Écourtage
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@ -27,6 +27,7 @@
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\usepackage{amsfonts}
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\usepackage{mathtools}
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\usepackage{setspace}
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\usepackage{pdfpc}
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\usepackage{geometry}
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\usepackage{subcaption}
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@ -203,7 +204,9 @@
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\author{Samy Avrillon}
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\title{Définition d'un préordre sur les programmes Featherweight Java}
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\subtitle{Notes sur mon stage au LACL}
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\logo{\includesvg[width=1.5cm]{logoEns}}
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\newif\ifplacelogo % create a new conditional
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\placelogotrue % set it to true
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\logo{\ifplacelogo\includesvg[width=1.5cm]{logoEns}\fi}
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\institute{ENS de Lyon}
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\begin{document}
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@ -242,7 +245,6 @@
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\end{center}
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\pause
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\[\fj{new Paire((D)new B().get(), new C(new A())).snd.apply()}\]
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\end{frame}
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\subsection{Ses structures}
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\begin{frame}
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@ -272,7 +274,7 @@
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\subsection{Son typage}
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\begin{frame}
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\pause
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\[\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{x} : \Gamma(\fj{x})}
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{\fj{x} \in \Gamma}
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@ -281,6 +283,7 @@
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{$e$.f} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{Cc} \quad \fj{C}\;\fj{f} \in \operatorname{fields}(\fj{Cc})}
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\]
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\pause
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\vspace{.2ex}
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\[
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\infer
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@ -487,29 +490,38 @@
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\end{frame}
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\subsection{Nouvelles applications de \eng{lookup}}
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\begin{frame}[plain]
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\placelogofalse
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\begin{frame}
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\ttfamily
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\vspace{-3ex}
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\pause
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\begin{center}
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\[
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\infer
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\onslide<2->{\infer
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{\operatorname{construct}(\fj{C}) = \overline{\fj{D}}}
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{\left[\fj{C($\overline{\texttt{D}}\;\overline{\texttt{?f}}$)}\right] \in \mathfrak{T}}
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{\left[\fj{C($\overline{\texttt{D}}\;\overline{\texttt{?f}}$)}\right] \in \mathfrak{T}}}
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\qquad
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\onslide<3->{
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\infer
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{\operatorname{fields}(\fj{C}) = \underbrace{\overline{\fj{D}}\;\overline{\fj{f}}}_{\text{\textrm{pour \fj{f} défini}}} + \bigcup_{C \subclass E}\operatorname{fields}(\fj{E})}
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{\left[\fj{ C ( $\overline{\texttt{D}}\;\overline{\texttt{f}}$)}\right] \in \mathfrak{T}}
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}
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\]
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\[
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\onslide<2->{
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\infer
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{\operatorname{construct}(\fj{C}) = \overline{\fj{D}}}
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{\fj{class C\{C($\overline{\texttt{D}}\;\overline{\texttt{f}}$)\{...\} ... \}}\in \mathcal{B}}
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}
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\quad
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\onslide<3->{
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\infer
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{\operatorname{fields}(\fj{C}) = \overline{\fj{D}}\;\overline{\fj{f}} + \bigcup_{C \subclass E}\operatorname{fields}(\fj{E})}
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{\left[\fj{ C \{ $\overline{\texttt{D}}\;\overline{\texttt{f}}$\}}\right] \in \mathfrak{T}}
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}
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\]
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\vspace{.2ex}
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\onslide<3->{
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\[
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\infer
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{\operatorname{fields}(\fj{C}) = \overline{\fj{D}}\;\overline{\fj{f}} + \bigcup_{C \subclass E}\operatorname{fields}(\fj{E})}
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@ -529,47 +541,50 @@
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{\operatorname{mtype}(\fj{m},\fj{C}) = \overline{\fj{D}}\rightarrow\fj{E}}
