curry-howard

diff --git a/main.tex b/main.tex
@@ -14,12 +14,6 @@
 
 \begin{frame}{Disclaimer}
   \begin{itemize}
-    \item Baseado em
-      \href{https://www.youtube.com/watch?v=T9ZqbQh-t9E}{Machine-Assisted
-      Proofs}
-
-      \pause
-
     \item Hacker\dots
       \begin{figure}
         \centering
@@ -315,7 +309,7 @@
 
     \item Tipos dependentes!
 
-    \item Fixo alguns tipos primitivos
+    \item Codifico meus objetos como tipos
 
         \begin{figure}
           \centering
@@ -326,41 +320,34 @@
 
 \begin{frame}{Provadores de Teoremas}
   \begin{itemize}
-    \item Provadores de Teoremas!
-      \begin{itemize}
-        \item Coq (\url{https://coq.inria.fr/})
+    \item Coq (\url{https://coq.inria.fr/})
 
-        \item Idris (\url{https://www.idris-lang.org/})
+    \item Agda (\url{https://wiki.portal.chalmers.se/agda/pmwiki.php})
 
-        \item Lean (\url{https://leanprover.github.io/})
+    \item Lean (\url{https://leanprover.github.io/})
 
-        \item Isabelle (\url{https://isabelle.in.tum.de/})
-      \end{itemize}
+    \item Idris (\url{https://www.idris-lang.org/})
+
+    \item Isabelle (\url{https://isabelle.in.tum.de/})
   \end{itemize}
 
   \begin{columns}
-    \begin{column}{.2\linewidth}
+    \begin{column}{.1\linewidth}
       \begin{figure}
         \centering
-        \includegraphics[scale=.6]{images/coq.png}
+        \includegraphics[width=\linewidth]{images/coq.png}
       \end{figure}
     \end{column}
-    \begin{column}{.2\linewidth}
-      \begin{figure}
-        \centering
-        \includegraphics[scale=.095]{images/idris.eps}
-      \end{figure}
-    \end{column}
-    \begin{column}{.2\linewidth}
+    \begin{column}{.45\linewidth}
       \begin{figure}
         \centering
-        \includegraphics[scale=.15]{images/lean.eps}
+        \includegraphics[width=\linewidth]{images/agda.eps}
       \end{figure}
     \end{column}
-    \begin{column}{.2\linewidth}
+    \begin{column}{.25\linewidth}
       \begin{figure}
         \centering
-        \includegraphics[scale=.4]{images/isabelle.png}
+        \includegraphics[width=\linewidth]{images/lean.eps}
       \end{figure}
     \end{column}
   \end{columns}
@@ -379,19 +366,15 @@
         \item
           \href{https://leanprover-community.github.io/mathlib-overview.html}{mathlib}
           \begin{itemize}
-            \item Algebra linear
-
             \item Algebra abstrata
 
             \item Topologia
 
-            \item Análise
-
             \item Geometria diferencial
 
             \item Teoria dos números
 
-            \item Combinatória
+            \item Análise funcional
 
             \item \dots
           \end{itemize}
@@ -401,17 +384,10 @@
 
   \pause
 
-  \begin{itemize}
-    \item A \emph{mathlib} ainda não tem suporte para tudo na matemática\dots
-
-      \pause
-
-    \item A \emph{mathlib} ``nunca foi usada para provar algo novo''\dots
-
-      \pause
-
-    \item Pra que tudo isso então?
-  \end{itemize}
+  \begin{figure}
+    \centering
+    \inputminted{lean}{examples/liquid.lean}
+  \end{figure}
 \end{frame}
 
 \begin{frame}{Pra que tudo isso?}
@@ -431,11 +407,12 @@
 
             \item<5-> A prova de Mochizuki da conjetura abc
 
-            \item<6-> A prova de Hales da conjectura de Kepler de 2015
+            \item<6-> A prova de Hales da conjectura de Kepler de 2015!
 
             \item<7->
+              A conclusão do
               \emph{\href{https://leanprover-community.github.io/liquid/}{Liquid
-              Tensor Experiment}}
+              Tensor Experiment}} em julho de 2022!
           \end{itemize}
 
         \item<8-> \emph{Who watches the Watchmen?}
@@ -449,5 +426,28 @@
     \end{column}
   \end{columns}
 \end{frame}
+
+\begin{frame}{Links}
+  \begin{enumerate}
+    \item
+      \href{https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/}
+           {The Natural Number Game}
+    \item
+      \href{https://leanprover-community.github.io/blog/posts/lte-final/}
+           {Completion of the Liquid Tensor Experiment}
+
+    \item
+      \href{https://www.youtube.com/watch?v=T9ZqbQh-t9E}
+           {Machine-Assisted Proofs}
+
+    \item 
+      \href{https://www.nature.com/articles/s41586-021-04086-x}
+           {Advancing mathematics by guiding human intuition with AI}
+
+    \item
+      \href{https://www.hedonisticlearning.com/posts/understanding-typing-judgments.html}
+           {Understanding typing judgments}
+  \end{enumerate}
+\end{frame}
 \end{document}