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Ajout slide fiabilité

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augustin64 2024-05-16 12:47:52 +02:00
parent b26ea09640
commit 17f989e97f
1 changed files with 30 additions and 8 deletions
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38
RapportPresentation/ex-presentation.tex
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@ -4,7 +4,9 @@
\usepackage{listings}
\usepackage{syntax}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
\newcommand{\Hquad}{\hspace{0.2em}}
\newcommand{\red}[1]{\textbf{\color{red}#1}}
\lstset{
language=caml,
@ -60,8 +62,24 @@
Preuve $\Leftrightarrow$ programme du $\lambda$-calcul simplement typé
\end{frame}
\begin{frame}{lambda-calcul}
la grammaire
\begin{frame}{$lambda$-calcul}
les types sont donnés par
\lstinline{<A, B> ::= X}
\lstinline{| A -> B}
\lstinline{| A /\\ B}
\lstinline{| A \\/ B}
\lstinline{| false}
On peut avoir les $\lambda$-termes suivants:
\lstinline{fun (x:A) => x}
\lstinline{fun (x:A) => exf(x:B)}
\end{frame}
%! liste des tactiques
@ -106,10 +124,10 @@
\frametitle{Prouvons $(A \rightarrow B \rightarrow C) \rightarrow A \rightarrow B \rightarrow C$}
Preuve: %rajouter les types
\only<1>{$$?$$}
\only<2>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow ?$$}
\only<3>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow (x_0 \Hquad ? \Hquad ?)$$}
\only<4>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow (x_0 \Hquad x_1 \Hquad ?)$$}
\only<1>{$$\red{?}$$}
\only<2>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow \red{?}$$}
\only<3>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow (x_0 \Hquad \red{?} \Hquad ?)$$}
\only<4>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow (x_0 \Hquad x_1 \Hquad \red{?})$$}
\only<5-6>{$$fun \Hquad (x_0:(A \rightarrow (B \rightarrow C))) \Rightarrow fun \Hquad (x_1:A) \Rightarrow fun \Hquad (x_2:B) \Rightarrow (x_0 \Hquad x_1 \Hquad x_2)$$}
Interface:
@ -146,8 +164,12 @@
\end{frame}
\begin{frame}
\frametitle{Fiabilité}
\begin{frame}{Fiabilité}
\begin{itemize}
\item Comment être sûrs de nos preuves
\pause
\item Envoyer nos termes de preuves à \textbf{\color{blue}{Coq}}.
\end{itemize}
\end{frame}
\end{document}