From a8f72535b76928e7374968ae7ae0407d4f82c5c5 Mon Sep 17 00:00:00 2001
From: Matthijs Kooijman <matthijs@stdin.nl>
Date: Mon, 14 Dec 2009 10:58:41 +0100
Subject: [PATCH] Fill in sheets about state.

---
 matthijs/introduction.lhs | 88 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 86 insertions(+), 2 deletions(-)

diff --git a/matthijs/introduction.lhs b/matthijs/introduction.lhs
index 433ffcd..369ab79 100644
--- a/matthijs/introduction.lhs
+++ b/matthijs/introduction.lhs
@@ -112,12 +112,96 @@
 
 \frame
 {
-  TODO: Impure (stateful) example.
+  \frametitle{Multiply-accumulate}
+  \begin{columns}
+    \begin{column}{5cm}
+      \begin{block}{}
+        \begin{tabular}{lll}
+          Input A & Input B & Output \\
+          \hline
+          1 & 1 & 0 \\
+          1 & 2 & 1 \\
+          1 & 1 & 3 \\
+          2 & 2 & 4 \\
+        \end{tabular}
+      \end{block}
+    \end{column}
+    \begin{column}{5cm}
+      \begin{figure}
+        TODO: Image of MAC with internal register
+      \end{figure}
+    \end{column}
+  \end{columns}
+}
+
+\note[itemize]
+{
+  \item Next sheet: MAC circuit and I/O values
+  \item MAC is common circuit
+  \item Multiplies pairs, one pair at a time
+  \item Stores sum so far
+  \item Not pure!
+  \item Depends on inputs \emph{and} current register value
+  \item Solution: Put register value (state) in argument
 }
 
+\frame
+{
+  \frametitle{Multiply-accumulate}
+  \begin{columns}
+    \begin{column}{5cm}
+      \begin{block}{}
+        \vspace{-0.5cm}
+\begin{verbatim}
+mac (a, b) (State s) = let
+  sum = s + (a * b)
+in (State sum, sum)
+\end{verbatim}
+      \end{block}
+    \end{column}
+    \begin{column}{5cm}
+      \begin{figure}
+        TODO: Image of MAC with external register
+      \end{figure}
+    \end{column}
+  \end{columns}
+}
+
+\note[itemize]
+{
+  \item Next sheet: MAC implementation
+  \item Current state as argument (annotated)
+  \item Two parts in the result: New state and output
+  \item Register is placed ``outside''
+  \item We want it inside!
+  \item Annotation allows compiler to put it inside
+}
+
+\begin{frame}[fragile]
+  \frametitle{Simulating}
+
+  \begin{block}{Recursive run function}
+    run f (i:is) s = let
+      (o, s') = f i s
+    in o : (run f is s')
+  \end{block}
+
+  \begin{block}{Remember \texttt{mac}}
+\vspace{-0.5cm}
+\begin{verbatim}
+mac (a, b) (State s) = let
+  sum = s + (a * b)
+in (State sum, sum)
+\end{verbatim}
+  \end{block}
+\end{frame}
+
 \note[itemize]
 {
-  \item TODO
+  \item Next sheet: run function
+  \item Used for simulation only
+  \item Recursion ``stores'' state
+  \item Each recursion step, \texttt{f} is evaluated once.
 }
 
 \subsection{\clash}
-- 
2.30.2