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{\operatorname{mtype}(\fj{m},\fj{C'}) = \overline{\fj{D}}\rightarrow\fj{E}\quad \fj{C} \subclass \fj{C'}}
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\]
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}
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\end{center}
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\end{frame}
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\subsection{Nouveau typage}
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\begin{frame}
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\begin{tcolorbox}
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\vspace{-1ex}
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{x} : \Gamma(\fj{x})}
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{\fj{x} \in \Gamma}
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\qquad
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{$e$.m($\overline{e_x}$)} : \fj{C}}
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{\begin{array}{c}\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{Cc} \quad \mathfrak{T},\mathcal{B},\Gamma \Vdash \overline{e_x} : \overline{\fj{CX}} \\ \overline{\fj{CX}} \subclass \overline{\fj{D}} \quad \operatorname{mtype}(\fj{m},\fj{Cc}) = \overline{\fj{D}} \rightarrow \fj{C} \end{array}}
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\]
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{new C(}\overline{e_x}\fj{)} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \overline{e_x} : \overline{\fj{CX}} \quad \overline{\fj{CX}} \subclass \overline{\fj{D}} \quad \operatorname{constructor}(\fj{C}) = \overline{\fj{D}}}
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\]
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\vspace{.3ex}
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{$e$.f} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{Cc} \quad \fj{C}\;\fj{f} \in \operatorname{fields}(\fj{Cc})}
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\]
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\vspace{.3ex}
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{(C)$e$} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{D} \quad \fj{C} \subclass \fj{D} \quad \fj{C} \neq \fj{D}}
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\qquad
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{(C)$e$} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{D} \quad \fj{D} \subclass \fj{C}}
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\]
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\end{tcolorbox}
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\vspace{-2ex}
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\pause
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{x} : \Gamma(\fj{x})}
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{\fj{x} \in \Gamma}
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\qquad
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{$e$.m($\overline{e_x}$)} : \fj{C}}
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{\begin{array}{c}\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{Cc} \quad \mathfrak{T},\mathcal{B},\Gamma \Vdash \overline{e_x} : \overline{\fj{CX}} \\ \overline{\fj{CX}} \subclass \overline{\fj{D}} \quad \operatorname{mtype}(\fj{m},\fj{Cc}) = \overline{\fj{D}} \rightarrow \fj{C} \end{array}}
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\]
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\pause
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{new C(}\overline{e_x}\fj{)} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \overline{e_x} : \overline{\fj{CX}} \quad \overline{\fj{CX}} \subclass \overline{\fj{D}} \quad \operatorname{constructor}(\fj{C}) = \overline{\fj{D}}}
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\]
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\vspace{.3ex}
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{$e$.f} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{Cc} \quad \fj{C}\;\fj{f} \in \operatorname{fields}(\fj{Cc})}
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\]
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\vspace{.3ex}
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\[
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{(C)$e$} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{D} \quad \fj{C} \subclass \fj{D} \quad \fj{C} \neq \fj{D}}
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\qquad
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\infer
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash \fj{(C)$e$} : \fj{C}}
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{\mathfrak{T},\mathcal{B},\Gamma \Vdash e : \fj{D} \quad \fj{D} \subclass \fj{C}}
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\]
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\end{frame}
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\placelogotrue
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\subsection{Théorème de cohérence}
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\begin{frame}
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\pause
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\begin{theorem}
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\label{thm:tiTyp}
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Soit une \eng{test interface} $\mathfrak{T}$, une \eng{class table} $\mathcal{A}$, un couple $(\mathcal{B},e)$ \eng{class table} $\times$ expression fermée appelée \enquote{test}, et un environnement de typage $\Gamma$ vérifiant
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@ -585,6 +600,7 @@
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\subsection{Définition du préordre}
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\begin{frame}
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\pause
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\begin{definition}
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Soit une \eng{test interface} $\mathfrak{T}$.
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@ -596,8 +612,6 @@
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\mathfrak{T},\mathcal{B} \Vdash e : \fj{D}\\
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\mathcal{A}\oplus\mathcal{B} \Downarrow v
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\end{array}\right. \implies \mathcal{A'}\oplus\mathcal{B}\Downarrow v\]
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où $\mathcal{A} \oplus \mathcal{B}$ dénote l'ensemble des classes de $\mathcal{A}$ auquel on a ajouté les classes de $\mathcal{B}$ dont les noms n'étaient pas déjà dans $\mathcal{A}$.
