Add rest of my presentation

[matthijs/master-project/final-presentation.git] / christiaan / recursion.lhs

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+\section{Recursion}
+%include talk.fmt
+\frame{
+\frametitle{Future Work: Recursion}
+\begin{itemize}
+  \item The most pressing future work is to support recursive functions.
+  \item Partially explored solution: static loop unrolling
+  \item Unexplored solution: Haskell language extensions, new source language
+\end{itemize}
+}
+
+\subsection{Static loop unrolling}
+\frame{
+\frametitle{Static loop unrolling}
+\begin{itemize}
+  \item Unroll, and simplify recursive definitions at compile time.
+  \item Explored solution: Unrolling number-guided recursive functions using Template Haskell
+\end{itemize}
+}
+
+\frame{
+\frametitle{Template Haskell}
+\begin{itemize}
+  \item Template Haskell allows for compile-time inspection, construction, and manipulation of Haskell code.
+  \item All these functions are expressible in normal Haskell
+\end{itemize}
+}
+
+\frame{
+\frametitle{Tree Adder}
+\begin{verbatim}
+$(do
+  [typ, _] <- [d|{
+treeSum :: Vector D8 (SizedWord D8) -> SizedWord D8;
+treeSum xs = undefined
+  }|]
+  [func] <- [d|{
+treeSum i xs | i < 1     = head xs
+             | otherwise = let (a,b) = split xs
+                           in (treeSum (i-1) a) + 
+                              (treeSum (i-1) b)
+  }|]
+  let func' = unroll Nothing 0 (IntegerL 3) funct
+  return [typ,func']
+)
+\end{verbatim}
+}
+
+\begin{frame}
+   \frametitle{Unrolled tree adder}
+   \begin{figure} 
+      \includegraphics[height=5cm]{treeadder} 
+    \end{figure}
+\end{frame}
+
+\subsection{Input Language}
+\frame{
+\frametitle{Input Language}
+\begin{itemize}
+  \item New source language: One of the problems is that Haskell does not properly support dependent types. Investigate languages with dependent type systems.
+  \item Haskell extentions: Invariant descriptions at the type-level.
+\end{itemize}
+}
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