--- a/slides/slides09.tex	Tue Nov 30 10:16:47 2021 +0000
+++ b/slides/slides09.tex	Fri Dec 03 17:45:11 2021 +0000
@@ -75,6 +75,157 @@
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c,fragile]
+\frametitle{\mbox{}\hspace{5cm}Factorial}
+
+\begin{textblock}{7}(0,1.0)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static facT(II)I 
+.limit locals 2
+.limit stack 6
+  iload 0
+  ldc 0
+  if_icmpne If_else_2
+  iload 1
+  goto If_end_3
+If_else_2:
+  iload 0
+  ldc 1
+  isub
+  iload 0
+  iload 1
+  imul
+  invokestatic fact/fact/facT(II)I
+If_end_3:
+  ireturn
+.end method 
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,7)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def facT(n, acc) = 
+  if n == 0 then acc 
+  else facT(n - 1, n * acc);
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[fragile]
+
+\begin{textblock}{7}(1,-0.2)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]
+.method public static facT(II)I 
+.limit locals 2
+.limit stack 6
+(*@\hl{facT\_Start:} @*)
+  iload 0
+  ldc 0
+  if_icmpne If_else_2
+  iload 1
+  goto If_end_3
+If_else_2:
+  iload 0
+  ldc 1
+  isub
+  iload 0
+  iload 1
+  imul
+  (*@\hl{istore 1} @*)
+  (*@\hl{istore 0} @*)
+  (*@\hl{goto facT\_Start} @*)
+If_end_3:
+  ireturn
+.end method 
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,7)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def facT(n, acc) = 
+  if n == 0 then acc 
+  else facT(n - 1, n * acc);
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+\frametitle{Tail Recursion}
+
+A call to \texttt{f(args)} is usually compiled as\medskip
+
+{\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
+  args onto stack
+  invokestatic  .../f 
+\end{lstlisting}}\pause
+
+
+A call is in tail position provided:\medskip
+
+{\small\begin{itemize}
+\item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}
+\item \texttt{Exp ; \hl{Exp}}
+\item \texttt{Exp  op Exp}
+\end{itemize}}\medskip
+
+then a call \texttt{f(args)} can be compiled as\medskip\small
+
+\begin{lstlisting}[numbers=none]
+  prepare environment
+  jump to start of function
+\end{lstlisting}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Tail Recursive Call}
+\footnotesize
+
+\begin{textblock}{13}(-0.3,3)
+\begin{lstlisting}[language=Scala, numbers=none]
+def compile_expT(a: Exp, env: Mem, name: String): Instrs = 
+  ...
+  case Call(n, args) => if (name == n)
+  {
+    val stores =
+      args.zipWithIndex.map { case (x, y) => i"istore $y" } 
+
+    args.map(a => compile_expT(a, env, "")).mkString ++
+    stores.reverse.mkString ++ 
+    i"goto ${n}_Start" 
+  } else {
+    val is = "I" * args.length
+    args.map(a => compile_expT(a, env, "")).mkString ++
+    i"invokestatic XXX/XXX/${n}(${is})I"
+  }
+\end{lstlisting}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]