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\end{definition}
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\end{frame}
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@ -606,10 +620,12 @@
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\subsection{Qu'est-ce qu'un context lemma}
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\begin{frame}
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\pause
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\[(\mathcal{A},e)\prec(\mathcal{B},f) \implies (\mathcal{A},h\bracket{e})\prec(\mathcal{A},h\bracket{f})\]
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\end{frame}
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\subsection{Pourquoi est-il faux ici}
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\placelogofalse
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\begin{frame}
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\begin{fjlisting}
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public Static \{\\
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@ -617,8 +633,13 @@
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\fjmethod{IList}{zeroList}{}{new IList(0, zeroList())}
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\}
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\end{fjlisting}
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\[e_i = \fj{intList(0)} \quad\text{et}\quad e_0 = \fj{zeroList()}\]
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\vspace{-3ex}
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\begin{gather*}
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e_i = \fj{intList(0)} \rightarrow^*\\ \fj{new IList(0,new IList(1,new IList(2,intList(3))))}\\
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e_0 = \fj{zeroList()} \rightarrow^*\\ \fj{new IList(0,new IList(0,new IList(0,zeroList())))}
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\end{gather*}
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\end{frame}
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\placelogotrue
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\begin{frame}
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\[
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\begin{array}{rcl}
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@ -641,9 +662,23 @@
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\subsection{Explication de la formalisation}
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\begin{frame}
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\textsc{E-Var} et \textsc{E-Cstr}
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\[\fj{new C(x,new S(new S(y,new G()),z))}\]
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\[(\mathcal{A},e)\pprec(\mathcal{B},f) \ssi \forall \hbar \forall \alpha \quad \left(e \rightarrow_\mathcal{A}^* \hbar\bracket{\alpha} \implies \exists \beta\quad f \rightarrow_\mathcal{B}^* \hbar\bracket{\beta}\right)\]
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\begin{center}
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Comment capturer ces \enquote{valeurs infinies} ?
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\vspace{1ex}
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\pause
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Valeurs à variable: $\hbar$
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\[\fj{new C(x,new S(new S(y,new G()),z))}\]
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\pause
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\[\boxed{e\rightarrow^* v \implies f\rightarrow^* v}\Rrightarrow \boxed{\forall \hbar \forall \alpha \; \left(e \rightarrow_\mathcal{A}^* \hbar\bracket{\alpha} \implies \exists \beta\quad f \rightarrow_\mathcal{B}^* \hbar\bracket{\beta}\right)}\]
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\pause
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\[e \rightarrow^* \fj{new C(new D(...))} \implies f \rightarrow^* \fj{new C(new D(...))}\]
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\begin{gather*}
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\fj{new IList(0,new IList(1,...))}\\
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\neq\\
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\fj{new IList(0,new IList(0,...))}
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\end{gather*}
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\end{center}
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\end{frame}
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\subsection{Redéfinition des préordres}
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@ -652,14 +687,15 @@
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\end{frame}
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\subsection{Propriétés}
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\begin{frame}
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\pause
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\begin{property}
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\[\forall \hbar \forall \alpha \quad \hbar\bracket{\alpha}\rightarrow^* e' \implies \exists \beta\quad e' = \hbar\bracket{\beta}\]
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\end{property}
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\pause
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\begin{property}
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\[\mathcal{A} \pprec \mathcal{B} \implies \mathcal{A} \prec \mathcal{B}\]
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\end{property}
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\pause
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\begin{property}[Context Lemma]
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\begin{gather*}
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\forall \mathcal{A} \quad\forall e,f \quad\forall (h,\mathcal{B})\\
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@ -667,35 +703,30 @@
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\end{gather*}
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\end{property}
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\end{frame}
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\section{Exemple concret}
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\begin{frame}
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\begin{tcolorbox}
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\lstinputlisting[language=Java,breaklines=true,linerange={2-26}]{FinalExample.java}
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\lstinputlisting[language=Java,breaklines=true,linerange={29-62}, texcl]{FinalExample.java}
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\lstinputlisting[language=FeatherweightJava,breaklines=true,linerange={65-78}]{FinalExample.java}
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\end{tcolorbox}
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\end{frame}
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\section{Conclusion}
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\subsection{Conclusion}
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\begin{frame}
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\begin{tcolorbox}
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\begin{itemize}
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\begin{exampleblock}{Résumé}
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\begin{itemize}[<+->]
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\item On a créé un préordre
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\item Assez puissant (sémantique)
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\item Assez tolérant
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\item Context Lemma
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\item Utilisable autre part
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\item Concepts réutilisables
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\end{itemize}
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\end{tcolorbox}
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\begin{tcolorbox}
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\begin{itemize}
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\end{exampleblock}
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\begin{exampleblock}{Futur}
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\begin{itemize}[<+->]
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\item Formalisation dans un assistant de preuve
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\item Comparer uniquement certains types de retour
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\item Théorèmes pour simplifier l'équivalence
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\item Obtenir des retours
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\end{itemize}
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\end{tcolorbox}
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\end{exampleblock}
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\end{frame}
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\begin{frame}
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\LARGE\[\mathfrak{FIN}\]
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\Huge\[\mathfrak{FIN}\]
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\end{frame}
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\end{document}
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