdot {\tv{r}},
\exptype{List}{Integer} \lessdot {\tv{r}},
\tv{r} \lessdotCC \exptype{List}{\wtv{x}},
\tv{r} \lessdotCC \exptype{List}{\wtv{x}}
\pause
\\
\hline
\exptype{List}{String} \lessdot \only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}},
\exptype{List}{Integer} \lessdot \only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}},\\
\only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}} \lessdotCC \exptype{List}{\wtv{x}},
\only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}} \lessdotCC \exptype{List}{\wtv{x}}
\pause
\\
\hline
\highlight{\type{String} \doteq \wtv{x1}, \wtv{x1} \lessdot \tv{u}, \tv{l} \lessdot \wtv{x1},
\type{Integer} \doteq \wtv{x2}, \wtv{x2} \lessdot \tv{u}, \tv{l} \lessdot \wtv{x2}}, \\
\only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}} \lessdotCC \exptype{List}{\wtv{x}},
\only<2>{\highlight}{\wctype{\wildcard{X}{\tv{u}}{\tv{l}}}{List}{\rwildcard{X}}} \lessdotCC \exptype{List}{\wtv{x}}
\end{array}$
\end{frame}
% wieso dürfen normale Typvariablen keine freien Variablen enthalten?